Algorithmic_Data_Science_Assignments_Yekailiang.ipynb

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      "name": "Algorithmic Data Science Assignments - Yekailiang",
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      "cell_type": "markdown",
      "metadata": {
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        "<a href=\"https://colab.research.google.com/github/z1qsx/qtcreat/blob/master/Algorithmic_Data_Science_Assignments_Yekailiang.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "id": "Z5s38lXg1pWy",
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      "cell_type": "markdown",
      "source": [
        "### Overview\n",
        "For this assessment you are asked to submit a Jupyter notebook that reports on what you have learnt about the complexity of different algorithms for finding the similarities of documents using a bag-of-words representation.\n",
        "\n",
        "Scenario\n",
        "\n",
        "Imagine, you have a collection of d (d > 10) documents each containing at least w (w > 50) English words. For testing purposes, you may wish to construct or collect such a collection. A document can be represented as a bag-of-words, i.e., as the set of the words it contains together with associated frequencies. This is naturally stored using a Python dictionary. This can be converted to a dense vector (e.g., a numpy array) where there is a dimension for each of the V words in the English vocabulary.\n",
        "\n",
        "During lab sessions you will have been expected to have implemented various algorithms that will enable you to address each of the following five questions:"
      ]
    },
    {
      "metadata": {
        "id": "_pNQhDWC1pW8",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Introduction"
      ]
    },
    {
      "metadata": {
        "id": "yBXLQlyL1pW_",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "This part contains a selection of two different similarity algorithms. Some question and analysis are about running time of Jaccard'similarity and the cosine similarity. Therefore, the report explores what is different algorithms for Jaccard' similarity and cosine similarity and running time respectively.\n",
        "Estimating the constant for two similarities.\n",
        "\n",
        "This report in question 1, I will examine and analyse what is the theoretical worst-case running time of Jaccard's similarity measure applied to documents represented as bags of words.\n",
        "\n",
        "In question 2, I also examine and analyse what is the theoretical worst-case running time of the cosine similarity measure applied to documents represented as dense vectors to estimate the constant. After examined, I need to compare using the implementation of the dot product in numpy with my own implementation.\n",
        "\n",
        "After, examine two similarities, I need to examine and analyse that cosine similarity directly computes documents from sparse(dictionary) representations without converting them into dense(vector) representations. Moreover, its result will compare the previous implementation of the two similarities in question 3.\n",
        "Question 4 is which computes all-pairs similarities for a collection of documents. Furthermore, I examine what is the theoretical worst-case running time for computing all-pairs similarities and give an estimate of how long it would take to compute all-pairs similarities for 200K documents for both measures.\n",
        "\n",
        "Finally, for question 5,I need to  use the map-reduce computing paradigm to implement a parallel version of all-pairs similarities for documents and test them for accuracyits and average running time for 50 documents. "
      ]
    },
    {
      "metadata": {
        "id": "LAkf7dHi1pXH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#import module\n",
        "from nltk.tokenize import word_tokenize\n",
        "from nltk.corpus import brown\n",
        "from timeit import default_timer as timer\n",
        "import nltk\n",
        "from nltk.corpus import semcor\n",
        "from nltk.corpus import inaugural\n",
        "from nltk.corpus import stopwords\n",
        "import re\n",
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy.stats as stats\n",
        "import pandas as pd\n",
        "import time\n",
        "\n",
        "import operator\n",
        "from multiprocessing import Pool\n",
        "from collections import defaultdict"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "s6xu1Xcb1urO",
        "colab_type": "code",
        "outputId": "c0ddddaa-2a91-4a15-d97e-a547f8810622",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 181
        }
      },
      "cell_type": "code",
      "source": [
        "nltk.download('brown')\n",
        "nltk.download('semcor')\n",
        "nltk.download('inaugural')\n",
        "nltk.download('stopwords')"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[nltk_data] Downloading package brown to /root/nltk_data...\n",
            "[nltk_data]   Package brown is already up-to-date!\n",
            "[nltk_data] Downloading package semcor to /root/nltk_data...\n",
            "[nltk_data]   Package semcor is already up-to-date!\n",
            "[nltk_data] Downloading package inaugural to /root/nltk_data...\n",
            "[nltk_data]   Package inaugural is already up-to-date!\n",
            "[nltk_data] Downloading package stopwords to /root/nltk_data...\n",
            "[nltk_data]   Package stopwords is already up-to-date!\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
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          "metadata": {
            "tags": []
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          "execution_count": 58
        }
      ]
    },
    {
      "metadata": {
        "id": "ozcy4cIj1pXR",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "*collecting d> 10 documents *"
      ]
    },
    {
      "metadata": {
        "id": "CF4tT2Bg1pXT",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#collecting 50 documents\n",
        "allfiles=semcor.fileids() #list of fileids\n",
        "len(allfiles)\n",
        "secor_doc=[]\n",
        "for temp in range(50):\n",
        "    secor_doc.append(semcor.words(allfiles[temp]))\n",
        "                                 "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "e9FHCpOP1pXe",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "*Calculate average running time*"
      ]
    },
    {
      "metadata": {
        "id": "KioW9C721pXf",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def timeit(somefunc,*args,repeats=10,**kwargs):\n",
        "    times=[]\n",
        "    while repeats>0:\n",
        "        starttime=time.time()\n",
        "        ans=somefunc(*args,**kwargs)\n",
        "        endtime=time.time()\n",
        "        timetaken=endtime-starttime\n",
        "        times.append(timetaken)\n",
        "        repeats-=1\n",
        "    \n",
        "    mean=np.mean(times)\n",
        " \n",
        "    return mean"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "hK0lMhvM1pXq",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def token_frequency(tokens):\n",
        "    freqs = {}\n",
        "    for token in tokens:\n",
        "        try :\n",
        "            freqs[token] += 1\n",
        "        except KeyError:\n",
        "            \n",
        "            freqs[token] = 1\n",
        "    return freqs"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "iR6XHQiR1pXw",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def normalise(tokenlist):\n",
        "    tokenlist=[token.lower() for token in tokenlist]\n",
        "    tokenlist=[\"NUM\" if token.isdigit() else token for token in tokenlist]\n",
        "    tokenlist=[\"Nth\" if (token.endswith((\"nd\",\"st\",\"th\")) and token[:-2].isdigit()) else token for token in tokenlist]\n",
        "    tokenlist=[\"NUM\" if re.search(\"^[+-]?[0-9]+\\.[0-9]\",token) else token for token in tokenlist]\n",
        "    return tokenlist\n",
        "\n",
        "def filter_stopwords(tokenlist):\n",
        "    stop = stopwords.words('english')\n",
        "    return [w for w in tokenlist if w.isalpha() and w not in stop]\n",
        "\n",
        "def make_bow(somestring):\n",
        "    rep=normalise(somestring)   \n",
        "    rep=filter_stopwords(rep)  \n",
        "    dict_rep={}\n",
        "    for token in rep:\n",
        "        dict_rep[token]=dict_rep.get(token,0)+1  #step 5\n",
        "    return(dict_rep)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "oagzvxZ_1pX8",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "my_doc=[]\n",
        "for doc_m in secor_doc:\n",
        "    my_doc.append(make_bow(doc_m))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "QVhr2fSH1pYD",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def draw_chart(num_mx,time_my,names):\n",
        "    logxs=[np.log10(x) for x in num_mx]\n",
        "    logys=[np.log10(y) for y in time_my]\n",
        "    \n",
        "    plt.subplots_adjust(1,0,2.5,0.5)\n",
        "    plt.subplot(121)\n",
        "    plt.plot(num_mx,time_my)\n",
        "    plt.xlabel(\"Length of List\")\n",
        "    plt.ylabel(\"Average time\")\n",
        "    plt.title(\"Worst Case Running Time of \"+ names)\n",
        "    #plt.ylim(-6,-3)\n",
        "    \n",
        "    plt.subplot(122)\n",
        "    plt.scatter(logxs,logys)\n",
        "    plt.xlabel(\"Length of List\")\n",
        "    plt.ylabel(\"Average time\")\n",
        "    plt.title(\"Worst Case Running Time of \"+ names)\n",
        "    plt.show()\n",
        "    \n",
        "    return logxs,logys\n",
        "def cal_slope(logxs, logys):\n",
        "    slope, intercept, r_value, p_value, std_err = stats.linregress(logxs, logys)\n",
        "    print(\"Slope is {} and intercept is {}\".format(slope,intercept))\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Epg_ueAl1pYQ",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "1.What is the theoretical worst case running time of Jaccard’s similarity measure applied to documents represented as bags of words? Show that this is the case empirically. Estimate the constant for your implementation and computer."
      ]
    },
    {
      "metadata": {
        "id": "Kfr6iIFZ1pYT",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## The Jaccard' s similarity formula\n",
        "$J(A,B)=\\cfrac{\\mid A\\cap B\\mid}{\\mid A \\cup B\\mid}$"
      ]
    },
    {
      "metadata": {
        "id": "E6nIa04F1pYZ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def jac_sim(A, B):\n",
        "    U = A.keys() | B.keys()\n",
        "    I = A.keys() & B.keys()\n",
        "    jac =  len(I) / len(U)\n",
        "    return jac    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "WByDCdi61pYj",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### The theoretical worst case running time analysis:\n",
        "Jaccard's similarity measure is the ratio of the cardinality (size) of the intersection of two sets to the cardinality of the union of two sets. If elements of two sets are the same, their similarity is 1. However, if elements of two sets are totally different, their similarity is 0. The Jaccard' similarity contains three steps. The first step is union of two sets. Its worst case running time is $O(len(doc1.keys)+len(doc2.keys))$. Secondly, the measure need to calculate intersection of two sets. So, its worst case running time is $O(len(document1.keys)*len(document2.keys))$. The final step is that results of union is divided by resluts of intersection. Therefore, according to the above analysis, the Jaccard' similarity worst running depend on document size, if the document size is n, the jaccard's similarity measure worst running is similar O(n) by the big O notation."
