notebooks/4_Vector_Semantics.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HddKEEiXn981"
      },
      "source": [
        "# Vector Semantics"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1UU2VyfLn983"
      },
      "source": [
        ">- [Extracting Co-occurrences](#Extracting-Co-occurrences)\n",
        ">\n",
        ">\n",
        ">- [Sparse Vectors](#Sparse-Vectors)\n",
        ">\n",
        ">\n",
        ">- [Calculating Cosine Similarities](#Calculating-Cosine-Similarities)\n",
        ">\n",
        ">\n",
        ">- [Visualizing Similarities](#Visualizing-Similarities)\n",
        ">\n",
        ">\n",
        ">- [Evaluating your Model](#Evaluating-your-Model)\n",
        ">\n",
        ">\n",
        ">- [Working with Dense Vectors](#Working-with-Dense-Vectors)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sa5cOJ8rn984"
      },
      "source": [
        "## Packages\n",
        "\n",
        "There are many Python packages that allows you to create or manipulate vector space models:\n",
        "\n",
        "- the NLTK [collocations](http://www.nltk.org/howto/collocations.html) and [metrics](http://www.nltk.org/howto/metrics.html) modules\n",
        "\n",
        "\n",
        "- the Scikit-learn [data transformation](http://scikit-learn.org/stable/data_transforms.html) libraries \n",
        "\n",
        "\n",
        "- the [Gensim](https://radimrehurek.com/gensim/) toolkit\n",
        "\n",
        "\n",
        "- the [Dissect](http://clic.cimec.unitn.it/composes/toolkit/) toolkit\n",
        "\n",
        "We will use some of them in more depth in the future, for now you mainly need NLTK."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f5HVh1x1n986"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hkWeB4W6n986"
      },
      "source": [
        "## Extracting co-occurrences\n",
        "\n",
        "We'll work with the **sentence splitted, tokenized, pos-tagged and lemmatized** version of the Brown corpus:\n",
        "\n",
        "\n",
        "- filtering out the punctuation marks and words tagged as \"X\" (i.e. \"OTHER\");\n",
        "\n",
        "\n",
        "- concatenating the lemma and the pos in the following way \"be-VERB\";"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vmAiRpdZn987"
      },
      "outputs": [],
      "source": [
        "import nltk"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "laDBuaLkn989"
      },
      "outputs": [],
      "source": [
        "from nltk.corpus import wordnet as wn\n",
        "un2wn_mapping = {\"VERB\" : wn.VERB, \"NOUN\" : wn.NOUN, \"ADJ\" : wn.ADJ, \"ADV\" : wn.ADV}\n",
        "\n",
        "brown_lemmatized = []\n",
        "\n",
        "for sentence in nltk.corpus.brown.tagged_sents(tagset='universal'):\n",
        "    lemmatized_sentence = []\n",
        "    for w, p in sentence:\n",
        "        if p in [\".\", \"X\"]:\n",
        "            continue\n",
        "        elif p in un2wn_mapping.keys():\n",
        "            lemma = nltk.WordNetLemmatizer().lemmatize(w, pos = un2wn_mapping[p])\n",
        "        else:\n",
        "            lemma = nltk.WordNetLemmatizer().lemmatize(w)\n",
        "        lemmatized_sentence.append(\"-\".join([lemma, p]))\n",
        "        \n",
        "    brown_lemmatized.append(lemmatized_sentence)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "asB6t0ecn98-",
        "outputId": "36925a1b-6f2e-432c-dcf3-df37fa52dbe8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "['The-DET',\n",
              " 'Fulton-NOUN',\n",
              " 'County-NOUN',\n",
              " 'Grand-ADJ',\n",
              " 'Jury-NOUN',\n",
              " 'say-VERB',\n",
              " 'Friday-NOUN',\n",
              " 'an-DET',\n",
              " 'investigation-NOUN',\n",
              " 'of-ADP',\n",
              " \"Atlanta's-NOUN\",\n",
              " 'recent-ADJ',\n",
              " 'primary-NOUN',\n",
              " 'election-NOUN',\n",
              " 'produce-VERB',\n",
              " 'no-DET',\n",
              " 'evidence-NOUN',\n",
              " 'that-ADP',\n",
              " 'any-DET',\n",
              " 'irregularity-NOUN',\n",
              " 'take-VERB',\n",
              " 'place-NOUN']"
            ]
          },
          "execution_count": 22,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "brown_lemmatized[0]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a0D6YjfAn98_"
      },
      "source": [
        "### from co-occurrences...\n",
        "\n",
        "```\n",
        "…ound and sonic power of a [new electric   guitar  played through] a guitar amp has play…\n",
        "                         …[Some electric   guitar  models feature] piezoelectric pickups…\n",
        "                               …[Playing   guitar  with a] pick produces a bright sound …\n",
        "…ings, he is known for [playing fretless   guitar  in his] performances…\n",
        "               …the neck of [a classical   guitar  is too] wide and the normal position …\n",
        "…t in the centre of Bristol [playing the   piano   , I was] punched in the head while, a…\n",
        "…r in Houston, Texanstagram [playing the   piano   in his] flooded home after Hurrican H…\n",
        "… some supplies, he stopped to [play the   piano   that was] sitting in knee-high water …\n",
        "…te and one black, who [played classical   piano   together]…\n",
        "                    …The [first electric   pianos  from the] late 1920s used metal strin…\n",
        "…technologies, for example [the electric    car    and the] integration of mobile commun… \n",
        "…study had each driver of [each electric    car    drive unimpeded], perform a task whil…\n",
        "…Honda to commence testing of [their new    car    and the] American was no doubt more t…\n",
        "…mary design considerations for [the new    car    were \"safety] innovations, performanc…\n",
        "…would be possible if almost [all private   cars   requiring drivers], which are not in …\n",
        "… who donate to groups [providing private  school  scholarships have] written pieces att…\n",
        "… that students participating [in private  school  choice programs] graduate high school…\n",
        "…s in the establishment of this [new high  school  , named the] Gavirate Business School…\n",
        "         …Anna heads into her [final high  school  year before] university wanting somet…\n",
        "… but he can prevent them from [playing at school]\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l4INsg1Sn99H"
      },
      "source": [
        "Before counting co-occurrences, it is crucial to have a clear idea of:\n",
        "\n",
        "- what our target words are : **what do we want to study?** \n",
        "    - E.g., in what follows we will focus on nouns.\n",
        "\n",
        "\n",
        "- what our contexts are: **how do we want to characterize our target words?** \n",
        "    - E.g., in what follows we will use the co-occurring words as contexts; \n",
        "    - other possibilities could have been: solely verbs, solely open class words, a mixture of PoS-tags and lexicalized elements...\n",
        "    \n",
        "**Textual co-coccurrence counts** between a target word and a contextual word are obtained by counting the number of text segments (i.e. sentences, in our case) in which they co-occur one or more times."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fGJ1eB5qn99I"
      },
      "outputs": [],
      "source": [
        "from itertools import permutations\n",
        "from collections import Counter"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QQ5UQ3-4n99J"
      },
      "outputs": [],
      "source": [
        "cooccs_textual = Counter()\n",
        "\n",
        "for sentence in brown_lemmatized:\n",
        "    cooccs_textual.update([pair for pair in set(permutations(sentence, 2)) if pair[0].split(\"-\")[-1] == \"NOUN\"])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "9eI2inFtn99J",
        "outputId": "cf1fa6fb-f85b-49d2-aac5-b0abe6d76e7c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[(('time-NOUN', 'be-VERB', 'the-DET'), 837),\n",
              " (('time-NOUN', 'the-DET', 'be-VERB'), 837),\n",
              " (('time-NOUN', 'the-DET', 'the-DET'), 783),\n",
              " (('time-NOUN', 'the-DET', 'of-ADP'), 779),\n",
              " (('time-NOUN', 'of-ADP', 'the-DET'), 779),\n",
              " (('year-NOUN', 'of-ADP', 'the-DET'), 751),\n",
              " (('year-NOUN', 'the-DET', 'of-ADP'), 751),\n",
              " (('year-NOUN', 'the-DET', 'the-DET'), 686),\n",
              " (('year-NOUN', 'the-DET', 'be-VERB'), 669),\n",
              " (('year-NOUN', 'be-VERB', 'the-DET'), 669)]"
            ]
          },
          "execution_count": 25,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "cooccs_textual.most_common(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hcqt7cz_n99K",
        "outputId": "32fcfdf5-ad1d-4473-88db-ce684a8c00c5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[(('place-NOUN', 'County-NOUN'), 1),\n",
              " (('Fulton-NOUN', 'Friday-NOUN'), 1),\n",
              " (('Fulton-NOUN', 'say-VERB'), 1),\n",
              " (('Jury-NOUN', 'Friday-NOUN'), 1),\n",
              " (('Jury-NOUN', 'say-VERB'), 1),\n",
              " (('irregularity-NOUN', 'Jury-NOUN'), 1),\n",
              " (('primary-NOUN', 'say-VERB'), 1),\n",
              " (('place-NOUN', 'Jury-NOUN'), 1),\n",
              " (('Fulton-NOUN', 'that-ADP'), 1),\n",
              " (('investigation-NOUN', 'produce-VERB'), 1)]"
            ]
          },
          "execution_count": 26,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# That's pretty dense code. Let's add some prints for logging, to see what is going on...\n",
        "\n",
        "logbool = 0 # logging boolean. set to 0 to let it run to the end and see the result.\n",
        "\n",
        "cooccs_textual = Counter()\n",
        "\n",
        "brown_lemmatized_one = brown_lemmatized[:1]\n",
        "\n",
        "for sentence in brown_lemmatized_one:\n",
        "    if logbool: print(sentence, \"\\n\")\n",
        "    for pair in set(permutations(sentence, 2)):\n",
        "        if pair[0].split(\"-\")[-1] == \"NOUN\":\n",
        "            if logbool: print(pair[0], pair[1])\n",
        "            if logbool: input(\"\")\n",
        "        \n",
        "cooccs_textual.update([pair for pair in set(permutations(sentence, 2)) if pair[0].split(\"-\")[-1] == \"NOUN\"])\n",
        "\n",
        "cooccs_textual.most_common(10)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZdIJcxtQn99K"
      },
      "source": [
        "**Surface co-coccurrence counts** between a target word and a contextual word are obtained by counting how many times a contextual word occurs in a collocational span surrounding the target word. The collocational span can be symmetric or asymmetric. \n",
        "\n",
        "\n",