      ]
    },
    {
      "metadata": {
        "id": "zUu5G8GF1pYl",
        "colab_type": "code",
        "outputId": "e55ccbe8-34d9-48fb-cf4f-80e383ef5f32",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 382
        }
      },
      "cell_type": "code",
      "source": [
        "timexs=[]\n",
        "sima_x=[]\n",
        "doc_num=[]\n",
        "cal_ti=0\n",
        "for i in range(20):\n",
        "    timess = []\n",
        "    for ca_num in range(10):\n",
        "        start = timer()\n",
        "        sim_A_B = jac_sim(my_doc[0],my_doc[i])\n",
        "        end = timer()\n",
        "        cal_ti+=(end - start)\n",
        "    timek=(cal_ti/10)\n",
        "    sima_x.append(str(round(sim_A_B,4)))\n",
        "    timexs.append(round(end - start,7))\n",
        "    doc_num.append(len(my_doc[0])+len(my_doc[i]))\n",
        "    temp_s=round((len(my_doc[0]) - len(my_doc[i])*sim_A_B))\n",
        "    print(round(timek,7),round(sim_A_B,4),len(my_doc[0])+len(my_doc[i]),temp_s)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.0001103 1.0 1294 0\n",
            "0.0004999 0.1438 1344 547\n",
            "0.0008841 0.0749 1335 595\n",
            "0.0010867 0.0918 1237 593\n",
            "0.0012137 0.0747 1324 596\n",
            "0.0013391 0.0965 1363 578\n",
            "0.0014627 0.0919 1283 589\n",
            "0.001592 0.0762 1441 587\n",
            "0.0017131 0.0839 1395 584\n",
            "0.0018874 0.0711 1476 588\n",
            "0.0020163 0.07 1436 592\n",
            "0.0021536 0.0732 1423 590\n",
            "0.0022672 0.0766 1251 601\n",
            "0.0023789 0.0704 1246 605\n",
            "0.0024981 0.096 1290 585\n",
            "0.0026005 0.0731 1130 612\n",
            "0.0027242 0.0716 1243 604\n",
            "0.0028581 0.0806 1301 594\n",
            "0.0029879 0.0665 1412 596\n",
            "0.0030975 0.0889 1188 599\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "KBG3Y5lx1pYz",
        "colab_type": "code",
        "outputId": "f95b77e9-1401-4304-b3d1-2f1fb0f39d65",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "store=[]\n",
        "store.append(timexs)\n",
        "\n",
        "store.append(sima_x)\n",
        "\n",
        "store.append(doc_num)\n",
        "\n",
        "df=pd.DataFrame(store, index=['Running time','similarity','number of words'])\n",
        "df=df.T\n",
        "df.sort_values('similarity')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Running time</th>\n",
              "      <th>similarity</th>\n",
              "      <th>number of words</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>9.05e-05</td>\n",
              "      <td>0.0665</td>\n",
              "      <td>1412</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>0.0001331</td>\n",
              "      <td>0.07</td>\n",
              "      <td>1436</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>0.0001138</td>\n",
              "      <td>0.0704</td>\n",
              "      <td>1246</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>0.0001627</td>\n",
              "      <td>0.0711</td>\n",
              "      <td>1476</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>0.0001064</td>\n",
              "      <td>0.0716</td>\n",
              "      <td>1243</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>0.0001206</td>\n",
              "      <td>0.0731</td>\n",
              "      <td>1130</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>9.33e-05</td>\n",
              "      <td>0.0732</td>\n",
              "      <td>1423</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>8.48e-05</td>\n",
              "      <td>0.0747</td>\n",
              "      <td>1324</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>8.48e-05</td>\n",
              "      <td>0.0749</td>\n",
              "      <td>1335</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>0.0001326</td>\n",
              "      <td>0.0762</td>\n",
              "      <td>1441</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>0.0001212</td>\n",
              "      <td>0.0766</td>\n",
              "      <td>1251</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>9.78e-05</td>\n",
              "      <td>0.0806</td>\n",
              "      <td>1301</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>9.05e-05</td>\n",
              "      <td>0.0839</td>\n",
              "      <td>1395</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>9.27e-05</td>\n",
              "      <td>0.0889</td>\n",
              "      <td>1188</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>9.1e-05</td>\n",
              "      <td>0.0918</td>\n",
              "      <td>1237</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>0.0001223</td>\n",
              "      <td>0.0919</td>\n",
              "      <td>1283</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>0.0001303</td>\n",
              "      <td>0.096</td>\n",
              "      <td>1290</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>9.5e-05</td>\n",
              "      <td>0.0965</td>\n",
              "      <td>1363</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>9.05e-05</td>\n",
              "      <td>0.1438</td>\n",
              "      <td>1344</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>6.71e-05</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1294</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Running time similarity number of words\n",
              "18     9.05e-05     0.0665            1412\n",
              "10    0.0001331       0.07            1436\n",
              "13    0.0001138     0.0704            1246\n",
              "9     0.0001627     0.0711            1476\n",
              "16    0.0001064     0.0716            1243\n",
              "15    0.0001206     0.0731            1130\n",
              "11     9.33e-05     0.0732            1423\n",
              "4      8.48e-05     0.0747            1324\n",
              "2      8.48e-05     0.0749            1335\n",
              "7     0.0001326     0.0762            1441\n",
              "12    0.0001212     0.0766            1251\n",
              "17     9.78e-05     0.0806            1301\n",
              "8      9.05e-05     0.0839            1395\n",
              "19     9.27e-05     0.0889            1188\n",
              "3       9.1e-05     0.0918            1237\n",
              "6     0.0001223     0.0919            1283\n",
              "14    0.0001303      0.096            1290\n",
              "5       9.5e-05     0.0965            1363\n",
              "1      9.05e-05     0.1438            1344\n",
              "0      6.71e-05        1.0            1294"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 68
        }
      ]
    },
    {
      "metadata": {
        "id": "KeVFc8Gx1pZa",
        "colab_type": "code",
        "outputId": "39fa3085-aab4-49aa-8d0d-e3cade4e9837",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "plt.bar(sima_x,timexs)\n",
        "plt.xticks(rotation=40)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19],\n",
              " <a list of 20 Text xticklabel objects>)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "IM0_8-Ac1pZj",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "From above chart, it show that relationship of Jaccard's similarity and running time. When the words of documents is approximately 650, their running time do not depend on the similarity. However, its running time was increase when its number of documents was growth. It will be estimated."
      ]
    },
    {
      "metadata": {
        "id": "xfcTk91bSmlv",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Jaccard's similiarity (chart 1.1)"
      ]
    },
    {
      "metadata": {
        "id": "zwlwEnme1pZk",
        "colab_type": "code",
        "outputId": "3a8955f0-d5a4-47ad-dbb3-e5649d2bdf96",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "times = []\n",
        "number=[]\n",
        "for n in range(1000, 300 * 100 + 1, 1000):\n",
        "    \n",
        "    A = token_frequency(brown.words()[:n])\n",
        "    B = token_frequency(brown.words()[n:2*n])\n",
        "    \n",
        "#     start = timer()\n",
        "#     sim_A_B = jac_sim(A,B)\n",
        "#     end = timer()\n",
        "    \n",
        "    run_time=timeit(jac_sim,A,B)\n",
        "#     print(n)\n",
        "    number.append(n)\n",
        "    times.append(run_time)\n",
        "\n",
        "lx,ly=draw_chart(number,times,'Jaccard')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.8910904900957792 and intercept is -6.849231802531387\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "p7ainLyP1pZ2",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Estimate the constant for my implementation and computer.\n",
        "Now I investigate the worst-case running time of this algorithm for different lengths of documents.\n",
        "From the above charts, the first chart is when the number of doucments words was a rise from 1000 to 30000, its running time had a significant growth. However, it difficult to observe its worst running time trend. So, if it is about linear $O(n^1)$, I need some Maths.\n",
        "If $y=c_a.x^n$ then it follows that: $\\log(y) = \\log(c_a) + n \\log(x)$\n",
        "therefore, if I plot a graph of $\\log(y)$ against $\\log(x)$ the gradient will be n and the y intercept will be $\\log(c_a)$. According to the second chart of worst- case running time of Jaccard's similarity measure. Its gradient and intercept were approximately 0.891 and -6.849 respectively. It means Jaccard's similarity  measure that this is fairly straight and the gradient is approximately 0.89 to 1. The y intercept is about -7 so $𝑐𝑎≈10^{−6.8}\\approx 0.0000001$. Based on this analysis, I estimate the worst running time $y\\approx c_a.x^1 \\longrightarrow$ $O(n)$ This illustrates that empirically we have$ 𝑂(𝑛^{0.89})$ which is slightly better than $𝑂(𝑛)$. Because in the algorithm, there are some instructions which are only carried out O(n) times (outside the inner loop). This will make the power appear lower than it really is unless n is asymptotically large. Therefore, if the number of words increases, it would close the O(n)"
      ]
    },
    {
      "metadata": {
        "id": "tLwYLUyB1paA",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#tag frequency for each words\n",
        "sims = []\n",
        "processed_docs=[]\n",
        "for i in range(len(docs)):\n",
        "    processed_docs.append(token_frequency(word_tokenize(docs[i])))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "c7YLYILJ1paS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "2.What is the theoretical worst case running time of the cosine similarity measure applied to documents represented as dense vectors? Show that this is the case empirically. Estimate the constant for your implementation and computer. You may wish to compare using the implementation of the dot product in numpy with your own implementation."
      ]
    },
    {
      "metadata": {
        "id": "CbkNfqiG1paX",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### The consine similarity formula  \n",
        "$cos\\theta = \\cfrac{A\\cdot B}{\\sqrt{A\\cdot A}\\sqrt{B\\cdot B}}$"
      ]
    },
    {
      "metadata": {
        "id": "JmyOuqFk1paa",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# The function is to make the dense vectors from dictionary\n",
        "def make_matrix(list_of_dicts):\n",
        "    #first of all make a list of all of the features that occur in any document - these will be the dimensions of the matrix\n",
        "    allfeatures={}    \n",
        "    for docdict in list_of_dicts:\n",
        "#         print('docdict',docdict)\n",
        "        for feat in docdict.keys():\n",
        "#             print('feat',feat)\n",
        "            allfeatures[feat]=1\n",
        "#             print('allfeatures',allfeatures)\n",
        "    dimensions=list(allfeatures.keys())\n",
        "#     print(dimensions)\n",
        "    #don't strictly need to sort it - but it is good practise to make sure it is reproducible\n",
        "    so=sorted(dimensions)\n",
        "    matrix=[]\n",
        "    #each row in the matrix will be one of the dimensions\n",
        "    for dimension in dimensions:\n",
        "        row=[]\n",
        "        #look up the appropriate value for each document\n",
        "        for docdict in list_of_dicts:\n",
        "            row.append(docdict.get(dimension,0)) #this will append the document's value if present, 0 otherwise\n",
        "        matrix.append(row)\n",
        "        \n",
        "        \n",
        "    return matrix\n",
        "\n",
        "## it might be useful to be able to transpose a matrix so we can compare documents\n",
        "def transpose(matrix):\n",
        "    transposed=[]\n",
        "    for i in range(0,len(matrix[0])):\n",
        "        transposed.append([row[i] for row in matrix])\n",
        "        \n",
        "    return transposed\n",
        "#call make_matrix on whatever variable holds your list of dictionaries representation of your documents"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "Y_R-Urxi1par",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#cosine similarity meansure\n",
        "def L2_norm(A):\n",
        "    sq_sum = 0\n",
        "    for i in range(len(A)):\n",
        "        sq_sum += A[i]**2\n",
        "    return sq_sum**0.5\n",
        "\n",
        "\n",
        "def cosine_sim(A, B):\n",
        "    \n",
        "    dot_prod = 0\n",
        "    for i in range(len(A)):\n",
        "        dot_prod += A[i] * B[i]\n",
        "\n",
        "    L2_A = L2_norm(A)\n",
        "    L2_B = L2_norm(B)\n",
        "    \n",
        "    return dot_prod / (L2_A * L2_B)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "z9O01baf1pbG",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### The theoretical worst-case running time analysis:\n",
        "Cosine similarity measure is that real-valued ‘vector’ representations of objects lead naturally to geometric notions of similarity. Before, calculation of cosine similarity, I need to compute documents represented as dense vectors. According to lab 6, I use the function make_matrix to make the matrix from a dictionary of frequency. When cosines similarity measure calculate dense vectors. it has three steps. Firstly, I apply the for loop to iterate through arrays and collection to dot product each corresponding vectors of a document. Therefore, its worst running time is O(n). Secondly, it computes the magnitude of two documents vectors and it has a for loop. Finally, results of dot product divided by results of magnitude. From these analyses, I assumed that running time of the measure is about O(n)by the big O notation. It will estimate the constant for my implementation and computer. Moreover, it would be compared using the implementation of the dot product in numpy with my own implementation."
      ]
    },
    {
      "metadata": {
        "id": "qAdCL9IF1pbJ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "times_1 = []\n",
        "\n",
        "for n in range(1000, 300 * 100 + 1, 1000):\n",
        "    \n",
        "    A = token_frequency(brown.words()[:n])\n",
        "    B = token_frequency(brown.words()[n:2*n])\n",
        "    \n",
        "    MT = np.array(transpose(make_matrix([A,B])))\n",
        "    \n",
        "    running_time=timeit(cosine_sim,MT[0], MT[1])\n",
        "    times_1.append(running_time)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "v5VmMUpC1pbV",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#dot dense vectors\n",
        "def cosine_sim_dot(A, B):\n",
        "    \n",
        "    dot_prod = 0\n",
        "    \n",
        "    dot_prod =np.dot(A,B)\n",
        "\n",
        "    L2_A = L2_norm(A)\n",
        "    L2_B = L2_norm(B)\n",
        "    \n",
        "    return dot_prod / (L2_A * L2_B)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "DS52w90T1pbk",
        "colab_type": "code",
        "outputId": "c8b43593-119e-4904-bb27-3e496181f34f",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "times_2 = []\n",
        "\n",
        "for n in range(1000, 300 * 100 + 1, 1000):\n",
        "    \n",
        "    A = token_frequency(brown.words()[:n])\n",
        "    B = token_frequency(brown.words()[n:2*n])\n",
        "\n",
        "    MT = np.array(transpose(make_matrix([A,B])))\n",
        "    \n",
        "    running_time=timeit(cosine_sim_dot,MT[0], MT[1])\n",
        "    times_2.append(running_time)\n",
        "\n",
        "    \n",
        "plt.plot(times_2)\n",
        "plt.ylabel('Cosine run time')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RKT+b9xzi7qkL6dkygYcv1SwtCZ9QBtuXAQ3DHYiIlJ+cvAJufSMVgPFjBxJfIzbCEUlVFkqL5M/AQjNbBhw5etDdLwlbVCLV1Nz1e/g8bSe/OrfrSX/5uzt/+OcyVmzL4h/XDaJtkzrlHKXI94WSSF4F/gosRetHRMJm855D3PxaClk5+czfsJeXrh10UoPjU+alMy01g7tGdOHs7s3CEKnI94XStbXb3Z9295nu/uXRn1AubmYjzSzNzNaa2X3FvF7LzN4Mvj7XzNoXee3+4PE0Mzu/yPGGZjbNzFaZ2UozGxZKLCKVWdGuqP/6cU+Wb83iJ8/PZuPugyd0ncXp+3lwxnLO7JrI3SO6hCNUkR8IJZGkmtmfzWyYmQ04+lPaScHV8M8BFwA9gTFm1vOYYjcC+9y9M/AEgZYPwXKjgV7ASOD54PUAngL+7e7dgX6A1rRIVHN3/l+wK+qJq0/h+lM7MPnmIWQezuMnL3zDws37QrrO3oO53PZGKon1a/Hk1acQG2OlnyRSDkJJJP2BoQRWsz8W/Hk0hPMGA2vdfX1wxtdUYNQxZUYR6DoDmAaMsMAenaOAqe5+xN03AGuBwWaWAJwBTARw91x33x9CLCKV1pvz03k7NYNfnNP5u82fBrZrzLu3n0r9+DjG/P1bPlq+/bjXKCh07pqykN0Hcxk/diCNtF5EKlCpicTdzy7mJ5Q1JK2B9CLPM4LHii3j7vlAJtDkOOd2BHYB/zCzhWb2kpnVLe7NzWycmaWYWcquXbtCCFek4i3NyOSPM5Zzepem/PLcrt97rUPTurxz23C6t0jg1jdSeWX2hhKv8/gnaXy9djd/GtWLPkkNwh22yPeUmEjMbGzw96+L+wnh2sW1q4/dIL6kMiUdjwMGAC+4e3/gIPCDsRcAd5/g7snunpyYmBhCuCIVa/+hXG59I5WmdWvy1Oj+xXZFNa1Xiyk3D+XcHs158P9W8MgHKygs/P4/o09W7OC5mesYPagNVw9qW1Hhi3zneC2So3/p1y/mp14I184A2hR5ngRsLamMmcUBDYC9xzk3A8hw97nB49MIJBaRqFJY6PzyzUXszM7h+VJuXVK7Zizjxw7k2mHt+PusDfxiykJy8goA2Lj7IL9+cxF9WjfgQd1HSyKkxOm/7v5i8OGn7j676GtmdmoI154PdDGzDsAWAoPnPz2mzAzgWmAOcAXwubu7mc0AJpvZ40AroAswz90LzCzdzLq5exqBG0muCCEWkUrlmc/X8kXaLv50aW9OaVP6et/YGOPBS3qR1KgOj3y4kh1ZOTw9pj+3vpFKbKzxwtgBWnQoERPKOpJn+OFf/cUd+x53zzezO4GPgFjgZXdfbmYPASnuPoPAoPnrZraWQEtkdPDc5Wb2FoEkkQ/c4e4FwUv/ApgU3FxrPXB9CHUQqTS+SNvJk5+t5if9WzN2SOhdUWbGzWd0pGXDeH795mLOevQL8goKeeX6wSQ10qJDiRxzP3bYIvhCYH3GcOCXBKbmHpUAXObu/cIfXvlITk72lJSUSIchQsa+Q1z8zNe0SIhn+u2nUrvmybUi5m3Yy11TFnLdqe259cxO5RylCJhZqrsnh1L2eC2SmgTGQuIIjIsclUWgG0pETkBOXgG3T1pAQYHzwtiBJ51EAAZ3aMyc+88hMFteJLKON0byJfClmb3i7psqMCaRKumh91ewJCOTF382kA5Ni521fkKURKSyCGUdiZKISBlNS81g8tzN3HpmJ87vpX1BpGoJZWW7iJTBiq1Z/H76UoZ1bMI953Ut/QSRKKNEIhJGWTl53D4plQa1a/D0mP7ExeqfnFQ9oWy1mwjcDLQvWt7dbwhfWCLRz9357dtLSN93mKnjhpJYv1akQxIJi1DWkbwHzAI+BQpKKSsiQRO/3sC/l2/n9xf2YFD7xpEORyRsQkkkddz9d2GPRKQKmb9xL3/+1yrO79Wcm07vEOlwRMIqlA7b983swrBHIlJF7D5whDsnLyCpUW3+98p+mqYrVV4oieRuAsnksJllmVm2mWWFOzCRaHR0X5D9h/J4/poBJMTXiHRIImFXateWu9cvrYyIBDz56Wq+WbeHv13el16ttC+IVA+hzNo6o7jj7v5V+YcjEr1mrtrJM5+v5arkJK4a1Kb0E0SqiFAG2+8t8jiewBa6qUAouySKVAsZ+w7xyzcX0b1FfR4a1TvS4YhUqFC6tn5c9LmZtQH+FraIRKLMkfzAzRgLC53xYwdqXxCpdkJpkRwrA9CfXCJBD7+/kiUZmYwfO5D25XAzRpFoE8oYyTP8Z6/1GOAUYHE4gxKJFu8t2sLr327i5tM7MLK3bsYo1VMoLZKiO0LlA1OO3XpXpDpatiWT+99dyqD2jfjtyO6RDkckYo6bSMwsFviRu4+toHhEKr3DuQU89dkaXpq1nsZ1a/LMmAHU0M0YpRo7biJx9wIzSzSzmu6eW1FBiVRWM1ft5P+9t4yMfYe5YmASD1zYg8Z1a0Y6LJGICqVrayMw28xmAAePHnT3x8MVlEh5c3cKHWJjTu52Jdszc3jo/eV8uHQ7nZvVY+q4oQzt2KScoxSJTqEkkq3Bnxi+v3e7SNR48tM1vPDFOoZ2asI53RI5p3tz2japU+p5BYXOa3M28tjHq8krKOSe87oy7oxO1IxTV5bIUebupZeKcsnJyZ6SklJ6QamS0rZnc9HTs+jVKoHsnHzW7w40rDs3q8eI7s04u3szBrZr9INxjqUZmTwwfSlLt2RyepemPHxpb9o10fReqR7MLNXdk0MpezLrSESiRmGh88D0pSTUrsEr1w+mUd2abNh9kM9X7WTmqp28PHsDL361noT4OM7omsiIHs1IbteYiV9v4LU5G2lSrxbPjOnPxX1b6i6+IiVQIpEqber8dFI37eOxK/vRKDgo3qFpXW48rQM3ntaB7Jw8vl6zO5BY0nby/pJtAJjB2CHtuOf8bjSorTv4ihyPEolUWTuzc/jLv1YyrGMTfjKgdbFl6sfX4II+LbmgT0sKC52lWzL5dv0ehnZsQr82DSs4YpHoFMrK9q7AC0Bzd+9tZn2BS9z94bBHJ1IGD7+/kpy8Qh65rHdI3VIxMUa/Ng2VQEROUChTT/4O3A/kAbj7EmB0OIMSKasvV+9ixuKt3HF2Zzom1ot0OCJVWiiJpI67zzvmWH44ghEpD4dzC/jDP5fSMbEut57VMdLhiFR5oYyR7DazTgRv3GhmVwDbwhqVSBk88/ka0vceZsrNQ6kVp1u6i4RbKInkDmAC0N3MtgAbAN17SyqltO3ZTPhqPVcMTGJYJ608F6kIoWxstR4418zqAjHunh3+sERO3NE1I/Xj43jgwh6RDkek2ghl1lYt4HKgPRB3dPaLuz8U1shETtDRNSOPXtlPN1IUqUChdG29B2QS2Kf9SHjDETk5R9eMDO3YmMtLWDMiIuERSiJJcveRYY9EpAz+s2akj25lIlLBQpn++42Z9Ql7JCIn6eiakdvP7kQnrRkRqXChtEhOA64zsw0EurYMcHfvG9bIRELw3ZqRpnW57axOkQ5HpFoKpUVyAdAFOA/4MXBx8HepzGykmaWZ2Vozu6+Y12uZ2ZvB1+eaWfsir90fPJ5mZucfc16smS00s/dDiUOqJnfnyU9Xk773MI9c1kdrRkQipMQWiZkluHsWcFLTfYP7vT8H/AjIAOab2Qx3X1Gk2I3APnfvbGajgb8CV5tZTwK3YekFtAI+NbOu7l4QPO9uYCWQcDKxSXTLzsnjnwu3MGnuZlZtz9aaEZEIO17X1mQCrY9UAqvai45gOlDavScGA2uD61Aws6nAKKBoIhkFPBh8PA141gIjpaOAqe5+BNhgZmuD15tjZknARcAjwK9Lq6BUHcu2ZDJp7ibeW7SVQ7kF9GqVwJ9/0qfEO/uKSMUoMZG4+8XB3x1O8tqtgfQizzOAISWVcfd8M8sEmgSPf3vMuUe/LZ4Efksp2/6a2ThgHEDbtm1PrgYScYdy83l/8TYmzd3E4oxM4mvEcEm/VlwzpB19kxpohpZIJRDKgsRTgUXuftDMxgIDgCfdfXNppxZz7Nh9fUsqU+xxM7sY2OnuqWZ21vHe3N0nELi1C8nJyVV/P+EqZvWObCbP3cw7CzLIzsmnS7N6PPjjnlw2IEkbTYlUMqHM2noB6Gdm/Qi0BCYCrwNnlnJeBtCmyPMkYGsJZTLMLA5oAOw9zrmXAJeY2YVAPJBgZm+4u+79VQUUFjoz03by0qwNzFm/h5qxMVzQpwXXDGnHoPaN1PoQqaRCSST57u5mNgp4yt0nmtm1IZw3H+hiZh2ALQQGz396TJkZwLXAHOAK4PPge80AJpvZ4wQG27sA89x9DoG9UQi2SO5REol+h3MLeGdBBi9/vYH1uw/SskE8vxvZnauSk2hSr1akwxORUoSSSLLN7H7gZ8DpwdlYpfYtBMc87gQ+AmKBl919uZk9BKS4+wyCrZvgYPpeghtmBcu9RWBgPh+4o8iMLakidmTl8NqcjUyau5n9h/Lom9SAp0afwoV9WlIjNpSZ6SJSGZj78YcPzKwFgZbEfHefZWZtgbPc/bWKCLA8JCcne0pKSqTDkKDlWzOZ+PUG/m/xVvILnfN6NufG0zqq+0qkEjGzVHdPDqVsKLeR325mk4BBwcHuedGURKTymLVmFy98sY5v1u2hTs1YrhnSjuuGt6d907qRDk1EyiCUWVtXAf8LfEFgNtUzZnavu08Lc2xSRbg7T3y6hqc/W0OLhHjuu6A7Ywa1pUEdzb4SqQpCGSP5PTDI3XcCmFki8CmBBYQix5WTV8Bvpy1hxuKtXDEwiUcu661bmYhUMaEkkpijSSRoD6Hdo0uquT0HjnDL66mkbNrHved34/azOmkMRKQKCiWR/NvMPgKmBJ9fDfwrfCFJVbB25wFueGU+O7JyeO6nA7iob8tIhyQiYRLKYPu9ZvYTAreTN2CCu08Pe2QStb5Zu5tb30ilZlwMU8YNZUDbRpEOSUTC6Hh3/+0MNHf32e7+LvBu8PgZZtbJ3ddVVJASPd6an84D05fSoWldXr5uEG0a14l0SCISZscb63iS4m8hfyj4msh3Cgudv/57Fb99ZwnDOjVh2m3DlUREqonjdW21d/clxx5095SiG1CJ5OQV8Ou3FvHh0u2MGdyWh0b10sp0kWrkeIkk/jiv1S7vQKRy+WzlDjbuOUSMQYwZZmBmGP95HmNgGJPmbWZJxn5+f2EPbjq9g2ZmiVQzx0sk883sZnf/e9GDZnYjgc2upIp6adZ6Hv5gZcjla9eIZfzYgZzfq0UYoxKRyup4ieSXwHQzu4b/JI5koCZwWbgDk8h4a346D3+wkgv7tOB/LusDQKEHVqcf/e1AYZHnCbVrkBCvVeoi1dXxdkjcAQw3s7OB3sHDH7j75xUSmVS4D5du4753l3BG10SeuPoUrUAXkZCEso5kJjCzAmKRCPpy9S7unrqQAW0bMX7sACUREQmZptYIqZv2cuvrqXRpVp+J1w2iTs1QbnggIhKgRFLNrdiaxXX/mE+LBvG8esNg7YcuIidMiaQaW7/rAD9/eS71a8Xxxk1DSKyvbW1F5MQpkVRTW/cf5mcT5+EOr980hNYNtTRIRE6OEkk1tPvAEcZOnEvW4TxevWEwnRLrRTokEYliGlWtZrJy8rj25Xls3X+Y128cQu/WDSIdkohEObVIqpHDuQXc+Mp8Vu/IZvzYgQxq3zjSIYlIFaAWSTWx58ARbn4thYXp+3lmTH/O6tYs0iGJSBWhRFINHLtb4YV9tFuhiJQfJZIqruhuhVPHDaW/disUkXKmRFKFvZWSzgPvardCEQkvJZIqqLDQefTjNJ7/Yh2ndW7Kc9cM0Ip1EQkbJZIqJievgN+8vZgPlmxjzOA2PDSqt3YrFJGwUiKpQnYHZ2YtSt/P/Rd0Z9wZHbVboYiEnRJJFbF2ZzbXvzKfXdlHeOGaAYzsrZlZIlIxlEgq2M6sHBrUqVGu+33MDs7MqhUXy5vjhtGvTcNyu7aISGnUeV6BdmblcPajX3Dpc9+wLfNwuVzzzfmbufblebRqUJt/3jFcSUREKpwSSQV6duZajuQXkrH3EKOenc2yLZknfa3CQuev/17F795ZyrBOTXhZsufpAAAKmElEQVT7tmEkNdL0XhGpeEokFSR97yGmzNvMlcltmHbbcGrExnDl+Dl8smLHCV8rJ6+AO6cs4IUv1vHTIW35x3WDSIjX9F4RiQwlkgry9GdrMDPuGtGZbi3qM/2O4XRtXo9xr6cw8esNuHtI19mVfYSrJ3zLv5Zt5w8X9eCRS3sTp+m9IhJB+gaqAOt2HeCdBRmMHdKOlg0CG0g1qx/P1HHDGNmrBX96fwV/fG85+QWFx73O6h3ZXPrcbFZvD9y996bTNb1XRCJPiaQCPPHJauJrxHL72Z2+d7x2zVie++kAbjmzI69/u4mbXkshOyev2GvMWrOLy5//htyCQt66ZRjn92pREaGLiJQqrInEzEaaWZqZrTWz+4p5vZaZvRl8fa6ZtS/y2v3B42lmdn7wWBszm2lmK81suZndHc74y8OKrVm8v2Qb15/anqb1frgnekyMcf8FPfjzT/owa81urhw/hy37vz+ja/LczVz3j/m0blSb9+44lT5J2oxKRCqPsCUSM4sFngMuAHoCY8ys5zHFbgT2uXtn4Angr8FzewKjgV7ASOD54PXygd+4ew9gKHBHMdesVB7/JI368XGMO73TccuNGdyWV68fzJb9h7n0udksydhPYaHzPx+u5IHpSzm9S1Om3TacVtpbXUQqmXC2SAYDa919vbvnAlOBUceUGQW8Gnw8DRhhgU7/UcBUdz/i7huAtcBgd9/m7gsA3D0bWAm0DmMdymTB5n18unInt5zRkQZ1Sp9VdVqXprx723BqxcVw1YtzuOaluUz4aj0/H9aOl36eTL1aWj8qIpVPOBNJayC9yPMMfvil/10Zd88HMoEmoZwb7AbrD8wt7s3NbJyZpZhZyq5du066EmXx2MdpNKlbk+tP7RDyOV2a12f67afSvUUC327Ywx8v7sl/X9JLM7NEpNIK55+4xU0nOnaOa0lljnuumdUD3gF+6e5Zxb25u08AJgAkJyeHNre2HH2zbjez1+7hDxf1oO4JtiQS69firVuGsT0zh7ZNtMhQRCq3cP6ZmwG0KfI8CdhaUhkziwMaAHuPd66Z1SCQRCa5+7thibyM3J1HP0qjRUI8Y4e2O6lr1IyLURIRkagQzkQyH+hiZh3MrCaBwfMZx5SZAVwbfHwF8LkHVubNAEYHZ3V1ALoA84LjJxOBle7+eBhjL5OZaTtZsHk/vxjRmfga5XdzRhGRyihsXVvunm9mdwIfAbHAy+6+3MweAlLcfQaBpPC6ma0l0BIZHTx3uZm9BawgMFPrDncvMLPTgJ8BS81sUfCtHnD3D8NVjxNVWOg8+tFq2jauw1XJbUo/QUQkyoV1GlDwC/7DY479scjjHODKEs59BHjkmGNfU/z4SaXxr2XbWbEti8ev6qedCUWkWtA3XTkqKHQe/ySNLs3qMeqUSjsrWUSkXCmRlKPpC7ewbtdBfv2jrsTGVOqGk4hIuVEiKSe5+YU8+elqerdOYGRv3QdLRKoPJZJy8mZKOhn7DvOb87rpjrwiUq0okZSDnLwCnv18DcntGnFW18RIhyMiUqGUSMrB63M2sSPrCPecr9aIiFQ/SiRldOBIPi98uY7TuzRlaMcmkQ5HRKTCKZGU0ctfb2DvwVx+c163SIciIhIRSiRlsP9QLn//aj0/6tmcU9o0jHQ4IiIRoURSBi9+tZ4Dufn85ryukQ5FRCRilEhO0s7sHF6ZvZEf921F9xYJkQ5HRCRilEhO0vMz15FbUMivfqTWiIhUb0okJ2HL/sNMnruZKwYk0aFp3UiHIyISUUokJ+GZz9YAcNe5XSIciYhI5CmRnKANuw/ydmoGPx3SltYNa0c6HBGRiFMiOUFPfrqaGrHG7Wd3inQoIiKVghLJCUjbns2MxVu5bngHmtWPj3Q4IiKVghLJCXjs4zTq1Yzj1jM7RjoUEZFKQ4kkRIvT9/Pxih3cdHpHGtapGelwREQqDSWSED36cRqN6tTghtPaRzoUEZFKRYkkBHPX72HWmt3cdlYn6sfXiHQ4IiKVihJJKdydRz9Oo1n9Wvx8WPtIhyMiUukokZTiy9W7mL9xH784pzPxNWIjHY6ISKWjRHIc7s5jH68mqVFtrh7UNtLhiIhUSkokx/HR8u0s3ZLJ3SO6UDNO/6lERIqjb8cSFBQGWiMdE+tyWf/WkQ5HRKTSiot0AJXV4bwCBrZrxJldE4mLVb4VESmJEkkJ6tWK4y+X9410GCIilZ7+1BYRkTJRIhERkTJRIhERkTJRIhERkTJRIhERkTJRIhERkTJRIhERkTJRIhERkTIxd490DGFnZruATSd5elNgdzmGE2lVrT5Q9epU1eoDVa9OVa0+8MM6tXP3xFBOrBaJpCzMLMXdkyMdR3mpavWBqlenqlYfqHp1qmr1gbLVSV1bIiJSJkokIiJSJkokpZsQ6QDKWVWrD1S9OlW1+kDVq1NVqw+UoU4aIxERkTJRi0RERMpEiaQEZjbSzNLMbK2Z3RfpeMqDmW00s6VmtsjMUiIdz8kws5fNbKeZLStyrLGZfWJma4K/G0UyxhNRQn0eNLMtwc9pkZldGMkYT4SZtTGzmWa20syWm9ndwePR/BmVVKeo/JzMLN7M5pnZ4mB9/jt4vIOZzQ1+Rm+aWc2Qr6murR8ys1hgNfAjIAOYD4xx9xURDayMzGwjkOzuUTv/3czOAA4Ar7l77+CxvwF73f0vwaTfyN1/F8k4Q1VCfR4EDrj7o5GM7WSYWUugpbsvMLP6QCpwKXAd0fsZlVSnq4jCz8nMDKjr7gfMrAbwNXA38GvgXXefambjgcXu/kIo11SLpHiDgbXuvt7dc4GpwKgIxySAu38F7D3m8Cjg1eDjVwn8I48KJdQnarn7NndfEHycDawEWhPdn1FJdYpKHnAg+LRG8MeBc4BpweMn9BkpkRSvNZBe5HkGUfw/ThEOfGxmqWY2LtLBlKPm7r4NAv/ogWYRjqc83GlmS4JdX1HTDVSUmbUH+gNzqSKf0TF1gij9nMws1swWATuBT4B1wH53zw8WOaHvPCWS4lkxx6pCH+Cp7j4AuAC4I9itIpXPC0An4BRgG/BYZMM5cWZWD3gH+KW7Z0U6nvJQTJ2i9nNy9wJ3PwVIItAD06O4YqFeT4mkeBlAmyLPk4CtEYql3Lj71uDvncB0Av8DVQU7gv3YR/uzd0Y4njJx9x3Bf+iFwN+Jss8p2O/+DjDJ3d8NHo7qz6i4OkX75wTg7vuBL4ChQEMziwu+dELfeUokxZsPdAnOYqgJjAZmRDimMjGzusGBQsysLnAesOz4Z0WNGcC1wcfXAu9FMJYyO/qFG3QZUfQ5BQdyJwIr3f3xIi9F7WdUUp2i9XMys0Qzaxh8XBs4l8C4z0zgimCxE/qMNGurBMGpfE8CscDL7v5IhEMqEzPrSKAVAhAHTI7GOpnZFOAsAncq3QH8F/BP4C2gLbAZuNLdo2IAu4T6nEWgu8SBjcAtR8cXKjszOw2YBSwFCoOHHyAwphCtn1FJdRpDFH5OZtaXwGB6LIHGxFvu/lDwO2Iq0BhYCIx19yMhXVOJREREykJdWyIiUiZKJCIiUiZKJCIiUiZKJCIiUiZKJCIiUiZKJCIiUiZKJCIiUiZKJCIiUib/H03ga/TAv/XrAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "7HBpsLf2QSlv",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosine similarity with vector iteration(chart 2.1 and chart 2.2)"