        "In what follows we use a symmetric ±5w span."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "v0SADMy1n99L"
      },
      "outputs": [],
      "source": [
        "spansize = 5\n",
        "\n",
        "cooccs_surface = Counter()\n",
        "\n",
        "for sentence in brown_lemmatized:\n",
        "    for i,w in enumerate(sentence):\n",
        "        if w.split(\"-\")[-1] == \"NOUN\":\n",
        "            span_range = list(range(max(i- spansize, 0), i)) # left side indices (range, then list so we can extend)\n",
        "            span_range.extend(range(i+1, min(i + spansize + 1, len(sentence)))) # extend by right side indices\n",
        "            for cw in [sentence[idx] for idx in span_range]:\n",
        "                cooccs_surface[(w, cw)] += 1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "GVrm-3lln99L",
        "outputId": "45631f82-3974-4716-9719-a8a1207e025e"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[(('time-NOUN', 'the-DET'), 1130),\n",
              " (('year-NOUN', 'the-DET'), 875),\n",
              " (('world-NOUN', 'the-DET'), 700),\n",
              " (('way-NOUN', 'the-DET'), 665),\n",
              " (('man-NOUN', 'the-DET'), 619),\n",
              " (('Af-NOUN', 'the-DET'), 610),\n",
              " (('day-NOUN', 'the-DET'), 608),\n",
              " (('man-NOUN', 'a-DET'), 601),\n",
              " (('time-NOUN', 'be-VERB'), 570),\n",
              " (('States-NOUN', 'the-DET'), 552)]"
            ]
          },
          "execution_count": 28,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "cooccs_surface.most_common(10)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "iZrCUL4Mn99L"
      },
      "outputs": [],
      "source": [
        "logbool = 0 # logging boolean. set to 0 to let it run to the end and see the result.\n",
        "\n",
        "spansize = 5\n",
        "\n",
        "cooccs_surface = Counter()\n",
        "\n",
        "for sentence in brown_lemmatized:\n",
        "    if logbool: print(\" \".join(sentence), \"\\n\")\n",
        "    for i,w in enumerate(sentence):\n",
        "        if logbool: print(\"word:\", i, w)\n",
        "        if w.split(\"-\")[-1] == \"NOUN\":\n",
        "            span_range = list(range(max(i-spansize, 0), i))  # left side indices (range, then list so we can extend)\n",
        "            span_range.extend(range(i+1, min(i + spansize + 1, len(sentence))))  # extend by right side indices\n",
        "            if logbool: print(\"span: \", span_range)\n",
        "            for cw in [sentence[idx] for idx in span_range]:\n",
        "                cooccs_surface[(w, cw)] += 1\n",
        "                if logbool: print(\"count:\", w, cw)\n",
        "        if logbool: input(\"\")\n",
        "        \n",
        "#for key, value in cooccs_surface.items():\n",
        "#    print(key, \",\", value)\n",
        "#    if value >= 2: break"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hg9IhzhAn99M"
      },
      "source": [
        "### ... to (Weighted) Counts\n",
        "\n",
        "\n",
        "|    *WORD*   |      play |  electric | classical |   private |      high |       ... |       the |       new | \n",
        "| ----------- |:---------:|:---------:|:---------:|:---------:|:---------:|:---------:|:---------:|:---------:|\n",
        "| **guitar**  |         3 |         2 |         1 |         0 |         0 |       ... |         0 |         1 | \n",
        "| **piano**   |         4 |         1 |         1 |         0 |         0 |       ... |         4 |         0 | \n",
        "| **car**     |         0 |         2 |         0 |         1 |         0 |       ... |         4 |         2 | \n",
        "| **school**  |         1 |         0 |         0 |         2 |         2 |       ... |         1 |         1 | "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_tuEp0wun99M"
      },
      "source": [
        "For different (yet related) reasons, it is good practice to **filter out**:\n",
        "\n",
        "- very **infrequent target** items\n",
        "    - we have too few empirical evidence to draw conclusion about them\n",
        "    - the minimal threshold is usually determined empirically, by looking at the word distribution\n",
        "    \n",
        "    \n",
        "- very **infrequent contextual** items\n",
        "    - they mainly slow down the computation, without adding much relevant information\n",
        "    - this is performed either by selecting the n-top frequent items or by deleting those below an empirically determined threshold\n",
        "    \n",
        "    \n",
        "- very **frequent contextual** items\n",
        "    - these elements carry little discriminative power\n",
        "    - this is usually performed by using a stoplist, or by selecting context belonging only to some parts of speech.\n",
        "    \n",
        "An example of a list of English stopwords (= words to filter out because they tend to be uninformative) is available in NLTK (but we won't use it yet): ``print(nltk.corpus.stopwords.words('english'))``"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AqwpgmTbn99N"
      },
      "source": [
        "#### What can be a suitable filtering strategy for our corpus?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TXWpbSMpn99N"
      },
      "outputs": [],
      "source": [
        "from itertools import chain\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.rcdefaults()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m-u75yLYn99N",
        "outputId": "dc194e3e-f6ef-4c7e-f29f-de401ffffcaf"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[('stupefy-VERB', 1), ('boucle-NOUN', 1), ('coral-colored-ADJ', 1), ('Cherokee-NOUN', 1), ('olive-flushed-ADJ', 1), ('aviary-NOUN', 1), ('Perelman-NOUN', 1), ('Compassionately-ADV', 1), ('bilharziasis-NOUN', 1), ('fluke-NOUN', 1), ('wilt-NOUN', 1), ('yaw-NOUN', 1), ('Bodhisattva-NOUN', 1), ('horoscope-NOUN', 1), ('pityingly-ADV', 1), ('bathos-NOUN', 1), ('plumb-VERB', 1), ('straightaway-ADV', 1), ('hubris-NOUN', 1), ('beggary-NOUN', 1)]\n"
          ]
        }
      ],
      "source": [
        "# all words, least frequent...\n",
        "brown_lemmas_frequencies = Counter(chain(*brown_lemmatized))\n",
        "print(list(reversed(brown_lemmas_frequencies.most_common()))[:20])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "UTEhROABn99N",
        "outputId": "057ba305-b66f-4b78-a903-7b807672bd69"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[('the-DET', 62710), ('be-VERB', 37099), ('of-ADP', 36078), ('and-CONJ', 27912), ('a-DET', 21872), ('in-ADP', 19066), ('to-PRT', 14742), ('have-VERB', 11675), ('to-ADP', 10985), ('for-ADP', 8833), ('The-DET', 7258), ('with-ADP', 7009), ('it-PRON', 6722), ('he-PRON', 6564), ('his-DET', 6428), ('that-ADP', 6422), ('on-ADP', 5837), ('a-ADP', 5656), ('I-PRON', 5155), ('by-ADP', 5044)]\n"
          ]
        }
      ],
      "source": [
        "# ...and most frequent\n",
        "print(brown_lemmas_frequencies.most_common(20))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e3Z256s0n99O"
      },
      "source": [
        "> Most of the **non-informative frequent contexts** can be filtered out by ignoring **closed class** words together with few semantically \"empty\" verbs like \"be\", \"have\", \"do\", \"would\", \"will\"..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BdO3T9f0n99O",
        "outputId": "4b1d0422-7ad5-4572-ca91-9ad10b75c0f8"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "x = np.arange(1, len(brown_lemmas_frequencies) + 1)\n",
        "y = np.array(sorted(brown_lemmas_frequencies.values(), reverse = True))\n",
        "\n",
        "plt.plot(x, y)\n",
        "\n",
        "plt.yscale('log') \n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E0s1WHhwn99O"
      },
      "source": [
        "> A Suitable frequency threshold for our contexts could be **10** (mainly due to the small corpus size)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "aqDrx0Stn99O",
        "outputId": "9f0c2925-b837-4289-a70e-716a2a567284"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            ">> 7576 context lemmas\n",
            "[('not-ADV', 4423), ('say-VERB', 2725), ('make-VERB', 2279), ('time-NOUN', 1815), ('go-VERB', 1778), ('when-ADV', 1746), ('can-VERB', 1741), ('other-ADJ', 1627), ('year-NOUN', 1589), ('take-VERB', 1521), ('come-VERB', 1501), ('know-VERB', 1462), ('get-VERB', 1427), ('so-ADV', 1336), ('may-VERB', 1290), ('only-ADV', 1281), ('give-VERB', 1238), ('more-ADV', 1188), ('man-NOUN', 1148), ('see-VERB', 1111)]\n"
          ]
        }
      ],
      "source": [
        "filtered_brown_lemmas_frequencies = Counter()\n",
        "selected_brown_noun_frequencies = Counter()\n",
        "\n",
        "for k,v in brown_lemmas_frequencies.items():\n",
        "    pos = k.split(\"-\")[-1]\n",
        "    if v >= 10 and \\\n",
        "    pos in [\"NOUN\", \"VERB\", \"ADJ\", \"ADV\"]\\\n",
        "    and k.split(\"-\")[0] not in [\"be\", \"have\", \"do\", \"would\", \"will\", \"could\"]:\n",
        "        filtered_brown_lemmas_frequencies[k] = v\n",
        "        if pos == \"NOUN\":\n",
        "            selected_brown_noun_frequencies[k] = v\n",
        "\n",
        "print(\">>\", len(filtered_brown_lemmas_frequencies), \"context lemmas\")\n",
        "print(filtered_brown_lemmas_frequencies.most_common(20))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wbOyxxD1n99P",
        "outputId": "6c4ecf9d-545a-4ab5-cf3e-e5baf0f624d7"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "4427 target nouns\n"
          ]
        }
      ],
      "source": [
        "print(len(selected_brown_noun_frequencies), \"target nouns\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "HNThm9gOn99P",
        "outputId": "64aaaf58-a0fa-43e9-cdbb-66dbea58c41f"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[(('Af-NOUN', 'Af-NOUN'), 460), (('States-NOUN', 'United-VERB'), 396), (('York-NOUN', 'New-ADJ'), 303), (('year-NOUN', 'ago-ADV'), 150), (('Mrs.-NOUN', 'Mrs.-NOUN'), 120), (('year-NOUN', 'last-ADJ'), 114), (('time-NOUN', 'same-ADJ'), 96), (('Rhode-NOUN', 'Island-NOUN'), 91), (('Island-NOUN', 'Rhode-NOUN'), 91), (('time-NOUN', 'time-NOUN'), 88), (('place-NOUN', 'take-VERB'), 87), (('year-NOUN', 'fiscal-ADJ'), 81), (('school-NOUN', 'high-ADJ'), 77), (('time-NOUN', 'first-ADJ'), 74), (('Mr.-NOUN', 'say-VERB'), 68), (('hand-NOUN', 'other-ADJ'), 66), (('House-NOUN', 'White-ADJ'), 65), (('man-NOUN', 'not-ADV'), 64), (('night-NOUN', 'last-ADJ'), 63), (('World-NOUN', 'War-NOUN'), 62)]\n"
          ]
        }
      ],
      "source": [
        "filtered_cooccs_surface = Counter()\n",
        "\n",
        "for k,v in cooccs_surface.items():\n",
        "    if k[0] in selected_brown_noun_frequencies and k[1] in filtered_brown_lemmas_frequencies:\n",
        "        filtered_cooccs_surface[k] = v\n",
        "\n",
        "print(filtered_cooccs_surface.most_common(20))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dh0gOyjWn99Q"