      ]
    },
    {
      "metadata": {
        "id": "Ew3WKBnN1pbq",
        "colab_type": "code",
        "outputId": "4b4a24ab-c20a-421d-ce07-bbeda22636a1",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#consine of documents iteration\n",
        "lx,ly=draw_chart(number,times_1,'cosine similary \\n with vector iteration')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.7554522128887582 and intercept is -5.246121743384572\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "TaulfslFQbVS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosine similarity with numpy dot product(chart 2.3 and chart 2.4)"
      ]
    },
    {
      "metadata": {
        "id": "goLqoHw01pcA",
        "colab_type": "code",
        "outputId": "2153e178-8a1d-42c0-8672-2599d21dcb83",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#consine of numpy dot product\n",
        "lx,ly=draw_chart(number,times_2,'cosine similary \\n with numpy dot product')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.7331657588181568 and intercept is -5.317878609469529\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "IHhyhwdkQF7q",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Comparing two measures(chart 2.5)"
      ]
    },
    {
      "metadata": {
        "id": "BiF-IqhI1pcZ",
        "colab_type": "code",
        "outputId": "c5cdc77a-8f8e-45b0-8d05-8670af6b3daa",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "plt.plot(times_1)\n",
        "plt.plot(times_2)\n",
        "plt.title(\"Comparing two measures\")\n",
        "\n",
        "label = [\"Cosine similarity with vector iteration\",\"Cosine similarity with numpy dot product\"]\n",
        "plt.legend(label, loc = 0, ncol = 2)\n",
        "plt.ylabel('Cosine run time')\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "_D0Erh5p1pco",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Estimate the constant for my implementation and computer.\n",
        "#### (NB: Cosine similarity measure with vector iteration means we apply for loop documents iteration to compute documents represented as dense vectors. Cosine similarity measure with numpy dot product means that it apply numpy dot product)\n",
        "\n",
        "The worst-case running time of this cosine similarly measure was investigated for different lengths of documents words between 1000 and 30000. Firstly, from the above charts of cosine similarity measure with vector iteration(chart 2.1 and chart 2.2), the first chart is when the number of documents words was an increase from 1000 to 30000, its running time was a significant growth. Moreover, the first chart of cosine similarity measure with numpy dot product had the same variation tendency. These results showed that cosine similarity with vector iteration and cosine similarity measure with numpy dot product had the same variation tendency. It observed that its worst running time trend similar linear $𝑂(𝑛^1)$.   \n",
        "\n",
        "Secondly, I also used some above maths. If $𝑦=𝑐𝑎.𝑥^𝑛$ then it follows that: log(𝑦)=log(𝑐𝑎)+𝑛log(𝑥). Therefore, according to the second charts of a worst-case running time of  cosine similarity with vector iteration and consine similarity measure with numpy dot product (chart 2.2 and  chart 2.4).  Gradient t of cosine similarity with vector iteration and cosine similarity measure with numpy dot product were approximately 0.755 and 0.733 respectively. Their intercept were approximately -5.2 and -5.3 respectively. It means the gradient and intercept of two cosine similarity measure were significantly similar. Moreover, this is fairly straight and the gradient is approximately 0.7 to 1. The y intercept is about -5 so $𝑐𝑎≈10^{−5}=0.00001$. \n",
        "\n",
        "Depend on the above analysis, I can estimate constant that the worst running times of first cosine similarity measure and second cosine similarity measure are $y=10^{-5}*x^{0.755}$ and $y=10^{-5}*x^{0.733}$. This illustrates that empirically we have$𝑂(𝑛^{0.755})$for original measure and $𝑂(𝑛^{0.733})$ for numpy which are slightly greater than 𝑂(𝑛). The same reason is that measures there are some instructions which are only carried out O(n) times (outside the inner loop). This will make the power appear lower than it really is unless n is asymptotically large. Finally, for the chart of comparing two functions(chart 2.5), two curves have a similar trend，However, the curve of cosine similarity measure with numpy dot product lower than the curve of cosine similarity measure with vector iteration. This means if we use the numpy dot, the running time would be reduced. According to the previous analysis, if, we apply numpy dot product, its time complexity is $𝑂(𝑛^{0.733}) $. However, the cosine similarity with vector iteration is $𝑂(𝑛^{0.755}). Therefore, if we apply cosine similarity with numpy dot product , it would more effective."
      ]
    },
    {
      "metadata": {
        "id": "nvL3_0061pct",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "3.Write a function which computes cosine similarity directly from sparse (dictionary) representations without converting them into dense (vector) representations? Make sure you test your function empirically for correctness and for efficiency and compare it to your previous implementatIon of the cosine similarity and your implementation of Jaccard’s measure."