      },
      "source": [
        "### Weighting the Counts\n",
        "\n",
        "- Association measures are used to **give more weight to surprising events** and less weight to expected events.\n",
        "\n",
        "\n",
        "- Many measures of this sort are available in NLTK (and the other above quoted toolkits as well).\n",
        "\n",
        "\n",
        "- Let's use the measures we've discussed in class to weight our counts."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "N_TcwhDSn99Q",
        "outputId": "37a813f0-724a-41d6-a095-55f0b337b2a3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "['chi_sq', 'dice', 'fisher', 'jaccard', 'likelihood_ratio', 'mi_like', 'phi_sq', 'pmi', 'poisson_stirling', 'raw_freq', 'student_t']\n"
          ]
        }
      ],
      "source": [
        "print([asm for asm in dir(nltk.collocations.BigramAssocMeasures) if not asm.startswith(\"_\")])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "sSRAU7m2n99Q"
      },
      "outputs": [],
      "source": [
        "from math import log\n",
        "\n",
        "# All functions receive as arguments:\n",
        "#\n",
        "#   o_11>> the joint frequency of w1 and w2 >> f(w1, w2)\n",
        "#   r_1 >> w1 marginals >> f(w1, *)\n",
        "#   c_1 >> w2 marginals >> f(*, w2)\n",
        "#   n >> total number of possible coccorrencies >> f(*, *)\n",
        "\n",
        "# These arguments can be arranged in a contingency table of the form:\n",
        "#\n",
        "#          w2    ~w2\n",
        "#        ------ ------\n",
        "#    w1 | o_11 | o_12 | = r_1\n",
        "#        ------ ------\n",
        "#   ~w1 | o_21 | o_22 | = r_2\n",
        "#        ------ ------\n",
        "#        = c_1  = c_2   = n\n",
        "\n",
        "\n",
        "def ppmi(o_11, r_1, c_1, n):\n",
        "    \"\"\"\n",
        "    Positive Pointwise Mutual Information (Church & Hanks, 1990)\n",
        "    \n",
        "    PMI is also available in NLTK:\n",
        "    from nltk.metrics import BigramAssocMeasures\n",
        "    print BigramAssocMeasures.pmi(8, (15828, 4675), 14307668)\n",
        "    \"\"\"\n",
        "    observed = o_11\n",
        "    expected = (r_1*c_1)/n \n",
        "    res = log(observed/expected,2)\n",
        "    return max(0, res)\n",
        "\n",
        "\n",
        "def plmi(o_11, r_1, c_1, n):\n",
        "    \"\"\"\n",
        "    Positive Local Mutual Information, useful for leveraging the \n",
        "    low-frequency bias of the PPMI\n",
        "    \"\"\"\n",
        "    res = o_11 * ppmi(o_11, r_1, c_1, n)\n",
        "    return res\n",
        "\n",
        "\n",
        "def log_likelihood(o_11, r_1, c_1, n):\n",
        "    \"\"\"\n",
        "    Log Likelihood measure (Dunning, 1993) or \"G-squared\" measure \n",
        "\n",
        "    NOTE that when o_ii is zero log_2(o_ii) is negative infinity and Python\n",
        "    raises a ValueError. However, we're summing up o_ii * log_2(o_ii/e_ii)\n",
        "    and the limit of this factor goes to zero, so that we can simply\n",
        "    ignore those cells where o_ii is zero\n",
        "    \"\"\"\n",
        "    obs_table = [o_11, r_1 - o_11, c_1 - o_11, n - (c_1 + r_1 - o_11)]  # o_11, o_12, o_21, o_22\n",
        "    exp_table = [(r_1 * c_1)/ n,\n",
        "                 (r_1 * (n - c_1))/ n,\n",
        "                 ((n - r_1) * c_1)/ n,\n",
        "                 ((n - r_1) * (n - c_1))/ n]  # e_11, e_12, e_21, e_22\n",
        "    res = 0\n",
        "    for i, obs in enumerate(obs_table):\n",
        "        try:\n",
        "            res += obs * log(obs / exp_table[i])\n",
        "        except ValueError:\n",
        "            continue\n",
        "    res = 2 * res\n",
        "    return res"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tAI3nqUZn99R",
        "outputId": "4c68c34a-3b64-4213-b1d1-de063117a2ff"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[(('Hong-NOUN', 'Kong-NOUN'), 17.654091187664235), (('Kong-NOUN', 'Hong-NOUN'), 17.654091187664235), (('Income-NOUN', 'Gross-ADJ'), 17.654091187664235), (('cellulose-NOUN', 'cellulose-NOUN'), 17.46966661652681), (('Income-NOUN', 'Adjusted-VERB'), 17.376557212135328), (('Viet-NOUN', 'Nam-NOUN'), 17.113522806301532), (('Nam-NOUN', 'Viet-NOUN'), 17.113522806301532), (('Pathet-NOUN', 'Lao-NOUN'), 17.026059965051196), (('Lao-NOUN', 'Pathet-NOUN'), 17.026059965051196), (('Simms-NOUN', 'Purdew-NOUN'), 17.026059965051196)]\n"
          ]
        }
      ],
      "source": [
        "ppmis_surface = Counter()\n",
        "\n",
        "N = sum(cooccs_surface.values())  # note that this is NOT the reduced dictionary\n",
        "\n",
        "for k,v in filtered_cooccs_surface.items():\n",
        "    ppmis_surface[k] = ppmi(v, brown_lemmas_frequencies[k[0]], brown_lemmas_frequencies[k[1]], N)\n",
        "    \n",
        "print(ppmis_surface.most_common(10))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ht1XQwEKn99R",
        "outputId": "1fd5b951-5e33-4664-a3bd-c27779415adf"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[(('States-NOUN', 'United-VERB'), 4787.77840883779), (('Af-NOUN', 'Af-NOUN'), 4620.612036095815), (('York-NOUN', 'New-ADJ'), 3621.1147930991538), (('year-NOUN', 'ago-ADV'), 1464.8885373164483), (('Rhode-NOUN', 'Island-NOUN'), 1258.5533261922783), (('Island-NOUN', 'Rhode-NOUN'), 1258.5533261922783), (('Mrs.-NOUN', 'Mrs.-NOUN'), 1187.8825846241932), (('year-NOUN', 'last-ADJ'), 928.5404042426062), (('House-NOUN', 'White-ADJ'), 851.4369612227013), (('World-NOUN', 'War-NOUN'), 810.2368093216919)]\n"
          ]
        }
      ],
      "source": [
        "plmis_surface = Counter()\n",
        "\n",
        "N = sum(cooccs_surface.values())  # note that this is NOT the reduced dictionary\n",
        "\n",
        "for k,v in filtered_cooccs_surface.items():\n",
        "    plmis_surface[k] = plmi(v, brown_lemmas_frequencies[k[0]], brown_lemmas_frequencies[k[1]], N)\n",
        "    \n",
        "print(plmis_surface.most_common(10))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "o04IRpGDn99S",
        "outputId": "3561ace1-eccf-41e9-b88a-9fd7ace5fbaa"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "[(('States-NOUN', 'United-VERB'), 6953.964479037217), (('Af-NOUN', 'Af-NOUN'), 5998.501456806236), (('York-NOUN', 'New-ADJ'), 5218.669840636507), (('year-NOUN', 'ago-ADV'), 1864.8375330848553), (('Rhode-NOUN', 'Island-NOUN'), 1771.6494950804188), (('Island-NOUN', 'Rhode-NOUN'), 1771.6494950804188), (('Mrs.-NOUN', 'Mrs.-NOUN'), 1465.3982476383976), (('House-NOUN', 'White-ADJ'), 1143.7883279065052), (('S.-NOUN', 'U.-NOUN'), 1133.8897390180484), (('U.-NOUN', 'S.-NOUN'), 1133.8897390180482)]\n"
          ]
        }
      ],
      "source": [
        "lls_surface = Counter()\n",
        "\n",
        "N = sum(cooccs_surface.values())  # note that this is NOT the reduced dictionary\n",
        "\n",
        "for k,v in filtered_cooccs_surface.items():\n",
        "    lls_surface[k] = log_likelihood(v, brown_lemmas_frequencies[k[0]], brown_lemmas_frequencies[k[1]], N)\n",
        "    \n",
        "print(lls_surface.most_common(10))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ae39Hnyen99S"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-xO7FZtIn99S"
      },
      "source": [
        "### Exercise\n",
        "\n",
        "Choose three (frequent) nouns and print their top-associates according to each one of the above implemented association measures."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MhC33Ehzn99S"
      },
      "outputs": [],
      "source": [
        "# your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_D8IL_4mn99S"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "T6lu4PYnn99S"
      },
      "outputs": [],
      "source": [
        "import math \n",
        "\n",
        "from itertools import chain, permutations, product\n",
        "from collections import Counter\n",
        "\n",
        "import nltk\n",
        "import numpy as np\n",
        "import scipy\n",
        "import sklearn\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from scipy import cluster\n",
        "from sklearn import manifold, metrics\n",
        "from nltk.corpus import wordnet as wn\n",
        "\n",
        "plt.rcdefaults()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lDBU4Lftn99T"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ynZlA5mIn99T"
      },
      "source": [
        "## Sparse Vectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "qsX0GitWn99T"
      },
      "source": [
        "![alt text](https://github.com/bloemj/AUC_TMCI_2022/blob/main/notebooks/images/3dvectors.png?raw=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "alZDCOgqn99T"
      },
      "source": [
        "Let's create our vectors by populating a matrix for each of our types of weighted co-occurrences:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KilrDQ-hn99T"
      },
      "outputs": [],
      "source": [
        "# lemma to row/column index mappings\n",
        "sorted_vectors = sorted(selected_brown_noun_frequencies)\n",
        "vectors_indices = dict((v,i) for i,v in enumerate(sorted_vectors))\n",
        "contexts_indices = dict((v,i) for i,v in enumerate(sorted(filtered_brown_lemmas_frequencies)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Cn8UyJ-1n99T"
      },
      "outputs": [],
      "source": [
        "# initialize the PPMI-Weighted matrix\n",
        "ppmiMat = np.zeros((len(vectors_indices), len(contexts_indices)))\n",
        "\n",
        "# populate the matrix\n",
        "for pair, weight in ppmis_surface.items():\n",
        "    ppmiMat[vectors_indices[pair[0]]][contexts_indices[pair[1]]] = weight"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kGe2MJLxn99U"
      },
      "outputs": [],
      "source": [
        "# initialize the PLMI-Weighted matrix\n",
        "plmiMat = np.zeros((len(vectors_indices), len(contexts_indices)))\n",
        "\n",
        "# populate the matrix\n",
        "for pair, weight in plmis_surface.items():\n",
        "    plmiMat[vectors_indices[pair[0]]][contexts_indices[pair[1]]] = weight"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZSN-dVV6n99U"
      },
      "outputs": [],
      "source": [
        "# initialize the LL-Weighted matrix\n",
        "llMat = np.zeros((len(vectors_indices), len(contexts_indices)))\n",
        "\n",
        "# populate the matrix\n",
        "for pair, weight in lls_surface.items():\n",
        "    llMat[vectors_indices[pair[0]]][contexts_indices[pair[1]]] = weight"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "47n8JXaLn99U"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f_Cve6ven99U"
      },
      "source": [
        "## Calculating Cosine Similarities"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "nfgDuJyFn99U"
      },
      "source": [