      ]
    },
    {
      "metadata": {
        "id": "0nZwWS-Y1pcx",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#cosine similarity directly from sparse (dictionary) representation\n",
        "A = token_frequency(brown.words()[0:100])\n",
        "B= token_frequency(brown.words()[100:200])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "RJrlc1O91pc5",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Sparse (dictionary) representations"
      ]
    },
    {
      "metadata": {
        "id": "jxjca6kK1pc5",
        "colab_type": "code",
        "outputId": "40fa34e8-0c1b-4433-f499-747b330a7639",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "print(A,'\\n',B)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'The': 1, 'Fulton': 1, 'County': 1, 'Grand': 1, 'Jury': 1, 'said': 1, 'Friday': 1, 'an': 1, 'investigation': 1, 'of': 1} \n",
            " {\"Atlanta's\": 1, 'recent': 1, 'primary': 1, 'election': 1, 'produced': 1, '``': 1, 'no': 1, 'evidence': 1, \"''\": 1, 'that': 1}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "mjfRZWiO1pdA",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from math import sqrt\n",
        "def dot(d1,d2):\n",
        "    if len(d1) < len(d2):\n",
        "        a = d1\n",
        "        b = d2\n",
        "    else:\n",
        "        a = d2\n",
        "        b = d1\n",
        "    dotproduct = 0\n",
        "    for word,count in a.items():\n",
        "        dotproduct += count * b.get(word,0)\n",
        "    return dotproduct\n",
        "\n",
        "def cos_sim_nlp(d1,d2):\n",
        "    numerator = dot(d1,d2)\n",
        "    denominator = sqrt(dot(d1,d1)*dot(d2,d2))\n",
        "    return numerator/denominator"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "W9CD9sxt1pdL",
        "colab_type": "code",
        "outputId": "a9d88c0c-21d0-457c-df9b-c6fd0af6ff13",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def cos_dense_nl():\n",
        "#     times_cose1 = []\n",
        "    times_cose2 = []\n",
        "    numberxs=[]\n",
        "    for n in range(1000, 300 * 100 + 1, 1000):\n",
        "    \n",
        "        A = token_frequency(brown.words()[:n])\n",
        "        B = token_frequency(brown.words()[n:2*n])\n",
        "    \n",
        "        numberxs.append(n)\n",
        "        \n",
        "        running_time=timeit(cos_sim_nlp,A, B)\n",
        "        times_cose2.append(running_time)\n",
        "   \n",
        "\n",
        "    plt.plot(times_cose2)\n",
        "    plt.ylabel('Cosine run time')\n",
        "    plt.show()\n",
        "        \n",
        "    return times_cose2,numberxs\n",
        "cos_den=cos_dense_nl()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "jfZznzJOTR1_",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosine similarity directly from sparse (dictionary) representations(chart 3.1 and 3.2)"
      ]
    },
    {
      "metadata": {
        "scrolled": true,
        "id": "TgCfWPDB1pdT",
        "colab_type": "code",
        "outputId": "7c5068fb-91b0-4f5a-ed2e-848d08fd1ba5",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "lcx,lcy=draw_chart(cos_den[1],cos_den[0],'cosine similary \\n with sparse dictionary')\n",
        "cal_slope(lcx,lcy)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.765139708177342 and intercept is -5.8486494815613215\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "YD88XZZJ1pde",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Estimate the constant for my implementation and computer.\n",
        "According to question 3, before to compute running time, I need to write a function which computes cosine similarity directly from sparse (dictionary) representations without converting them into dense (vector) representations. It means that it compute cosine similarity by keys and frequency of dictionary. From the above two charts of the worst-case running time of cosine similary measure as dictionary reoresentation, the first chart illustrates that the running time was an increase with the increase in the number of words. Its curve also similar linear growth. So that, I use the same math method to analyse the linear relationship of this algorithm. According to the second chart of worst case running time of cosine similary measure as dictionary. Its gradient t was approximately 0.765. Its intercept was approximately -5.84. Moreover, this is fairly straight and the gradient is approximately 0.765 to 1. The y intercept is about $-6$ so $𝑐𝑎≈10^{−5.8}=0.000001$. Likewise, I can estimate the worst running time $𝑦=𝑐𝑎.𝑥^{0.765}$ This illustrates that empirically we have$𝑂(𝑛^{0.765})$ which is slightly greater than 𝑂(𝑛). The same reason is that some instructions of the algorithm are executed only O (n) times (outside the inner loop). This will make the power appear to be lower than the actual value, unless n is asymptotically large."
      ]
    },
    {
      "metadata": {
        "id": "KplbZAIVUAcK",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Compare four measures(chart 3.3)"
      ]
    },
    {
      "metadata": {
        "id": "0H4yRvu41pdg",
        "colab_type": "code",
        "outputId": "f6b0cea6-749e-4ffb-a7ac-4ac02112de1f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        }
      },
      "cell_type": "code",
      "source": [
        "def cos_dense_nl():\n",
        "    times_cose1 = []\n",
        "    times_cose2 = []\n",
        "    times_jac=[]\n",
        "    times_cos_dot=[]\n",
        "    for n in range(1000, 300 * 100 + 1, 1000):\n",
        "    \n",
        "        A = token_frequency(brown.words()[:n])\n",
        "        B = token_frequency(brown.words()[n:2*n])\n",
        "    \n",
        "    \n",
        "        MT = np.array(transpose(make_matrix([A,B])))\n",
        "        \n",
        "       \n",
        "        #cosine's similarly of vectors\n",
        "        \n",
        "        running_time1=timeit(cosine_sim,MT[0], MT[1])\n",
        "        times_cose1.append(running_time1)\n",
        "        \n",
        "\n",
        "        #cosine's similarly of dictionary\n",
        "        \n",
        "        running_time2=timeit(cos_sim_nlp,A, B)\n",
        "        times_cose2.append(running_time2)\n",
        "        \n",
        "         # jaccard's similarly\n",
        "\n",
        "        \n",
        "        running_time3=timeit(cos_sim_nlp,A, B)\n",
        "        times_jac.append(running_time3)\n",
        "        \n",
        "        #cosine's similarly of numpy dot\n",
        "        running_time4=timeit(cosine_sim_dot,MT[0], MT[1])\n",
        "        times_cos_dot.append(running_time4)\n",
        "        \n",
        "    plt.plot(times_jac)   \n",
        "    plt.plot(times_cose1)\n",
        "    plt.plot(times_cose2)\n",
        "    plt.plot(times_cos_dot)\n",
        "    \n",
        "    plt.xlabel(\"Length of List\")\n",
        "    plt.title(\"Compared four measure\")\n",
        "    label = [\"jaccard\", \"cosine of vector\",\"cosine of dictionary\",\"cosine numpy dot\"]\n",
        "    plt.legend(label, loc = 0, ncol = 4)\n",
        "    plt.ylabel('run time')\n",
        "    plt.show()\n",
        "        \n",
        "    return times_cose2\n",
        "cos_den=cos_dense_nl()"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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r2skL+a/Rae/izPGnckHGWTJ35ygiV2p4LQcuAVBKzQTKtNbNAFrrIiBMKZWm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\nRK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f4ca49efda0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "Rswpy-681pdr",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "From the above charts( chart 3.3). it indicates that four algorithms have a similar increase trend. However, the curve of the cosine of vector is significantly higher than the others. This means the running time is greater than others. Moreover, the curve of the cosine of numpy dot product is lower than the curve of vector and higher than the curve of Jaccard and cosine of the dictionary. The curve of Jaccard  and cosine of the dictionary not only had the lowest worst running time but also had a most similar trend in the chart of compare four algrothm. For analysis of chart, firstly, the cosine similarity measure applied to documents represented as dense vectors. It needs to compute where there is a dimension for each of the V words in the English vocabulary. This means it needs to compute all words frequency to make the vector, if some words do not occur in other documents, the vectors will be interpolated with zero.  Therefore, it leads to the length of the list was increased with the number of document words. Similarly, if  we apply the numpy dot product, it also computes the expended vectors. However, it is more efficient than the first measure by previous analysis. If cosine similarity measure is directly from sparse (dictionary) representations without converting them into dense (vector) representations, its bag of a list is lower than the first and second method. It not only does not expend the frequency of each word as vectors but also only compute the frequency of each word. This reduces the size of data and running time. For the Jaccard' similarity. its running time was the lowest. Because it does not iterate through arrays and collections and their running time of intersection and union only depend on the number of words in documents. This is the cause of this distribution.  Finally,  four measures depend on length of documents, if the length is an increase, their running time also rise.Different algorithms running time is significant different. Even if the algorithm is the same, different method lead to different running time."
      ]
    },
    {
      "metadata": {
        "id": "lEuDv2uj1pdt",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "4.Write a function which computes all-pairs similarities for a collection of documents. The function should take a list of dictionaries (the document collection) and a parameter specifying the similarity measure to be used. What is the theoretical worst-case running time for computing all-pairs similarities? Does it matter what the similarity measure is? Can you give an estimate of how long it would take to compute all-pairs similarities for 200K documents for both measures? (Note: that whilst you should test your function for all-pairs similarities (with d > 10), you do not need to prove the theoretical worst case empirically or test with 200K documents!)"
      ]
    },
    {
      "metadata": {
        "id": "SVMGApRa1pdu",
        "colab_type": "code",
        "outputId": "d301f545-8fb3-49de-be76-2a2ec002c125",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "len(brown.words())"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1161192"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        }
      ]
    },
    {
      "metadata": {
        "id": "zpvl0ebv1pd9",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def all_pair(func,flag):\n",
        "    sims= []\n",
        "    time_collection=[]\n",
        "    number_collection=[]\n",
        "    k_num=0\n",
        "    j_num=0\n",
        "\n",
        "    most_similar = (0,0,0)\n",
        "    \n",
        "    if flag==1:\n",
        "        for i in range(len(my_doc)-1):\n",
        "            for j in range(i+1, len(my_doc)):\n",
        "                start = timer()\n",
        "                sim_i_j = func(my_doc[i], my_doc[j])\n",
        "                end = timer()\n",
        "                k_num=k_num+(end-start)\n",
        "                time_collection.append(k_num)\n",
        "                j_num+=1\n",
        "                number_collection.append(j_num)\n",
        "    else: \n",
        "        for numk in range(48):\n",
        "            my_docs=my_doc[0:numk+1]\n",
        "            start = timer()\n",
        "            k_num=0\n",
        "            for i in range(len(my_docs)-1):\n",
        "                for j in range(i+1, len(my_docs)):\n",
        "                    sim_i_j = func(my_doc[i], my_doc[j])\n",
        "            end = timer()\n",
        "            k_num=(end-start)\n",
        "            time_collection.append(k_num)\n",
        "            number_collection.append(len(my_docs))       \n",
        "            \n",
        "#     plt.plot(number_collection,time_collection)\n",
        "#     plt.ylabel('run time')\n",
        "#     plt.show()\n",
        "    return number_collection,time_collection"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "62HSeVMv1peA",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Charts of Jaccard's all-pairs similarity (chart 4.1 and chart 4.2)"
      ]
    },
    {
      "metadata": {
        "id": "bYskBQLE1peC",
        "colab_type": "code",
        "outputId": "9df17747-b5cb-4e9d-f709-a4e4cb973abf",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#only compuating Jaccard's similary \n",
        "xj,yj=all_pair(jac_sim,1)\n",
        "lx,ly=draw_chart(xj,yj,'Jaccard all-pairs')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.9911309621556481 and intercept is -3.985751662733678\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "cRDHIC3pV-p7",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosider documents iteration(chart 4.3 and chart 4.4)"
      ]
    },
    {
      "metadata": {
        "scrolled": false,
        "id": "6st9-5jU1peK",
        "colab_type": "code",
        "outputId": "b29a2314-48bc-458d-c6cc-ec1dc042943c",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "xj,yj=all_pair(jac_sim,0)\n",
        "lx,ly=draw_chart(xj,yj,'Jaccard all-pairs \\n of documents iteration')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 2.2563101396445706 and intercept is -4.650829511828043\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "9US-R_LI1peP",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "From above four chars of all- pairs Jaccard's similarity measure, the first and second charts did not consider the document iteration(chart 4.1 and chart 4.2). They show that if the funcion only compuate runing time of a collection of 49 documents each containing at least 600 English words.The worst running time of Jaccard' similarity measure also was similar O(n). According to the second chart, its slope and intercept were 0.991 and -3.98 respectively.  Based on previous maths. If $y=c_a.x^n$ then it follows that: $\\log(y) = \\log(c_a) + n \\log(x)$ This is fairly straight and the gradient is approximately 0.991 to 1. The y intercept is about $−3$ 𝑠𝑜 $𝑐𝑎≈10^{−3}=0.001$. Likewise, I also estimate the worst running time $𝑦=𝑐𝑎.𝑥^{0.991}$ This illustrates that empirically we have $𝑂(𝑛^{0.991})$ which is slightly greater than 𝑂(𝑛). The reason is same previous analysis that the algorithm there are some instructions which are only carried out O(n) times (outside the inner loop).\n",
        "According to the results $y=10^{-3}x^{0.991}$, I can give an estimate of 200k documents that it is $y=10^{-3}(200000)^{0.991} \\approx 200 $. However, according to the third chart and fourth chart, if we consider two for loop for documents iteration(chart 4.3 and chart 4.4), its slope and intercept were 3.18 and -4.96 respectively. This illustrates that empirically we have $𝑂(𝑛^{2.25})$ which is slightly better than $𝑂(𝑛^{3})$ . Because in the algorithm, there are some instructions which are only carried out  instructions out the inner loop. This will make the power appear lower than it really.If length of document is increase. it would close the $O(n^3)$. Its Therefore, number of documents was increase with growth of running time. Its running time is that y is $10^{-4}*x^{2.25} \\approx 0.0001*(200000)^{2.25} $.Its worst running time is that $10^{-4}*x^{3} $"
      ]
    },
    {
      "metadata": {
        "id": "O82LGJzb1peS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Graphs of  Consine all-pair similarity (chart 4.5 and chart 4.6)"
      ]
    },
    {
      "metadata": {
        "id": "c8z-cvNv1peT",
        "colab_type": "code",
        "outputId": "1eef2642-345d-409a-8bc9-8c69918e4f7b",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "xc,yc=all_pair(cos_sim_nlp,1)\n",
        "lx,ly=draw_chart(xc,yc,'cosine all-pairs')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 0.9567871513715874 and intercept is -3.3273323302705573\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "QVKFksvMW3X1",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosider documents iteration(chart 4.7 and chart 4.8)"
      ]
    },
    {
      "metadata": {
        "id": "W2PL_s3O1pea",
        "colab_type": "code",
        "outputId": "f976758e-48f4-4449-d4f0-60fa0698896a",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "xc,yc=all_pair(cos_sim_nlp,0)\n",
        "lx,ly=draw_chart(xc,yc,'Consine all-pairs \\n of documents iteration')\n",
        "cal_slope(lx,ly)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Slope is 2.454480750184999 and intercept is -4.416865388520684\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "KsqFCQd71ped",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "The parameter is a collection of 49 documents each containing at least 600 English words. According to above graphs, the first graph and second graph illustrate that when I only compuate the consine similarity measure without documents itration(chart 4.5 and chart 4.6). Its slope and intercept were 0.956 and -3.327. So that, Based on previous maths,the gradient is approximately 0.956 to 1. The y intercept is about $−3$ 𝑠𝑜 $𝑐𝑎≈10^{−3}\\approx 0.001$.I estimate the worst running time $𝑦=𝑐𝑎.𝑥^𝑛⟶𝑂(𝑛^{0.956})$ This illustrates that empirically we have $𝑂(𝑛^{0.956})$ which is slightly greater than 𝑂(𝑛). The reason is same previous analysis that the algorithm there are some instructions which are only carried out O(n) times (outside the inner loop). From above analysis, if the number of documents are 200k, I have an estimate that $y=10^{-3}*200000 \\approx 200 $. Similarly，when we consider documents itration, its slope and intercept were 2.45 and -4.416. Therefore,it have $O(n^{2.45})$ and $Ca \\approx -4.416$. I estimate that its y is $10^{-4.416}*(200000)^{2.45}$. Moreover, if the documnets have a increase, its worst running time is estimated about $10^{-4.416}*(200000)^{3}$ by previous analysis. "
      ]
    },
    {
      "metadata": {
        "id": "velxDZdZ1ped",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "5.Use the map-reduce computing paradigm to implement a parallel version of all-pairs similarities for documents. Make sure you test your function empirically for correctness and for efficiency. Investigate the number of map processes and reduce processes which give optimal results for your implementation and computer."
      ]
    },
    {
      "metadata": {
        "id": "vuszXspF1peg",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def all_pair(func):\n",
        "    sims= []\n",
        "    for i in range(len(my_doc)-1):\n",
        "        sims.append([])\n",
        "        for j in range(i+1, len(my_doc)):\n",
        "            sims[i].append([i,j])\n",
        "    return sims"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "nfKeN6G-2N9K",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# my mapper function\n",
        "def wc_mapper_parallelxx(document):\n",
        "     output=[]\n",
        "    \n",
        "     for num in document:\n",
        "        output.append((str(num[0]),num))\n",
        "        \n",
        "#         print(num)\n",
        "#         print(str(document[0][0]))\n",
        "\n",
        "     return output"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "rJvF_SMU2QBo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#my Jaccard'similarity reducer function\n",
        "def wc_reducer_parallelxx_jac(item):\n",
        "    output=[]\n",
        "    (word,counts)=item\n",
        "    for couns in counts:\n",
        "#       print(word,couns)\n",
        "      \n",
        "      A=my_doc[couns[0]]\n",
        "      B=my_doc[couns[1]]\n",
        "      U = A.keys() | B.keys()\n",
        "      I = A.keys() & B.keys()\n",
        "      jac =  len(I) / len(U)\n",
        "      \n",
        "      output.append(((couns[0],couns[1]),jac))\n",
        "    return output"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "wWVtegjx2R1h",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#my cosine similarity reducer  function\n",
        "def wc_reducer_parallelxx_cos(item):\n",
        "    output=[]\n",
        "    (word,counts)=item\n",
        "    for couns in counts:\n",
        "#       print(word,couns)\n",
        "      \n",
        "      A=my_doc[couns[0]]\n",
        "      B=my_doc[couns[1]]\n",
        "      numerator = dot(A,B)\n",
        "      denominator = sqrt(dot(A,A)*dot(B,B))\n",
        "      cos_sim=numerator/denominator\n",
        "      \n",
        "      output.append(((couns[0],couns[1]),cos_sim))\n",
        "    return output"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "zjdtyy3c2TwT",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def map_reduce_parallel(docm,mapper,reducer,mapprocesses=3,reduceprocesses=2):\n",
        "  outputs=[]\n",
        "  collector=defaultdict(list)  #this dictionary is where we will store intermediate results\n",
        "                                 #it will map keys to lists of values (default value of a list is [])\n",
        "                                 #in a real system, this would be stored in individual files at the map nodes\n",
        "                                 #and then transferred to the reduce nodes\n",
        "        \n",
        "  docm1=all_pair(docm)\n",
        "  mapprocesses=4\n",
        "  reduceprocesses=4\n",
        "\n",
        "  mappool = Pool(processes=mapprocesses)\n",
        "  #map stage\n",
        "  mapresults=mappool.map(mapper,docm1)\n",
        "  mappool.close()\n",
        "\n",
        "  collector=defaultdict(list)\n",
        "  for mapresult in mapresults:\n",
        "    for (key, value) in mapresult:     #pass each input to the mapper function and receive back each key,value pair yielded\n",
        "      collector[key].append(value)     #append the value to the list for that key in the intermediate store\n",
        "\n",
        "\n",
        "  reducepool = Pool(processes=reduceprocesses)\n",
        "  #reduce stage\n",
        "  reduceresults=reducepool.map(reducer,collector.items())\n",
        "  reducepool.close()\n",
        "  for reduceresult in reduceresults:\n",
        "    outputs+=reduceresult\n",
        "  return outputs"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "gQESTkzB3pLW",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#test 50 documents average running time\n",
        "def tests(func,ti):\n",
        "  my_docs=my_doc\n",
        "  k_num=0\n",
        "  time_collection=[]\n",
        "  start = timer()\n",
        "\n",
        "  for tii in range(ti):\n",
        "    for i in range(len(my_docs)-1):\n",
        "        for j in range(i+1, len(my_docs)):\n",
        "            sim_i_j = func(my_doc[i], my_doc[j])\n",
        "    end = timer()\n",
        "    k_num=(end-start)\n",
        "    time_collection.append(k_num)\n",
        "  means_time=np.mean(time_collection)\n",
        "  print('(50 documents all-pair) Jaccard similiarity average running time',means_time)\n",
        "  return means_time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "wri4hpcG5L90",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "#test 50 documents average running time\n",
        "def tests_pall(func,my_docs,mapper,reducer,ti):\n",
        "  my_docs\n",
        "  k_num=0\n",
        "  time_collection=[]\n",
        "\n",
        "  for tii in range(ti):\n",
        "    start = timer()\n",
        "    map_reduce_parallel(my_doc,mapper,reducer)\n",
        "  \n",
        "    end = timer()\n",
        "    k_num=(end-start)\n",
        "    time_collection.append(k_num)\n",
        "  means_time=np.mean(time_collection)\n",
        "  print('(50 documents all-pair) parallel Jaccard similiarity average running time',means_time)\n",
        "  return means_time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "l35Hs5Jp2Zn8",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Jaccard's similarity map-reduce implementation"
      ]
    },
    {
      "metadata": {
        "id": "jTtcexg1YvEx",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Compare two Jaccard's similarity measures average running time  "
      ]
    },
    {
      "metadata": {