        "![alt text](https://github.com/bloemj/AUC_TMCI_2022/blob/main/notebooks/images/vectors-similarity.png?raw=1)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "2NuB71xAn99U"
      },
      "source": [
        "The diverse similarity measures we've mentioned in class can be calculated by using the **distance** measures available in virtually all the above cited toolkits, or can be easily implemented. \n",
        "\n",
        "For instance, the **cosine similarity** between the two Numpy arrays `v_1` and `v_2` can be calculated by using one of the following functions:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hFqld_NJn99V"
      },
      "outputs": [],
      "source": [
        "v_1 = np.array([-0.012813841, -0.024518383, -0.002765056,  0.079496744,  0.063928973, 0.476156960, 0.122111977, 0.322930189, \n",
        "                0.400701256,  0.454048860, 0.525526219])\n",
        "\n",
        "v_2 = np.array([0.64175768,  0.54625694,  0.40728261,  0.24819750,  0.09406221, 0.16681692, -0.04211932, -0.07130129, \n",
        "                -0.08182200, -0.08266852,  -0.07215885])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ab36o3uhn99V"
      },
      "outputs": [],
      "source": [
        "def scipy_cosine(v1, v2):\n",
        "    return 1 - scipy.spatial.distance.cosine(v1,v2)\n",
        "\n",
        "def nltk_cosine(v1, v2):\n",
        "    return 1 - nltk.cluster.cosine_distance(v1,v2)\n",
        "\n",
        "def numpy_cosine(v1, v2):\n",
        "    mag_v1 = np.linalg.norm(v1)\n",
        "    mag_v2 = np.linalg.norm(v2)\n",
        "    return np.dot(v1, v2) / ( mag_v1 * mag_v2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "VD9_AX-On99V",
        "outputId": "437771b6-0b84-47c8-e610-d95b137cc889"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "31.7 µs ± 1.05 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit scipy_cosine(v_1, v_2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XS2ZUTldn99V",
        "outputId": "a3de3c9d-4fa8-4d71-8fa0-0ece457a7e5e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "4.05 µs ± 52.7 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit nltk_cosine(v_1, v_2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oyB6Rs0en99V",
        "outputId": "53147764-b44d-42db-ccbc-7bff7b6e7744"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "9.66 µs ± 91.5 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit numpy_cosine(v_1, v_2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tPT12KUen99W"
      },
      "source": [
        "If (for some reason) you're working on lists, maybe the best solution is to rely on the `math` library."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KWwl0w7Xn99W"
      },
      "outputs": [],
      "source": [
        "def math_cosine(l1, l2):\n",
        "    d = sum(p*q for p,q in zip(l1, l2))\n",
        "    mag_l1 = math.sqrt(sum([n**2 for n in l1]))\n",
        "    mag_l2 = math.sqrt(sum([n**2 for n in l2]))\n",
        "    return d/( mag_l1 * mag_l2)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hM0lWkHxn99W",
        "outputId": "10bf3e14-7bc7-4b7a-f907-8a8efedd93cf"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "5.25 µs ± 466 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)\n"
          ]
        }
      ],
      "source": [
        "%timeit math_cosine(v_1.tolist(), v_2.tolist())"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k1P6-7-Dn99W"
      },
      "source": [
        "However, the calculation of the similarity is (together with the extraction of the co-occurrences) the **main bottleneck** of these models, and the above mentioned solutions become **impractical** when comparing all the vectors in a reasonably sized model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ynXuYDfn99X"
      },
      "source": [
        "If you want to calculate the similarity on the **whole matrix** at once, a viable solution is to use the methods available in the `sklearn.metrics.pairwise` module, among which the `cosine_similarity` one"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "peCUwd0fn99X"
      },
      "outputs": [],
      "source": [
        "ppmiSimMat = sklearn.metrics.pairwise.cosine_similarity(ppmiMat)\n",
        "plmiSimMat = sklearn.metrics.pairwise.cosine_similarity(plmiMat)\n",
        "llSimMat = sklearn.metrics.pairwise.cosine_similarity(llMat)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_h8Sm4Ojn99X"
      },
      "source": [
        "### Let's print the k most similar nouns to \"year\" according to each of our spaces"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nq4HwNd4n99X"
      },
      "outputs": [],
      "source": [
        "k = 10\n",
        "target_idx = vectors_indices[\"year-NOUN\"]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qb9jOTern99X",
        "outputId": "c7066bd5-6aec-4f2a-a490-ff64a305c8e9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "according to the ppmi space:\n",
            "\n",
            "time-NOUN 0.36400868601184766\n",
            "school-NOUN 0.33877559884002595\n",
            "day-NOUN 0.3357394963192104\n",
            "state-NOUN 0.33443475981094495\n",
            "work-NOUN 0.31279579879462693\n",
            "men-NOUN 0.30523953193695125\n",
            "program-NOUN 0.3008332006165108\n",
            "month-NOUN 0.3000585304373374\n",
            "man-NOUN 0.29794708066681236\n",
            "people-NOUN 0.2963328655205712\n"
          ]
        }
      ],
      "source": [
        "print(\"according to the ppmi space:\\n\")\n",
        "\n",
        "for idx in ppmiSimMat[target_idx,].argsort()[::-1][1:k+1]:\n",
        "    print(sorted_vectors[idx], ppmiSimMat[target_idx, idx])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bUvk8ugLn99Y",
        "outputId": "b5225a84-b71b-45e6-d43b-9bdc7af7a72c"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "according to the plmi space:\n",
            "\n",
            "week-NOUN 0.6529282841812108\n",
            "month-NOUN 0.5773419825212871\n",
            "night-NOUN 0.43125780037970113\n",
            "day-NOUN 0.4216641387637767\n",
            "decade-NOUN 0.39203911951936243\n",
            "minute-NOUN 0.34951487475646675\n",
            "hour-NOUN 0.3365417850787026\n",
            "September-NOUN 0.3316338570011183\n",
            "year's-NOUN 0.30906166822988546\n",
            "time-NOUN 0.3002857451353878\n"
          ]
        }
      ],
      "source": [
        "print(\"according to the plmi space:\\n\")\n",
        "\n",
        "for idx in plmiSimMat[target_idx,].argsort()[::-1][1:k+1]:\n",
        "    print(sorted_vectors[idx], plmiSimMat[target_idx, idx])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Vdl3vyVHn99Y",
        "outputId": "553edd9d-ac13-47b9-8cfe-b903492c3c45"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "according to the log-likelihood space:\n",
            "\n",
            "week-NOUN 0.6363850145687364\n",
            "month-NOUN 0.5455905693069585\n",
            "night-NOUN 0.4053597393163634\n",
            "day-NOUN 0.372638065173422\n",
            "decade-NOUN 0.36140585500541617\n",
            "minute-NOUN 0.321193715703064\n",
            "September-NOUN 0.3163356538833567\n",
            "hour-NOUN 0.2957833992834735\n",
            "year's-NOUN 0.2927927910986083\n",
            "June-NOUN 0.27940793908501504\n"
          ]
        }
      ],
      "source": [
        "print(\"according to the log-likelihood space:\\n\")\n",
        "\n",
        "for idx in llSimMat[target_idx,].argsort()[::-1][1:k+1]:\n",
        "    print(sorted_vectors[idx], llSimMat[target_idx, idx])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PZebrDECn99Y"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v-_XnmTNn99Y"
      },
      "source": [
        "## Visualizing Similarities"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CqKDo8nEn99Y"
      },
      "source": [
        "Sometimes it is convenient to look at the distances between your word in order to have an idea of what's going on with your data. Unfortunately, human being do not cope well with more than 3 dimensions (the novel [Flatland: A Romance of Many Dimensions](https://en.wikipedia.org/wiki/Flatland) may be an insightful reading on this topic). "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iAdPoijcn99Y"
      },
      "source": [
        "### Dimensionality Reduction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tS0qW_Xkn99Z"
      },
      "source": [
        "A usual solution is to reduce the dimensionality of your dataset to **2 or 3 dimensions** trying to preserve the pairwise distances as much as possible. Among the several **non-linear dimensionality reduction techniques** to date available (a quick review is available in the [scikit-learn documentation](http://scikit-learn.org/stable/modules/manifold.html)), **multidimensional scaling** is used to display the information contained in a distance matrix. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BetU5Ulvn99Z"
      },
      "source": [
        "Let's try to use MDS to plot the distance between an (arbitrarily chosen) subset of our nouns:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "CL__OqOln99Z"
      },
      "outputs": [],
      "source": [
        "lemmas2plot = selected_brown_noun_frequencies.most_common()[100:125]\n",
        "lemmas2plot_idxs = [vectors_indices[lem[0]] for lem in lemmas2plot]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MOTRS8uOn99Z",
        "outputId": "c09ad1d7-d956-42e9-894a-ddd9be1d1a30"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "measure2mat = {\"ppmi\": ppmiMat, \"plmi\": plmiMat, \"loglikelihood\": llMat}\n",
        "\n",
        "labels = [p[0].split(\"-\")[0] for p in lemmas2plot]\n",
        "\n",
        "for i, (m, mat) in enumerate(measure2mat.items()):\n",
        "    # we need a DISTANCE matrix\n",
        "    distMat = sklearn.metrics.pairwise.pairwise_distances(mat[lemmas2plot_idxs,:], metric=\"cosine\")\n",
        "    \n",
        "    # let's reduce the dimensionality\n",
        "    mds = sklearn.manifold.MDS(n_components = 2, max_iter = 300, eps = 1e-9, \n",
        "                               random_state = np.random.RandomState(seed = 6), \n",
        "                               dissimilarity = \"precomputed\")\n",
        "\n",
        "    coords = mds.fit(distMat).embedding_\n",
        "    \n",
        "    # let's plot the distances\n",
        "    plt.scatter(coords[:, 0], coords[:, 1], marker = '.', c = 'r')\n",
        "    \n",
        "    \n",
        "    \n",
        "    for label, x, y in zip(labels, coords[:, 0], coords[:, 1]):\n",
        "        plt.annotate(label, xy = (x,y), horizontalalignment = 'center', verticalalignment='bottom')\n",
        "\n",
        "    plt.title(\"MDS on the \" + m +\"-based space\")\n",
        "\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2hPhFr-n99Z"
      },
      "source": [
        "#### Exercise\n",
        "\n",
        "Try other dimensionality reduction techniques, e.g., PCA."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nK9hJV75n99Z"
      },
      "outputs": [],
      "source": [
        "# Your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HRtQpkmMn99a"
      },
      "source": [
        "### Clustering"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D5P-PFj6n99a"
      },
      "source": [
        "Another viable option is to perform use the pairwise similarities in order to organize our words into groups (i.e. to perform **clustering**). The general idea is to organize clusters so as to maximize the **within-group similiarities** and the **between-group differences**. There are many clustering algorithms and techniques, all of them with their pros and cons. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OzoHEhzDn99a"
      },
      "source": [
        "**Hierachical clustering** techniques do not try to produce a single clustering, but try to produce a hierarchy of groups. As such, they are quite useful in exploratory analysis. In this class, the **Ward** algorithm is an example of **agglomerative** clustering:  each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. In the Ward's method, the distance between two clusters is the change in the sum of squared distances when they are merged."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8rIv9wGKn99a"
      },
      "source": [
        "We can use the `scipy.cluster.hierarchy.ward()` function to create our hierarchical clustering and the  `scipy.cluster.hierarchy.dendrogram()` function to visualize it (i.e. to create a dendrogram)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fcocFu2Vn99a",
        "outputId": "6ff12af1-2944-4936-9d9a-0ed7de0deefa"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "measure2mat = {\"ppmi\": ppmiMat, \"plmi\": plmiMat, \"loglikelihood\": llMat}\n",
        "\n",
        "labels = [p[0].split(\"-\")[0] for p in lemmas2plot]\n",
        "\n",
        "for i, (m, mat) in enumerate(measure2mat.items()):\n",
        "    \n",
        "    # let's built a DISTANCE matrix\n",
        "    distMat = sklearn.metrics.pairwise.pairwise_distances(mat[lemmas2plot_idxs,:], metric=\"cosine\")\n",
        "    \n",
        "    # as we'll rely the scikit learn function to perform clustering, it is safer to convert our redundant distance matrix \n",
        "    # into a condensed distance matrix (i.e. into a flat array containing the upper triangular of the distance matrix)\n",
        "    condensed_distMat = scipy.spatial.distance.squareform(distMat)\n",
        "    \n",
        "    # we could alternatively have used scipy.spatial.distance.pdist() to obtain the distance matric in this format\n",
        "    # scipyPdist = scipy.spatial.distance.pdist(mat[lemmas2plot_idxs,:], \"cosine\")\n",
        "    \n",
        "    # let's perform the hierarchical clustering\n",
        "    linkage_matrix = scipy.cluster.hierarchy.ward(condensed_distMat)\n",
        "    \n",
        "    # let's create the dendrogram (i.e. let's visualize the structure of the groups)\n",
        "    scipy.cluster.hierarchy.dendrogram(linkage_matrix, orientation=\"right\", labels=labels)\n",
        "    \n",
        "    plt.xlabel (\"distance (not cosines, but those used by the Ward's method)\")\n",
        "\n",
        "    plt.title(\"MDS on the \" + m +\"-based space\")\n",
        "    \n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Pzc85zQn99a"
      },
      "source": [
        "## Evaluating your Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B9Uw6BQGn99b"
      },
      "source": [
        "VSMs can be evaluated on **semantic similarity tasks**, in which they are required to simulate the pairwise similarity judgments collected from speakers."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xWxf5KGFn99b"
      },
      "source": [
        "In what follows we evaluate our models against the [WordSim-353 dataset](http://www.cs.technion.ac.il/~gabr/resources/data/wordsim353/):\n",
        "\n",
        "\n",
        "- 353 noun pairs rated on a 0-10 scale \n",
        "\n",
        "\n",
        "- measure: [Spearman's correlation](https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient) between algorithm and human word similarity ratings"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FbPSstUdn99b"
      },
      "outputs": [],
      "source": [
        "# let's select the pairs of nouns for which we have enough distributional information\n",
        "\n",
        "wordSim353 = dict()\n",
        "\n",
        "with open(\"data/wordSim353.csv\",\"r\") as infile:\n",
        "    for line in infile:\n",
        "        raw_w1, raw_w2, rating = line.strip().split(\",\")\n",
        "        w1 = raw_w1+\"-NOUN\"\n",
        "        w2 = raw_w2+\"-NOUN\"\n",
        "        if all([w in vectors_indices for w in [w1,w2]]):\n",
        "            wordSim353[(w1, w2)] = float(rating)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Vuem_1jJn99b"
      },
      "source": [
        "- Note that due to the size of our corpus we've lost 1/3 of the dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "h3Bug8vEn99b",
        "outputId": "b4ad7b1d-0482-462c-9a24-3cded3cb00f6"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "219\n"
          ]
        }
      ],
      "source": [
        "print(len(wordSim353))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "11G0Vje8n99c",
        "outputId": "c7b2ca3d-464e-4c60-a7d7-d9179e93c314"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "positivePMI-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.2173225657554284\n",
            "positiveLMI-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.24707088416441894\n",
            "log-likelihood-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.2617730910733136\n"
          ]
        }
      ],
      "source": [
        "measure2mat = {\"positivePMI\": ppmiSimMat, \"positiveLMI\": plmiSimMat, \"log-likelihood\": llSimMat}\n",
        "\n",
        "rhos = []\n",
        "measures = []\n",
        "\n",
        "for m, mat in measure2mat.items():\n",
        "    print(m+\"-based space vs. wordSim353 -> spearman's rho:\\t\", )\n",
        "    \n",
        "    wordSim_ratings = []\n",
        "    vsm_sims = []\n",
        "    for (w1, w2), r in wordSim353.items():\n",
        "        w1idx = vectors_indices[w1]\n",
        "        w2idx = vectors_indices[w2]\n",
        "        \n",
        "        wordSim_ratings.append(r)\n",
        "        vsm_sims.append(mat[w1idx, w2idx])\n",
        "        \n",
        "    rho, pval = scipy.stats.spearmanr(wordSim_ratings, vsm_sims)\n",
        "    \n",
        "    print(rho)\n",
        "    rhos.append(rho)\n",
        "    measures.append(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "kinsStpqn99c",
        "outputId": "39282f7f-2338-4d98-effb-1cb73ce860db"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.bar(range(0, len(rhos)), rhos)\n",
        "plt.xticks(range(0, len(rhos)), measures, size='small')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v8LCV0NNn99c"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Nxbu2PJn99c"
      },
      "source": [
        "## Working with Dense Vectors"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "XsqDPM34n99d"
      },
      "source": [
        "Up to this moment, we've worked with **long** and **sparse** vectors:\n",
        "\n",
        "\n",
        "- the proportion of non-zeros in our ppmi weighted matrix is:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "7014m7wLn99d",
        "outputId": "76ab7e31-0e6d-4e61-db5f-5e66eaf38eaf"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.016530421105584933"
            ]
          },
          "execution_count": 68,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "np.count_nonzero(ppmiMat) / ppmiMat.size"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "epgbrR2Fn99d"
      },
      "source": [
        "- the length of our vectors:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "zT1zs1oen99d",
        "outputId": "38b1267b-9661-45db-8e0c-36e2e9b95537"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "7576"
            ]
          },
          "execution_count": 69,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "ppmiMat.shape[1]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0jfiilO-n99d"
      },
      "source": [
        "**Denser** representations have a number of **advantages**, among which:\n",
        "\n",
        "- their computationally easier to manipulate (e.g. to create  or to use as ML features)\n",
        "\n",
        "\n",
        "- they tend to be less noisy\n",
        "\n",
        "\n",
        "- they exploit latent meaning dimensions (e.g. they may tend to merge together correlated contexts like *car* and *automobile*)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "11NXyurnn99d"
      },
      "source": [
        "> **Dimensionality Reduction**: the process of reducing the number of features (i.e. contextual markers) by mapping data points (i.e. the vectors describing the target words) into a **low-dimensional subspace**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5xoxFdqQn99e"
      },
      "source": [
        "### Dimensionality Reduction via Singular Value Decomposition"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KtG4zYI6n99e"
      },
      "source": [
        "SVD is a method for finding, for a given dataset, the **dimensions on which the data varies the most** (J&M)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OiPjGqabn99e"
      },
      "source": [
        "**Intuitive Idea**: rotate the axes of the dataset into a new space, so that the order of the dimension is related to the quantity of captured variance\n",
        "\n",
        "- first dimension capture the most variance, then the second captures most of the variance unexplained by the first dimension and so on...\n",
        "\n",
        "\n",
        "- many related methods: PCA, Factor Analysis, **SVD**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ro5LfJMan99e"
      },
      "source": [
        "#### Matrix Factorization\n",
        "\n",
        "SVD **factorizes** a (non-symmetric, non-square) $w \\times c$ matrix $M$ into the **product of three matrices**: $U \\cdot\\Sigma \\cdot V^T$, where:\n",
        "\n",
        "\n",
        "- $U$: the rows correspond to the rows of M (i.e. our target words) and the columns represent the dimensions of the **latent space**:\n",
        "    - dimensions are orthogonal\n",
        "    - dimensions are sorted according to the amount of variance they explain\n",
        "    - e.g. the word frequency distribution for any latent topic\n",
        "    \n",
        "    \n",
        "- $\\Sigma$: a diagonal $m \\times m$ matrix (where $m$ is the rank of our matrix $M$) of singular values in decreasing order:\n",
        "    - intuitively, the **square** of each singular value $\\sigma$ express the importance of each dimension\n",