        "id": "wYu6wxDO6rJl",
        "colab_type": "code",
        "outputId": "d36e1bbd-0948-4840-ad2e-124b1917eab1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "tests_pall(map_reduce_parallel,my_doc,wc_mapper_parallelxx,wc_reducer_parallelxx_jac,10)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50 documents all-pair) parallel Jaccard similiarity average running time 0.2999086957001055\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.2999086957001055"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "metadata": {
        "id": "4WHwNEvB7KCX",
        "colab_type": "code",
        "outputId": "9ea02a62-b136-4fbc-83f9-9f59053f7c5c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "tests(jac_sim,10)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50 documents all-pair) Jaccard similiarity average running time 0.8409540088001449\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8409540088001449"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "metadata": {
        "id": "752h5hIBYgXn",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Make sure my Jaccard's similiarity function empirically for correctness and for efficiency"
      ]
    },
    {
      "metadata": {
        "id": "GnYrXRAHqNLm",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Map-reduce"
      ]
    },
    {
      "metadata": {
        "id": "oug_uezFaaMo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "jac_sim_all=map_reduce_parallel(my_doc,wc_mapper_parallelxx,wc_reducer_parallelxx_jac)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "5iI3248Q2cWW",
        "colab_type": "code",
        "outputId": "6197106b-f9e2-4a43-8fbc-9e8439abc9a5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "print('Map-reduce compute document 0 and document 1 similarity:',jac_sim_all[0])\n",
        "\n",
        "jac_df=pd.DataFrame(jac_sim_all,columns=['document','similiarity'])"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Map-reduce compute document 0 and document 1 similarity: ((0, 1), 0.14382978723404255)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "9j7Uxzd8nfs_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "c4dc9272-1d46-4c3d-93a1-e2120ed66ad1"
      },
      "cell_type": "code",
      "source": [
        "jac_df.head()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>document</th>\n",
              "      <th>similiarity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>(0, 1)</td>\n",
              "      <td>0.143830</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>(0, 2)</td>\n",
              "      <td>0.074879</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>(0, 3)</td>\n",
              "      <td>0.091792</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>(0, 4)</td>\n",
              "      <td>0.074675</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>(0, 5)</td>\n",
              "      <td>0.096541</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  document  similiarity\n",
              "0   (0, 1)     0.143830\n",
              "1   (0, 2)     0.074879\n",
              "2   (0, 3)     0.091792\n",
              "3   (0, 4)     0.074675\n",
              "4   (0, 5)     0.096541"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "metadata": {
        "id": "ClVtfUBMqPFu",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Original Jaccard similarity measure"
      ]
    },
    {
      "metadata": {
        "id": "ntiKQtdn2ffJ",
        "colab_type": "code",
        "outputId": "cb956174-31f0-41ba-dbbc-7f9ac93d2016",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "print('Jaccrad similarity document 0 and document 1 similarity:',jac_sim(my_doc[0],my_doc[1]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Jaccrad similarity document 0 and document 1 similarity: 0.14382978723404255\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "zzMMgcfFnvpf",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "jac_o=[]\n",
        "for i in range(len(my_doc)-1):\n",
        "  for j in range(i+1, len(my_doc)):\n",
        "    sim_i_j = jac_sim(my_doc[i], my_doc[j])\n",
        "    jac_o.append(sim_i_j)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "eeJM0Lb-oXo8",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 108
        },
        "outputId": "3b5f3c6c-7c0c-4dfd-a0a8-ba08ed28cdee"
      },
      "cell_type": "code",
      "source": [
        "#Only show first four similarity of the  all-pairs\n",
        "jac_o[:5]"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.14382978723404255,\n",
              " 0.0748792270531401,\n",
              " 0.09179170344218888,\n",
              " 0.07467532467532467,\n",
              " 0.09654062751407884]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "metadata": {
        "id": "lx4QwEZd2jGy",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Cosine similarity map-reduce implementation"
      ]
    },
    {
      "metadata": {
        "id": "0MxEAxok2iA5",
        "colab_type": "code",
        "outputId": "403c843e-0e7a-4086-8409-7d04aa4c7c2d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "tests_pall(map_reduce_parallel,my_doc,wc_mapper_parallelxx,wc_reducer_parallelxx_cos,10)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50 documents all-pair) parallel Jaccard similiarity average running time 0.5778577745001258\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.5778577745001258"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "metadata": {
        "id": "gQdBod7x8JF9",
        "colab_type": "code",
        "outputId": "04c795bd-8677-4c85-d3fc-fed1e48d6aeb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "cell_type": "code",
      "source": [
        "tests(cos_sim_nlp,10)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(50 documents all-pair) Jaccard similiarity average running time 3.1967310019001616\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.1967310019001616"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "metadata": {
        "id": "pqubioGCZp-D",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Make sure my cosine similiarity function empirically for correctness and for efficiency"
      ]
    },
    {
      "metadata": {
        "id": "ogQdYAsIp66A",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Map-reduce"
      ]
    },
    {
      "metadata": {
        "id": "pKkh9FsNo-2d",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "cos_sim_all=map_reduce_parallel(my_doc,wc_mapper_parallelxx,wc_reducer_parallelxx_cos)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "fES9kMEx2md0",
        "colab_type": "code",
        "outputId": "805e312a-ec64-4826-d413-e75e717f3afa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "print('Map-reduce cosine measure document 0 and document 1 similarity:',cos_sim_all[0])"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Map-reduce cosine measure document 0 and document 1 similarity: ((0, 1), 0.4670035096857264)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "lLnbRPJ4pR62",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "87b1cd3c-7109-4683-8902-455b2d431665"
      },
      "cell_type": "code",
      "source": [
        "cos_df=pd.DataFrame(cos_sim_all,columns=['document','similiarity'])\n",
        "cos_df.head()"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>document</th>\n",
              "      <th>similiarity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>(0, 1)</td>\n",
              "      <td>0.467004</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>(0, 2)</td>\n",
              "      <td>0.371672</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>(0, 3)</td>\n",
              "      <td>0.406700</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>(0, 4)</td>\n",
              "      <td>0.376800</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>(0, 5)</td>\n",
              "      <td>0.331278</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  document  similiarity\n",
              "0   (0, 1)     0.467004\n",
              "1   (0, 2)     0.371672\n",
              "2   (0, 3)     0.406700\n",
              "3   (0, 4)     0.376800\n",
              "4   (0, 5)     0.331278"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "metadata": {
        "id": "WGNPYE9sp8_h",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Original cosine measure"
      ]
    },
    {
      "metadata": {
        "id": "i8J1xOIj2oAD",
        "colab_type": "code",
        "outputId": "c0d5bd87-7f5a-47e5-d1de-dc7fa193b5a9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        }
      },
      "cell_type": "code",
      "source": [
        "print('document 0 and document 1 similarity:',cos_sim_nlp(my_doc[0],my_doc[1]))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "document 0 and document 1 similarity: 0.4670035096857264\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "6r-zhoE1peZE",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "cos_o=[]\n",
        "for i in range(len(my_doc)-1):\n",
        "  for j in range(i+1, len(my_doc)):\n",
        "    sim_i_j = jac_sim(my_doc[i], my_doc[j])\n",
        "    cos_o.append(sim_i_j)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "5LeWy7sDpvBv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 90
        },
        "outputId": "7ea4c836-1c09-4577-ca75-b2b258f1f996"
      },
      "cell_type": "code",
      "source": [
        " cos_o[:4]"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.14382978723404255,\n",
              " 0.0748792270531401,\n",
              " 0.09179170344218888,\n",
              " 0.07467532467532467]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "metadata": {
        "id": "_Ari-vTUvnid",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Map-reduce achieves reliability by distributing large-scale operations to each node on the network; each node periodically returns its completed work and the latest state. In question 5,  I used the map-reduce computing paradigm to implement a parallel version of all-pairs similarities  for documents.  Firstly, before  I wrote the map and reduce computing paradigm to implement a parallel version of all-pairs similarities for documents, Documents need to compute all-pair  group. For example,  if we have 10 documnets, we need to compute  combination  of all documents to make a list. Moreover, map tasks (paralle mapper ) was written to divide the combination of  all documents and turn a chunk into a sequence of key-value pairs. The sequence  would store key-value pairs. For example, key-value (document1,(document 1 and document 2))-(1,(1,2)) and (document1,(document 1 and document 3))-(1,(1,3)) . It means It map all-pair  combination of individul documents. Futhermore,If a token w appears m times among all the documents assigned to a given map task, then there will be m key-value pairs (w,(w,m)) among its output. After map tasks, Key-value pairs are grouped by key and values associated with each key formed into a list of values. Finally,the Reduce function’s argument is a pair consisting of a key and a list of values. Moreover, I wrote the reduce task. This pair I have divide two reducer for Jaccard's similarity and cosine similarity. The reducer can compute the previous key-values pair. For two similarity reduce, if input (1,(1,2)) and(1,(1,3)) from the list of grouby.  Reducer can compute similarity of documents1 and 2, document 1 and 3 at same time by multiprocess parallel computing. Then, it can \n",
        "output is a sequence of 0 or more key-value pairs.For example, ((document1,document 2),similarity)-((1,2)sim). \n",
        "\n",
        "Comparing original similarity functions and Map-reduce through above experiments. Two method results were same. Moreover,according to the above average test results, average running time of the parallel version Jacarrd's similarity measure was significance lower than original Jaccard's measure when we have test 50 documents. Similarly, average running time of the parallel version cosine similarity measure also was smaller than original cosine measure. The reason is that  if we use 4 process to compute all-pairs similarity, they can run four programs at the same time. Therefore, when I applied map-reduce to compute similarity, its running time obviously lower than original similarity measure. \n"
      ]
    },
    {
      "metadata": {
        "id": "icZpmkLW1pei",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "### Summary\n",
        "\n",
        "This report has analysed Jaccard' similarity measure, cosine similarity measure, and map-reduce. Firstly, for question 1 and question 2, Jaccard's similarity measure worst running time and cosine similarity measure worst running time were analysed and estimate the constant for my implementation and computer. The results show that the time complexity of Jaccard's similarity measure, cosine similarity measure of documents represented as dense vectors and cosine similarity of numpy dot product were $ 𝑂(𝑛^{0.89}) $, $𝑂(𝑛^{0.755})$ and $𝑂(𝑛^{0.733}) $ respectively. According to the previous analysis, if the length of documents is an increase, Time complexity of three measure would close $O(n)$. Secondly, based on the analysis of question 2 and question 3, their results illustrate that Jaccard' similarity measure and cosine similarity of sparse (dictionary) representations have a similar growth trend. Their running time lower than cosine of vectors representations. So that, if we apply Jaccard' similarity measure and cosine similarity measure, processing speed will be faster. Finally, for the map-reduce computing paradigm to implement a parallel version of all-pairs similarities for documents, I wrote the map-reduce measure for Jaccard's similarity and cosine similarity to compute all-pairs similarity. Because it is multithread parallel computing that it can process multiple requests in parallel. Therefore, its process speed is significantly faster than the previous measure. Moreover, this is a map-reduce computing paradigm. if we use it to process mass data processing, this method reduced running time greatly and increased cutting efficiency available. "
      ]
    }
  ]
}