        "    - e.g. the prior frequency of each latent topic\n",
        "\n",
        "    \n",
        "- $V^T$: the columns correspond the columns of M and the rows correspond to the singular values:\n",
        "    - e.g. the contribution of each latent topic to each context"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f95EKdnMn99e"
      },
      "source": [
        "$$\\mathop{\\begin{bmatrix}\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & M & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        "\\end{bmatrix}}_{\\textstyle w \\times c} \\ = \\\n",
        "\\mathop{\\begin{bmatrix}\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        " & & U & & \\\\\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        " & & & & \\\\\n",
        "\\end{bmatrix}}_{\\textstyle w \\times m}\\ \n",
        "\\mathop{\\begin{bmatrix}\n",
        "\\sigma_1 & 0 & 0 & \\cdots & 0 \\\\\n",
        "0 & \\sigma_2 & 0 & \\cdots & 0 \\\\\n",
        "0 & 0 & \\sigma_3 & \\cdots & 0 \\\\\n",
        "\\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
        "0 & 0 & 0 & \\cdots & \\sigma_m \\\\\n",
        "\\end{bmatrix}}_{\\textstyle m \\times m}\\ \n",
        "\\mathop{\\begin{bmatrix}\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & V^T & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        "\\end{bmatrix}}_{\\textstyle m \\times c}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Uj5OeeTtn99f"
      },
      "source": [
        "#### Truncation\n",
        "\n",
        "If we use the **first $d$ singular values**, we obtain a **truncated matrix** $\\tilde{M}_d$ that is **a least-squares approximation** to the original $M$\n",
        "\n",
        "\n",
        "- dimensions $d < x < m$ are descarded\n",
        "    - by removing the dimensions that encode the least variance, we **remove noise**\n",
        "\n",
        "\n",
        "- generally $50 < d < 1000$ (with a soft spot around 300)\n",
        "\n",
        "\n",
        "- some authors (Lapesa & Evert, 2014) suggest that for some task it may be useful to get rid of the very first dimensions as well"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7-CkFobBn99f"
      },
      "source": [
        "$$\\mathop{\\begin{bmatrix}\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & \\tilde{M}_d & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        " & & & & & &\\\\\n",
        "\\end{bmatrix}}_{\\textstyle w \\times c} \\ = \\\n",
        "\\mathop{\\begin{bmatrix}\n",
        " & & \\\\\n",
        " & & \\\\\n",
        " & & \\\\\n",
        " & & \\\\\n",
        " & U_d &\\\\\n",
        " & & \\\\\n",
        " & & \\\\\n",
        " & & \\\\\n",
        " & & \\\\\n",
        "\\end{bmatrix}}_{\\textstyle w \\times d}\\ \n",
        "\\mathop{\\begin{bmatrix}\n",
        " & &\\\\\n",
        " & \\Sigma_d & \\\\\n",
        " & & \\\\\n",
        "\\end{bmatrix}}_{\\textstyle d \\times d}\\\n",
        "\\mathop{\\begin{bmatrix}\n",
        " & & & & & &\\\\\n",
        " & & & V^T_d & & &\\\\\n",
        " & & & & & &\\\\\n",
        "\\end{bmatrix}}_{\\textstyle d \\times c}$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j4cIn1eKn99f"
      },
      "source": [
        "#### Embedding\n",
        "\n",
        "We can take advantage of the fact that **dot-products between** the rows of $W = U_d \\cdot \\Sigma_d$ are equal to those of the rows of $\\tilde{M}_d = U_d \\cdot \\Sigma_d\\cdot V^T_d$, so that we can **ignore $V^T_d$** and take the rows of $W$ as our word representations.\n",
        "\n",
        "Recently, it has been showed that an additional parameter $p$ should be added to control the eigenvalue matrix $\\Sigma$, so that we will take as **word representations** the rows of the $W'$ matrix, defined as:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SkbugnTCn99g"
      },
      "source": [
        "$$W' = U_d \\cdot \\Sigma_d^p$$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "elwFdYF8n99g"
      },
      "source": [
        "- note that for some tasks, it has been suggested that ignoring $\\Sigma$ alltogether (i.e. setting $p = 0$) may lead to an increase in performance\n",
        "\n",
        "\n",
        "- some authors (e.g., J&M) use this setting as the default, but it is wise to spend some time tuning this hyperparameters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wQvGgyCon99g"
      },
      "source": [
        "#### With Python"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fx90KlHtn99g"
      },
      "source": [
        "METHOD 1: **using Scikit-learn**\n",
        "\n",
        "\n",
        "- you cannot set $p$ (it's always $p = 1$)\n",
        "\n",
        "\n",
        "- you cannot discard the first dimensions, if you want to"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cRY9LXL1n99g"
      },
      "outputs": [],
      "source": [
        "dimensions = 300"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Zsvj1e6Tn99g"
      },
      "outputs": [],
      "source": [
        "# note that the default SVD solver is the randomized algorithm proposed by Halko (2009), but we select the ARPACK wrapper \n",
        "# in SciPy (scipy.sparse.linalg.svds) because is more efficient (but slower)\n",
        "ppmiMat_tr300 = sklearn.decomposition.TruncatedSVD(n_components = dimensions, algorithm = \"arpack\").fit_transform(ppmiMat)\n",
        "\n",
        "ppmiSVD300SimMat = sklearn.metrics.pairwise.cosine_similarity(ppmiMat_tr300)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ygrJ1mqMn99g",
        "outputId": "04934f26-81a3-4098-f3b9-40f6c73468d5"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "ppmi_SVD300-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.3935508179426513\n"
          ]
        }
      ],
      "source": [
        "measure2mat = {\"ppmi_SVD300\": ppmiSVD300SimMat}\n",
        "\n",
        "for m, mat in measure2mat.items():\n",
        "    print(m+\"-based space vs. wordSim353 -> spearman's rho:\\t\",)\n",
        "    \n",
        "    wordSim_ratings = []\n",
        "    vsm_sims = []\n",
        "    for (w1, w2), r in wordSim353.items():\n",
        "        w1idx = vectors_indices[w1]\n",
        "        w2idx = vectors_indices[w2]\n",
        "        \n",
        "        wordSim_ratings.append(r)\n",
        "        vsm_sims.append(mat[w1idx, w2idx])\n",
        "        \n",
        "    rho, pval = scipy.stats.spearmanr(wordSim_ratings, vsm_sims)\n",
        "    \n",
        "    print(rho)\n",
        "    rhos.append(rho)\n",
        "    measures.append(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "6Z56MkxVn99h",
        "outputId": "792a94c6-ed41-46f1-8284-8cfa910d736d"
      },
      "outputs": [
        {
          "data": {
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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.bar(range(0, len(rhos)), rhos)\n",
        "plt.xticks(range(0, len(rhos)), measures, size='small')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s6jFNEhfn99h"
      },
      "source": [
        "METHOD 2: **using Scipy modules**\n",
        "\n",
        "We can (roughly) re-implement what we've done with scikit-learn as follows:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dDRyaxP7n99h"
      },
      "outputs": [],
      "source": [
        "from scipy import linalg, dot\n",
        "\n",
        "# let's decompose our matrix (we can safely ignore Vt)\n",
        "U, s, Vt = linalg.svd(ppmiMat)  \n",
        "\n",
        "# SVD suffers from a problem called \"sign indeterminancy\", so that the sign of the components (i.e. U and Vt) depends\n",
        "# on the initial state and on the algorithm. As a consequence, if U (and V) are mostly negative, \n",
        "# their sign should be inverted\n",
        "if not U[U>0].size > (U.size / 2):\n",
        "    U = -U\n",
        "    Vt = -Vt"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_kMjjbg6n99h"
      },
      "outputs": [],
      "source": [
        "# let's filter out all dimensions but the first 300\n",
        "W = U[:, 0 : dimensions]\n",
        "sigma = s[:dimensions]  # note that for efficiency reasons sigma is an array, not a matrix\n",
        "C = Vt[0 : dimensions, :]\n",
        "\n",
        "ppmiMat_tr300_alt = np.dot(W, linalg.diagsvd(sigma, dimensions, len(C)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JlSs5B2Ln99h"
      },
      "source": [
        "Re. explained variance, see the **Scree Plot**, a graph plotting variances against singular values."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O4DhQOQBn99i"
      },
      "source": [
        "We can choose how many dimensions to retain by checking the portion of variance each dimension is able to explain:\n",
        "\n",
        "- given that the square of each singular value is proportional to the variance explained by each singular vector, we compute the relative contribution of each singular value by dividing the square of the singular value $k$ by the sum of the squares of all the singular values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m-fPuYkwn99i",
        "outputId": "e473505d-167a-44d7-9946-3fe38670a8cd"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "rel_variance = ( s**2 / sum(s**2) ) * 100\n",
        "y_values =  rel_variance\n",
        "x_values = np.arange(len(y_values))\n",
        "\n",
        "plt.plot(x_values, y_values, linestyle = '-')\n",
        "\n",
        "plt.xlabel(\"Singular Values\", labelpad = 20)\n",
        "plt.ylabel(\"Relative Variance (%)\", labelpad = 10)\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pRy5u8RCn99i"
      },
      "source": [
        "Let's focus on the first singular values..."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KJyrhVgtn99i",
        "outputId": "f1f84f6a-dad0-4c3d-fc53-df0048c8758c"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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oTn+zsygeAACm8frR0o4dO9SuXbtyx9u2basdO3b4pSiXm2++WVlZWR7H7r//frVo0UKPPfaYxzo2kuRwOORwOPxaw0+xWS0qLDZUxBgZAACCzusg43A49N133yk1NdXj+JEjR2S3+zTk5qLi4uKUlpbmcSwmJkZ169Ytd9ws59eScdIjAwCACbx+tNSjRw/3IxyXkydPavLkyQGbtRTKbGwcCQCAabzuQvnDH/6gG2+8USkpKe4F8DIzM9WgQQO98cYbfi/wQmvXrg34NbzBGBkAAMzjdZBp1KiRtm/frr///e/6/PPPVaNGDd1///265557FBEREYgaQ5qNjSMBADCNT4NaYmJi9H//93/+riUs0SMDAIB5fAoyu3bt0tq1a3Xs2DE5L+iJeOqpp/xSWLhw7bfEGBkAAILP6yAzf/58PfTQQ6pXr54SExNlKbPfkGvLgsuJawdsemQAAAg+r4PMtGnTNH36dD322GOBqCfsuMfIsI4MAABB5/X06x9//FEDBgwIRC1hybUDNj0yAAAEn9dBZsCAAfrvf/8biFrCErOWAAAwj9ePlpo3b64nn3xSGzZsUKtWrcpNuR4zZozfigsH9pLBvk52vwYAIOi8DjLz5s1TbGys1q1bp3Xr1nm8Z7FYLrsgwxgZAADM43WQ2bdvXyDqCFusIwMAgHm8HiMDT+y1BACAeXxaEO/bb7/V8uXLlZ2drYKCAo/3Zs6c6ZfCwgXryAAAYB6vg8yHH36ofv36qVmzZtq5c6fS0tK0f/9+GYahdu3aBaLGkEaPDAAA5vH60dKkSZP0m9/8Rl988YWioqL0z3/+UwcPHlTXrl0vy/VlSsfIMP0aAIBg8zrIfPXVVxo6dKgkyW636+zZs4qNjdWUKVP0/PPP+73AUEePDAAA5vE6yMTExCg/P1+SlJSUpD179rjfO378uP8qCxOudWQYIwMAQPB5PUbm2muv1f/+9z+1bNlSffr00W9+8xtlZWVpyZIluvbaawNRY0izlQz2ZR0ZAACCz+sgM3PmTJ06dUqS9Mwzz+jUqVNavHixmjdvrpdeesnvBYY61pEBAMA8XgeZ1NRU99fR0dGaPXu2XwsKN4yRAQDAPCyIV0Wlu18zawkAgGCrVI9MnTp1tGvXLtWrV0+1a9eWpeSXd0V++OEHvxUXDmw2emQAADBLpYLMSy+9pLi4OEnSrFmzAllP2HGNkXESZAAACLpKBRnXujFFRUWSpF69eikxMTFwVYURxsgAAGAer8bI2O12PfTQQ+51ZMCsJQAAzOT1YN9OnTpp27ZtgaglLLnXkSHIAAAQdF5Pv3744Yf1m9/8Rt9++63at2+vmJgYj/dbt27tt+LCAT0yAACYx+sgc/fdd0uSxowZ4z5msVhkGIYsFouKi4v9V10YKB0jw/RrAACCzesgs2/fvkDUEbbokQEAwDxeB5mUlJRA1BG23OvIsNcSAABB53WQcdmxY4eys7NVUFDgcbxfv35VLiqc0CMDAIB5vA4ye/fu1R133KGsrCz32BhJ7tV+L78xMsxaAgDALF5Pvx47dqyaNWum7777TtHR0fryyy/10UcfqUOHDlq7dm0ASgxt9MgAAGAer3tkPv30U61evVr169eX1WqV1WpVly5dlJ6erjFjxlx2a8wwawkAAPN43SNTXFys2NhYSVK9evV0+PBhSecHAe/cudO/1YUBGz0yAACYxusembS0NG3fvl2pqanq1KmTZsyYocjISM2bN0+pqamBqDGksdcSAADm8TrI/O53v9Pp06clSdOmTdNtt92mG264QXXr1tXixYv9XmCoY4wMAADmqXSQadOmjX79619r0KBBql27tiQpNTVVO3bs0A8//KDatWu7Zy5dTni0BACAeSo9RqZTp0763e9+p6SkJN1777368MMP3e/VqVPnsgwxkmRn+jUAAKapdJCZO3eujh49qnnz5uno0aPq2bOnmjZtqilTpig7OzuQNYY0emQAADCPV7OWoqKiNGTIEK1evVrffPONhgwZoldffVWpqanq1auX/vGPfwSqzpBlZ7AvAACm8Xr6tUuzZs00depU7d+/X4sWLdJnn32me+65x5+1hQXXXkvFrCMDAEDQ+bzXkiStWbNGGRkZWrJkiex2u4YPH+6vusKGu0eGTSMBAAg6r3tksrOzNWXKFKWmpurmm2/WgQMHNHv2bB05ckR/+ctf/FrcnDlz1Lp1a9WsWVM1a9ZU586dtWLFCr9eo6oYIwMAgHkq3SPz5ptvKiMjQ2vWrFGDBg1033336cEHH1Tz5s0DVlzjxo313HPPua/x2muvqX///tq2bZuuuuqqgF3XG65ZSwQZAACCr9JBZtiwYerTp4+WLVumW2+9VVarz8NrKq1v374e30+fPl1z5szRhg0bQibIsLIvAADmqXSQ+fbbb5WQkBDIWi6puLhYb7/9tk6fPq3OnTtX2CY/P1/5+fnu73NzcwNeFyv7AgBgnkp3q5gVYrKyshQbGyuHw6GRI0dq6dKlatmyZYVt09PTFR8f734lJycHvD52vwYAwDyBfz5URT//+c+VmZmpDRs26KGHHtLQoUO1Y8eOCttOmjRJOTk57tfBgwcDXh+DfQEAME+Vpl8HQ2RkpHuwb4cOHbR582b98Y9/1Ny5c8u1dTgccjgcQa2PBfEAADBPyPfIXMgwDI9xMGajRwYAAPP41CNz8uRJvfPOO9qzZ48effRR1alTR1u3blWDBg3UqFEjvxU3efJk9e7dW8nJycrLy9OiRYu0du1arVy50m/XqCqmXwMAYB6vg8z27dt1yy23KD4+Xvv379fw4cNVp04dLV26VAcOHNDrr7/ut+K+++47DRkyREeOHFF8fLxat26tlStXqkePHn67RlW5tijg0RIAAMHndZCZMGGChg0bphkzZiguLs59vHfv3rr33nv9Wtyrr77q1/MFAtOvAQAwj9djZDZv3qwRI0aUO96oUSMdPXrUL0WFk7JjZAyDMAMAQDB5HWSioqIqXGhu586dql+/vl+KCieuHhmJXhkAAILN6yDTv39/TZkyRYWFhZIki8Wi7OxsPf7447rzzjv9XmCos5UJMoyTAQAguLwOMi+++KK+//57JSQk6OzZs+ratauaN2+uuLg4TZ8+PRA1hjR7mT2n6JEBACC4vB7sW7NmTa1fv16rV6/W1q1b5XQ61a5dO91yyy2BqC/k0SMDAIB5vA4y+/fvV9OmTXXTTTfppptuCkRNYYUxMgAAmMfrR0upqanq0qWL5s6dqx9++CEQNYUVq9UiS0mWYeNIAACCy+sg89lnn6lz586aNm2akpKS1L9/f7399tshtW1AsNksrCUDAIAZvA4y7dq10wsvvKDs7GytWLFCCQkJGjFihBISEvTAAw8EosaQ5xonU1RMkAEAIJh83jTSYrGoe/fumj9/vj744AOlpqbqtdde82dtYYPVfQEAMIfPQebgwYOaMWOG2rRpo44dOyomJkavvPKKP2sLG+7VfVnZFwCAoPJ61tK8efP097//Xf/73//085//XIMGDdKyZcvUtGnTAJQXHuw2dsAGAMAMXgeZqVOnauDAgfrjH/+oNm3aBKCk8MMYGQAAzOF1kMnOzpbFYvnphpcRxsgAAGCOSgWZ7du3Ky0tTVarVVlZWZds27p1a78UFk7cPTKsIwMAQFBVKsi0adNGR48eVUJCgtq0aSOLxSKjzMBW1/cWi0XFxcUBKzZU0SMDAIA5KhVk9u3bp/r167u/hqfSHhmCDAAAwVSpIJOSkuL++sCBA7ruuutkt3t+tKioSJ988olH28uFawdsemQAAAgur9eR6d69e4V7LOXk5Kh79+5+KSrc0CMDAIA5vA4yrrEwFzpx4oRiYmL8UlS4sdtcY2QY7AsAQDBVevr1L3/5S0nnB/YOGzZMDofD/V5xcbG2b9+u6667zv8VhgHWkQEAwByVDjLx8fGSzvfIxMXFqUaNGu73IiMjde2112r48OH+rzAMsPs1AADmqHSQycjIkCQ1bdpUv/3tby/bx0gVYYwMAADm8Hpl36effjoQdYS10jEyBBkAAILJ6yAjSe+8847+8Y9/KDs7WwUFBR7vbd261S+FhRMb068BADCF17OWXn75Zd1///1KSEjQtm3bdM0116hu3brau3evevfuHYgaQx4r+wIAYA6vg8zs2bM1b948vfLKK4qMjNTEiRO1atUqjRkzRjk5OYGoMeQxRgYAAHN4HWSys7Pd06xr1KihvLw8SdKQIUP01ltv+be6MFHaI8M6MgAABJPXQSYxMVEnTpyQdH7rgg0bNkg6vwdT2Y0kLyf0yAAAYA6vg8xNN92kd999V5L04IMPavz48erRo4fuvvtu3XHHHX4vMBwwRgYAAHN4PWtp3rx5cpY8Qhk5cqTq1Kmj9evXq2/fvho5cqTfCwwHrllL9MgAABBcXgcZq9Uqq7W0I+dXv/qVfvWrX/m1qHBDjwwAAOaoVJDZvn17pU/YunVrn4sJVzYbey0BAGCGSgWZNm3ayGKx/ORgXovFouLiYr8UFk6YtQQAgDkqFWT27dsX6DrCGrOWAAAwR6WCTEpKSqDrCGvsfg0AgDm8nn4tSW+88Yauv/56JSUl6cCBA5KkWbNm6V//+pdfiwsX7jEyBBkAAILK6yAzZ84cTZgwQbfeeqtOnjzpHhNTq1YtzZo1y9/1hQVmLQEAYA6vg8yf/vQnzZ8/X0888YRsNpv7eIcOHZSVleXX4sIFu18DAGAOr4PMvn371LZt23LHHQ6HTp8+7Zeiwo2dwb4AAJjC6yDTrFkzZWZmlju+YsUKtWzZ0h81hR0b068BADCF10Hm0Ucf1ahRo7R48WIZhqFNmzZp+vTpmjx5sh599FG/Fpeenq6OHTsqLi5OCQkJuv3227Vz506/XsMf6JEBAMAcXm9RcP/996uoqEgTJ07UmTNndO+996pRo0b64x//qIEDB/q1uHXr1mnUqFHq2LGjioqK9MQTT6hnz57asWOHYmJi/HqtqrAx2BcAAFN4HWQkafjw4Ro+fLiOHz8up9OphIQESdKhQ4fUqFEjvxW3cuVKj+8zMjKUkJCgLVu26MYbb/TbdaqKHhkAAMzh0zoyLvXq1VNCQoKOHj2q0aNHq3nz5v6qq0I5OTmSpDp16gT0Ot6y2UpmLbHXEgAAQVXpIHPy5EkNGjRI9evXV1JSkl5++WU5nU499dRTSk1N1YYNG/S3v/0tYIUahqEJEyaoS5cuSktLq7BNfn6+cnNzPV7BQI8MAADmqPSjpcmTJ+ujjz7S0KFDtXLlSo0fP14rV67UuXPntGLFCnXt2jWQdeqRRx7R9u3btX79+ou2SU9P1+9///uA1lERZi0BAGCOSvfI/Oc//1FGRoZefPFFLV++XIZh6Morr9Tq1asDHmJGjx6t5cuXa82aNWrcuPFF202aNEk5OTnu18GDBwNalws9MgAAmKPSPTKHDx92rxOTmpqqqKgo/frXvw5YYdL5x0mjR4/W0qVLtXbtWjVr1uyS7R0OhxwOR0BrqgizlgAAMEelg4zT6VRERIT7e5vNFvAp0KNGjdKbb76pf/3rX4qLi9PRo0clSfHx8apRo0ZAr+0NGz0yAACYotJBxjAMDRs2zN3jce7cOY0cObJcmFmyZInfipszZ44kqVu3bh7HMzIyNGzYML9dp6rYNBIAAHNUOsgMHTrU4/vBgwf7vZgLGUZ4BAPXppH0yAAAEFyVDjIZGRmBrCOsuXpknAQZAACCqkoL4uE8xsgAAGAOgowf2FlHBgAAUxBk/IAeGQAAzEGQ8QO7jVlLAACYgSDjB+5ZS2waCQBAUBFk/IB1ZAAAMAdBxg8YIwMAgDkIMn7ArCUAAMxBkPEDemQAADAHQcYP7CWDfRkjAwBAcBFk/KAkx9AjAwBAkBFk/IAeGQAAzEGQ8QNbmenX4bJjNwAA1QFBxg9cs5YkiU4ZAACChyDjBzZbaZApYgo2AABBQ5Dxg7I9MoyTAQAgeAgyfmCzlu2RIcgAABAsBBk/cM1akqRiNo4EACBoCDJ+UKZDhh4ZAACCiCDjBxaLhR2wAQAwAUHGT0r3W2LWEgAAwUKQ8RN6ZAAACD6CjJ+wAzYAAMFHkPETu439lgAACDaCjJ9YLSU9Mky/BgAgaAgyfsIYGQAAgo8g4yfMWgIAIPgIMn5iL9k40mnQIwMAQLAQZPzE3SPDGBkAAIKGIOMnjJEBACD4CDJ+YivZOJJ1ZAAACB6CjJ/QIwMAQPARZPyElX0BAAg+goyflPbIMP0aAIBgIcj4CT0yAAAEH0HGT1zryDBGBgCA4CHI+Il71hLryAAAEDQEGT9h1hIAAMFHkPET9+7XBBkAAIKGIOMnzFoCACD4CDJ+YmOwLwAAQRfSQeajjz5S3759lZSUJIvFomXLlpld0kXZmX4NAEDQhXSQOX36tK6++mq98sorZpfyk2wM9gUAIOjsZhdwKb1791bv3r3NLqNS6JEBACD4QjrIeCs/P1/5+fnu73Nzc4N2bdc6MvTIAAAQPCH9aMlb6enpio+Pd7+Sk5ODdm16ZAAACL5qFWQmTZqknJwc9+vgwYNBu7aN6dcAAARdtXq05HA45HA4TLk2PTIAAARfteqRMZN7HRn2WgIAIGhCukfm1KlT+uabb9zf79u3T5mZmapTp46aNGliYmXl0SMDAEDwhXSQ+eyzz9S9e3f39xMmTJAkDR06VAsWLDCpqooxawkAgOAL6SDTrVs3GUZ4BAN6ZAAACD7GyPgJs5YAAAg+goyf1IiwSZJ2fXcqbHqRAAAIdwQZP7m1VUM57FZlHjypNTuPmV0OAACXBYKMnyTGR2nodU0lSS+8v0tOxsoAABBwBBk/eqjrzxTnsOurI7l6d/ths8sBAKDaI8j4Ue2YSP3fjamSpJmrdqmwmIG/AAAEEkHGzx7o0kz1YiN14MQZLd4cvL2eAAC4HBFk/CzGYdcj3ZtLkl7+cLfOFhSbXBEAANUXQSYA7unURI1q1dCxvHy99ul+s8sBAKDaIsgEgMNu0/geV0qS5qzdo9xzhSZXBABA9USQCZA72jbSz+rHKOdsoZZuPWR2OQAAVEsEmQCxWS26r3NTSdIbGw6w2i8AAAFAkAmgO9o1Uo0Im745dkob9/1gdjkAAFQ7BJkAqhkVodvbNpIkLdxwwORqAACofggyATb42iaSpJVfHNWxvHMmVwMAQPVCkAmwq5Li1bZJLRU5Df2DBfIAAPArgkwQDLk2RZL05sZsFbOZJAAAfkOQCYJbWzVU7egIHc45p9VfHzO7HAAAqg2CTBBERdg0oEOyJAb9AgDgTwSZIBnU6fyg3492f68DJ06bXA0AANUDQSZIUurG6MYr68swpNc+oVcGAAB/IMgE0f3XNZUkLfhknz7Zc9zcYgAAqAYIMkHUvUWCBrRvLKchjXkrk3VlAACoIoJMkE3pn6afN4jT8VP5GvtWJtOxAQCoAoJMkNWItOnPg9opOtKmT/ee0B8/2GV2SQAAhC2CjAmaJ8Qq/ZetJEl/WvON1u363uSKAAAITwQZk/Rv00iDOjWRYUjjF2dq/3GmZAMA4C2CjImevK2l0hrV1A+nCzRw3gbtI8wAAOAVgoyJoiJsyhh2ja5sEKujued099xPtef7U2aXBQBA2CDImKx+nENvDr9WP28Qp2N5+Ro4b4O+OZZndlkAAIQFgkwIqBfr0JvDO6lFYpy+z8vXwHkb9f6XR/X10Vz9eLpAhsEUbQAAKmIxqvFvydzcXMXHxysnJ0c1a9Y0u5yf9MPpAg3+60btOJLrcTzSblXD+Cj9rH6srmgQqysS4nRlyZ81Im0mVQsAQGB48/ubIBNiTp4p0JR/79COw7n6LvecfjxTeNG2Vot0ZYM4tWoUr9aN45XWKF7NE2IVFxURxIoBAPAvgkyJcAwyFzpXWKzv8/J16ORZ7T52St98l6dd353S7mN5On6qoMLP1I9zqFm9GP2sfoxS68XqZwkx+ln9WDWuHS2b1RLknwAAAO8QZEpUhyBzKd/lntP2b3OU9e1JbT+Uoy8P5+r7vPyLto+0WdWsXoyuTIxTi8Q4/aJhnFok1lTD+ChZLAQcAEBoIMiUqO5BpiK55wq1//hp7f3+tPZ+f0p7jp/WnmOntO/4aeUXOSv8jMNuVe3oSNWKjlB8jQjVio5Q7ehI1YkpfdWKjlCU3SZHhE1REVbViLCpQc0oxTjsQf4JAQDVnTe/v/ktVM3UjIpQ68a11LpxLY/jTqehQyfP6ptjp/T10Tx9fTRXXx/J057vTym/yKmjued0NNf73bgTa0bpZwnnH2E1qROtqEibHDarIu1WRZT86bCX/umw2xQfHaFaNSIUHWmjJwgAUCX0yFzm8ouKdSw3XzlnC/XjmQKdPFOok2cK9OOZQv1wusD9yjlbqHOFxcovcupcYbHOFhQrL7+oSte2Wy2qFR2hWIddURG280Gn5E+71SKb1SKLxSKbxaIIu1XRETbViDz/io6wKaKknd1qkc1mVYTVUuY850OT3WqR3WaR3WqVrczXETaLImxW2W3nz+9isVhk0fmZYpEl5ydsAUBw0SODSnPYbUquE61kHz6bc6ZQe46f0p5jp7T3+Gkd+vGs8ouKVVhsqKDIef5V7FR+kVMFRaUhKOdsoQqLDRU5DR0/VXDRQcuhwGI5P7YowmaVxSJZLRb3nzarRRFWi+y20uBltVhktVpkLWljLwlM589hkc3qOo9kUem5XJ+xlXxtkev4+XDlOl/Z61stktV6PoiVDX2u4xbX+Uo+U1F9tjLvuc5RtjZJspTcB5UcK1ub6z6cP0/p+55fe35WJe+7zm2zlqnBYnG3l/uzZX5e13lLAmfZNhadb6Oy96rks5aSWst+xnLBNSyWC/5OLKV1AghdBBn4LD46Qu2a1Fa7JrW9+pxhGDpbWFzS+1OoMwVFOlfoVH5RsfvPIqchp9NQsXH+T3dPUGGxzhQU61zh+cBUVOxUkdNQUbGhwuKS4FTmXIVOp4pL3i92GipyOt2fKyw2VOh06lJ9koYh5Rc5Lzq+CNXfxQLYhaGy7HsqE+hc71kvCHRlg5PH9TyuXba3sGw95Y+7glrZoFc25Lnalg2hlpKDngGv9Nrlgp9HOPVU9n6U/axH7bqwtov//GWPW1QS6svU4PEZd2gtc32Pz3v+HO57dEFYLx/gK7j/7rBb5h5ZSoP0xf5e3XWU/Xsq8/dSLphXcIILa7jw77jsRzz/PkqvXWFNF96bC47JUtq29N/0+XNL5/9PyG2tk8r/wEFCkEHQWSwWRUfaFR1pV1KtGmaXI+l8uHIFGqdhuHuV8kt6koqdhoyS9wzDULFT7mDkClJFJaHIaRhyGufHJRWWBK3C4vM9VEXO89cxdL6NXG2N80HLWXJuQyXtynzvLPne3abkM66w53Rf25DTqfPHS36usjWVXqu0fXFJXa4aDEkyytRR9j5J7lqKnaV1u46Vfrb0e9fPLNfXRun5POou+drVzuOaZWq+MHyWrbOi96v2b6P05/c8cbV9Kg94hSBTCbNnz9YLL7ygI0eO6KqrrtKsWbN0ww03mF0WqpGy/+/MKovsNpWsmsziguHK6TTcYerCgOQRquQZuFwBrmzAOt+4zLnLtnGWBsaygc9ZkuguDFiu61cUtsoeu7BG13mNcm3LXKNM4NYFZRsX/FxGSeD1bHPh+S/8uUrrKluD+x6WvF9cQQemZ8j1PG/58xke51bZQFzmJrm+cofoCq5f9j6663D/vV9Qi+vfyAU1lf/34vl/NioToi8M9Z73zvMnKq214vvhrqnc37Hh0cbpvmYF4b+SdVz4b8PjfzMl1zB7fbKQDzKLFy/WuHHjNHv2bF1//fWaO3euevfurR07dqhJkyZmlwcgRFnd/3FlnAtQnYX8rKVOnTqpXbt2mjNnjvvYL37xC91+++1KT0+/5GeZtQQAQPjx5vd3SO9+XVBQoC1btqhnz54ex3v27KlPPvnEpKoAAECoCOlHS8ePH1dxcbEaNGjgcbxBgwY6evRoufb5+fnKzy9doj83N7dcGwAAUH2EdI+My4XT0AzDqHBqWnp6uuLj492v5GRfVkcBAADhIqSDTL169WSz2cr1vhw7dqxcL40kTZo0STk5Oe7XwYMHg1UqAAAwQUgHmcjISLVv316rVq3yOL5q1Spdd9115do7HA7VrFnT4wUAAKqvkB4jI0kTJkzQkCFD1KFDB3Xu3Fnz5s1Tdna2Ro4caXZpAADAZCEfZO6++26dOHFCU6ZM0ZEjR5SWlqb33ntPKSkpZpcGAABMFvLryFQF68gAABB+qs06MgAAAJdCkAEAAGGLIAMAAMIWQQYAAIQtggwAAAhbIT/9uipcE7LYcwkAgPDh+r1dmYnV1TrI5OXlSRJ7LgEAEIby8vIUHx9/yTbVeh0Zp9Opw4cPKy4ursJNJqsiNzdXycnJOnjwIGvUBBj3Oni418HDvQ4e7nXw+OteG4ahvLw8JSUlyWq99CiYat0jY7Va1bhx44Begz2dgod7HTzc6+DhXgcP9zp4/HGvf6onxoXBvgAAIGwRZAAAQNgiyPjI4XDo6aeflsPhMLuUao97HTzc6+DhXgcP9zp4zLjX1XqwLwAAqN7okQEAAGGLIAMAAMIWQQYAAIQtgowPZs+erWbNmikqKkrt27fXxx9/bHZJYS89PV0dO3ZUXFycEhISdPvtt2vnzp0ebQzD0DPPPKOkpCTVqFFD3bp105dffmlSxdVHenq6LBaLxo0b5z7GvfafQ4cOafDgwapbt66io6PVpk0bbdmyxf0+99p/ioqK9Lvf/U7NmjVTjRo1lJqaqilTpsjpdLrbcL9989FHH6lv375KSkqSxWLRsmXLPN6vzH3Nz8/X6NGjVa9ePcXExKhfv3769ttvq16cAa8sWrTIiIiIMObPn2/s2LHDGDt2rBETE2McOHDA7NLCWq9evYyMjAzjiy++MDIzM40+ffoYTZo0MU6dOuVu89xzzxlxcXHGP//5TyMrK8u4++67jYYNGxq5ubkmVh7eNm3aZDRt2tRo3bq1MXbsWPdx7rV//PDDD0ZKSooxbNgwY+PGjca+ffuMDz74wPjmm2/cbbjX/jNt2jSjbt26xr///W9j3759xttvv23ExsYas2bNcrfhfvvmvffeM5544gnjn//8pyHJWLp0qcf7lbmvI0eONBo1amSsWrXK2Lp1q9G9e3fj6quvNoqKiqpUG0HGS9dcc40xcuRIj2MtWrQwHn/8cZMqqp6OHTtmSDLWrVtnGIZhOJ1OIzEx0Xjuuefcbc6dO2fEx8cbf/nLX8wqM6zl5eUZV1xxhbFq1Sqja9eu7iDDvfafxx57zOjSpctF3+de+1efPn2MBx54wOPYL3/5S2Pw4MGGYXC//eXCIFOZ+3ry5EkjIiLCWLRokbvNoUOHDKvVaqxcubJK9fBoyQsFBQXasmWLevbs6XG8Z8+e+uSTT0yqqnrKycmRJNWpU0eStG/fPh09etTj3jscDnXt2pV776NRo0apT58+uuWWWzyOc6/9Z/ny5erQoYMGDBighIQEtW3bVvPnz3e/z732ry5duujDDz/Url27JEmff/651q9fr1tvvVUS9ztQKnNft2zZosLCQo82SUlJSktLq/K9r9Z7Lfnb8ePHVVxcrAYNGngcb9CggY4ePWpSVdWPYRiaMGGCunTporS0NEly39+K7v2BAweCXmO4W7RokbZu3arNmzeXe4977T979+7VnDlzNGHCBE2ePFmbNm3SmDFj5HA4dN9993Gv/eyxxx5TTk6OWrRoIZvNpuLiYk2fPl333HOPJP5tB0pl7uvRo0cVGRmp2rVrl2tT1d+fBBkfXLiTtmEYft9d+3L2yCOPaPv27Vq/fn2597j3VXfw4EGNHTtW//3vfxUVFXXRdtzrqnM6nerQoYOeffZZSVLbtm315Zdfas6cObrvvvvc7bjX/rF48WItXLhQb775pq666iplZmZq3LhxSkpK0tChQ93tuN+B4ct99ce959GSF+rVqyebzVYuPR47dqxcEoVvRo8ereXLl2vNmjUeO5cnJiZKEvfeD7Zs2aJjx46pffv2stvtstvtWrdunV5++WXZ7Xb3/eReV13Dhg3VsmVLj2O/+MUvlJ2dLYl/1/726KOP6vHHH9fAgQPVqlUrDRkyROPHj1d6erok7negVOa+JiYmqqCgQD/++ONF2/iKIOOFyMhItW/fXqtWrfI4vmrVKl133XUmVVU9GIahRx55REuWLNHq1avVrFkzj/ebNWumxMREj3tfUFCgdevWce+9dPPNNysrK0uZmZnuV4cOHTRo0CBlZmYqNTWVe+0n119/fbllBHbt2qWUlBRJ/Lv2tzNnzshq9fy1ZrPZ3NOvud+BUZn72r59e0VERHi0OXLkiL744ouq3/sqDRW+DLmmX7/66qvGjh07jHHjxhkxMTHG/v37zS4trD300ENGfHy8sXbtWuPIkSPu15kzZ9xtnnvuOSM+Pt5YsmSJkZWVZdxzzz1Mm/STsrOWDIN77S+bNm0y7Ha7MX36dGP37t3G3//+dyM6OtpYuHChuw332n+GDh1qNGrUyD39esmSJUa9evWMiRMnuttwv32Tl5dnbNu2zdi2bZshyZg5c6axbds299IjlbmvI0eONBo3bmx88MEHxtatW42bbrqJ6ddm+fOf/2ykpKQYkZGRRrt27dxThOE7SRW+MjIy3G2cTqfx9NNPG4mJiYbD4TBuvPFGIysry7yiq5ELgwz32n/effddIy0tzXA4HEaLFi2MefPmebzPvfaf3NxcY+zYsUaTJk2MqKgoIzU11XjiiSeM/Px8dxvut2/WrFlT4X+jhw4dahhG5e7r2bNnjUceecSoU6eOUaNGDeO2224zsrOzq1wbu18DAICwxRgZAAAQtggyAAAgbBFkAABA2CLIAACAsEWQAQAAYYsgAwAAwhZBBgAAhC2CDAAACFsEGQAAELYIMgAAIGwRZAAAQNgiyAAAgLBFkAEAAGGLIAMAAMIWQQYAAIQtggwAAAhbBBkAABC2CDIAACBsEWQAAEDYIsgAAICwRZABAABhiyADAADCFkEGAACELYIMAAAIWwQZAAAQtggyAAAgbBFkAABA2CLIAACAsEWQAQAAYYsgAwAAwhZBBoAHi8WiZcuWBf263bp107hx44J+3crYv3+/LBaLMjMzzS4FwAUIMsBl5NixYxoxYoSaNGkih8OhxMRE9erVS59++qm7zZEjR9S7d28Tq/Sf7777ThEREVq4cGGF748YMUKtW7cOclUA/IkgA1xG7rzzTn3++ed67bXXtGvXLi1fvlzdunXTDz/84G6TmJgoh8NhYpW+MQxDRUVFHscaNGigPn36KCMjo1z7s2fPatGiRXrwwQeDVSKAACDIAJeJkydPav369Xr++efVvXt3paSk6JprrtGkSZPUp08fd7uyj5Zcj1SWLFmi7t27Kzo6WldffbVHD44kzZ8/X8nJyYqOjtYdd9yhmTNnqlatWu73hw0bpttvv93jM+PGjVO3bt0uWu/ChQvVoUMHxcXFKTExUffee6+OHTvmfn/t2rWyWCx6//331aFDBzkcDn388cflzvPggw9qzZo12r9/v8fxd955R+fOndPgwYO1cuVKdenSRbVq1VLdunV12223ac+ePRetbcGCBR4/nyQtW7ZMFovF49i7776r9u3bKyoqSqmpqfr973/vEbaeeeYZd+9YUlKSxowZc9FrAqgYQQa4TMTGxio2NlbLli1Tfn6+V5994okn9Nvf/laZmZm68sordc8997h/If/vf//TyJEjNXbsWGVmZqpHjx6aPn16lestKCjQ1KlT9fnnn2vZsmXat2+fhg0bVq7dxIkTlZ6erq+++qrCx0S33nqrEhMTtWDBAo/jf/vb33T77berbt26On36tCZMmKDNmzfrww8/lNVq1R133CGn0+lz/e+//74GDx6sMWPGaMeOHZo7d64WLFjgvjfvvPOOXnrpJc2dO1e7d+/WsmXL1KpVK5+vB1y2DACXjXfeeceoXbu2ERUVZVx33XXGpEmTjM8//9yjjSRj6dKlhmEYxr59+wxJxl//+lf3+19++aUhyfjqq68MwzCMu+++2+jTp4/HOQYNGmTEx8e7vx86dKjRv39/jzZjx441unbt6v6+a9euxtixYy9a+6ZNmwxJRl5enmEYhrFmzRpDkrFs2bKf/Lkfe+wxIyUlxXA6nYZhGMbevXsNi8VivP/++xW2P3bsmCHJyMrKMgyj9D5s27bNMAzDyMjI8Pj5DMMwli5dapT9T+oNN9xgPPvssx5t3njjDaNhw4aGYRjGH/7wB+PKK680CgoKfrJ+ABdHjwxwGbnzzjt1+PBhLV++XL169dLatWvVrl27cr0VFyrb09GwYUNJcj/m2blzp6655hqP9hd+74tt27apf//+SklJUVxcnPsxVHZ2tke7Dh06/OS5HnzwQR04cECrV6+WdL43pnHjxrrlllskSXv27NG9996r1NRU1axZU82aNavwWt7YsmWLpkyZ4u4Ji42N1fDhw3XkyBGdOXNGAwYM0NmzZ5Wamqrhw4dr6dKl5cb4APhpBBngMhMVFaUePXroqaee0ieffKJhw4bp6aefvuRnIiIi3F+7xoG4HrsYhlFubIhhGB7fW63WcscKCwsver3Tp0+rZ8+eio2N1cKFC7V582YtXbpU0vlHTmXFxMRcsnZJuuKKK3TDDTcoIyNDTqdTr732mu6//35Zref/E9i3b1+dOHFC8+fP18aNG7Vx48YKr+XNz+N0OvX73/9emZmZ7ldWVpZ2796tqKgoJScna+fOnfrzn/+sGjVq6OGHH9aNN954yfsCoDy72QUAMFfLli2rtG5MixYttGnTJo9jn332mcf39evX1xdffOFxLDMz0yMglfX111/r+PHjeu6555ScnFzhOb314IMP6qGHHlL//v317bff6v7775cknThxQl999ZXmzp2rG264QZK0fv36S56rfv36ysvL0+nTp91B6sI1Ztq1a6edO3eqefPmFz1PjRo11K9fP/Xr10+jRo1SixYtlJWVpXbt2lXhJwUuLwQZ4DJx4sQJDRgwQA888IBat26tuLg4ffbZZ5oxY4b69+/v83lHjx6tG2+8UTNnzlTfvn21evVqrVixwqOX5qabbtILL7yg119/XZ07d9bChQv1xRdfqG3bthWes0mTJoqMjNSf/vQnjRw5Ul988YWmTp3qc42SNGDAAI0ZM0YjRozQzTffrKZNm0qSateurbp162revHlq2LChsrOz9fjjj1/yXJ06dVJ0dLQmT56s0aNHa9OmTeUezz311FO67bbblJycrAEDBshqtWr79u3KysrStGnTtGDBAhUXF7vP9cYbb6hGjRpKSUmp0s8JXG54tARcJmJjY9WpUye99NJLuvHGG5WWlqYnn3xSw4cP1yuvvOLzea+//nr95S9/0cyZM3X11Vdr5cqVGj9+vKKiotxtevXqpSeffFITJ05Ux44dlZeXp/vuu++i56xfv74WLFigt99+Wy1bttRzzz2nF1980ecaJSk6OloDBw7Ujz/+qAceeMB93Gq1atGiRdqyZYvS0tI0fvx4vfDCC5c8V506dbRw4UK99957atWqld566y0988wzHm169eqlf//731q1apU6duyoa6+9VjNnznQHlVq1amn+/Pm6/vrr1bp1a3344Yd69913Vbdu3Sr9nMDlxmJc+KAXAKpo+PDh+vrrrytc1wUA/IlHSwCq7MUXX1SPHj0UExOjFStW6LXXXtPs2bPNLgvAZYAeGQBV9qtf/Upr165VXl6eUlNTNXr0aI0cOdLssgBcBggyAAAgbDHYFwAAhC2CDAAACFsEGQAAELYIMgAAIGwRZAAAQNgiyAAAgLBFkAEAAGGLIAMAAMIWQQYAAISt/w9ZCtRCUZDdaAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "y_values =  rel_variance[:100] \n",
        "x_values = np.arange(len(y_values))\n",
        "\n",
        "plt.plot(x_values, y_values, linestyle = '-')\n",
        "\n",
        "plt.xlabel(\"Singular Values\", labelpad = 20)\n",
        "plt.ylabel(\"Relative Variance (%)\", labelpad = 10)\n",
        "\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B2t6M23Hn99i"
      },
      "source": [
        "A value between 5 and 20 seems reasonable (inflection point)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hlwk5TfWn99j"
      },
      "outputs": [],
      "source": [
        "dimensions = 20\n",
        "\n",
        "W = U[:, 0 : dimensions]\n",
        "sigma = s[:dimensions]\n",
        "C = Vt[0 : dimensions, :]\n",
        "\n",
        "ppmiMat_tr50 = np.dot(W, linalg.diagsvd(sigma, dimensions, len(C)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TpRPKIZbn99j",
        "outputId": "4e67a252-a5ba-48c1-d365-d68c6e50df34"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "ppmi_SVD50-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.4505230122547882\n"
          ]
        }
      ],
      "source": [
        "measure2mat = {\"ppmi_SVD50\": ppmiMat_tr50}\n",
        "\n",
        "for m, mat in measure2mat.items():\n",
        "    print(m+\"-based space vs. wordSim353 -> spearman's rho:\\t\",)\n",
        "    \n",
        "    sim = sklearn.metrics.pairwise.cosine_similarity(mat)\n",
        "    \n",
        "    wordSim_ratings = []\n",
        "    vsm_sims = []\n",
        "    for (w1, w2), r in wordSim353.items():\n",
        "        w1idx = vectors_indices[w1]\n",
        "        w2idx = vectors_indices[w2]\n",
        "        \n",
        "        wordSim_ratings.append(r)\n",
        "        vsm_sims.append(sim[w1idx, w2idx])\n",
        "        \n",
        "    rho, pval = scipy.stats.spearmanr(wordSim_ratings, vsm_sims)\n",
        "    \n",
        "    print(rho)\n",
        "    rhos.append(rho)\n",
        "    measures.append(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QlwnoY20n99j",
        "outputId": "8d058063-471b-4f2c-92d9-5046728693d4"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.bar(range(0, len(rhos)), rhos)\n",
        "plt.xticks(range(0, len(rhos)), measures, size='small', rotation='vertical')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zrnzJAk6n99j"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0FAV0cz6n99j"
      },
      "source": [
        "WEIGHTING $\\Sigma$\n",
        "\n",
        "Some authors suggested to downgrade the influence of $\\Sigma$ on the final word representation by applying a weight $0 < p < 1$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JgRPdywxn99k"
      },
      "outputs": [],
      "source": [
        "dimensions = 50"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "fI9uMfBhn99k"
      },
      "outputs": [],
      "source": [
        "# let's use only U, i.e. if p == 0\n",
        "\n",
        "p = 0.\n",
        "\n",
        "W = U[:, 0 : dimensions]\n",
        "sigma = s[:dimensions]\n",
        "C = Vt[0 : dimensions, :] \n",
        "\n",
        "ppmiMat_tr50_p0 = np.dot(W, linalg.diagsvd(sigma ** p , dimensions, len(C)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DrhjHXHFn99k"
      },
      "outputs": [],
      "source": [
        "# let's use only U, i.e. if p == 0\n",
        "\n",
        "p = 0.\n",
        "\n",
        "W = U[:, 0 : dimensions]\n",
        "sigma = s[:dimensions] ** p\n",
        "C = Vt[0 : dimensions, :] \n",
        "\n",
        "ppmiMat_tr50_p0 = np.dot(W, linalg.diagsvd(sigma, dimensions, len(C)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dqtUcPa9n99k",
        "outputId": "3144c374-7336-4435-caa2-70e24f696208"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "execution_count": 76,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# this is equivalent to using only W\n",
        "np.allclose(ppmiMat_tr50_p0, W)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ItFV5VnPn99l"
      },
      "outputs": [],
      "source": [
        "p = 0.5\n",
        "\n",
        "W = U[:, 0 : dimensions]\n",
        "sigma = s[:dimensions]\n",
        "C = Vt[0 : dimensions, :] \n",
        "\n",
        "ppmiMat_tr50_p5 = np.dot(W, linalg.diagsvd(sigma ** p, dimensions, len(C)))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_v_2dMFon99l",
        "outputId": "832b5d05-59c3-4ff0-9f23-b66dc48b3645"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "ppmi_SVD50_p.0-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.4787163334922676\n",
            "ppmi_SVD50_p.5-based space vs. wordSim353 -> spearman's rho:\t\n",
            "0.48067750369425066\n"
          ]
        }
      ],
      "source": [
        "measure2mat = {\"ppmi_SVD50_p.0\": ppmiMat_tr50_p0,\n",
        "              \"ppmi_SVD50_p.5\": ppmiMat_tr50_p5,}\n",
        "\n",
        "for m, mat in measure2mat.items():\n",
        "    print(m+\"-based space vs. wordSim353 -> spearman's rho:\\t\",)\n",
        "    \n",
        "    sim = sklearn.metrics.pairwise.cosine_similarity(mat)\n",
        "    \n",
        "    wordSim_ratings = []\n",
        "    vsm_sims = []\n",
        "    for (w1, w2), r in wordSim353.items():\n",
        "        w1idx = vectors_indices[w1]\n",
        "        w2idx = vectors_indices[w2]\n",
        "        \n",
        "        wordSim_ratings.append(r)\n",
        "        vsm_sims.append(sim[w1idx, w2idx])\n",
        "        \n",
        "    rho, pval = scipy.stats.spearmanr(wordSim_ratings, vsm_sims)\n",
        "    \n",
        "    print(rho)\n",
        "    rhos.append(rho)\n",
        "    measures.append(m)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5gGxNp-mn99l",
        "outputId": "b04e08df-0056-4779-bdc7-b59d6646c40d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.bar(range(0, len(rhos)), rhos)\n",
        "plt.xticks(range(0, len(rhos)), measures, size='small', rotation='vertical')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Wzx5aN_6n99l"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dNP-uaKPn99l"
      },
      "source": [
        "### Exercise 1.\n",
        "\n",
        "Apply SVD to the PLMI Weighted dense matrix `plmiMat` and evaluate the model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "dttMIBpBn99m"
      },
      "outputs": [],
      "source": [
        "# your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "36Bj0n0jn99m"
      },
      "source": [
        "### Exercise 2.\n",
        "\n",
        "Create and evaluate a plmi-weighted vector space model based on the co-occurrences in a ±10 words collocational span."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "x8dtKKnVn99m"
      },
      "outputs": [],
      "source": [
        "# your code here"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hgscCy6Dn99m"
      },
      "source": [
        "---"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    },
    "toc": {
      "base_numbering": 1,
      "nav_menu": {},
      "number_sections": true,
      "sideBar": true,
      "skip_h1_title": false,
      "title_cell": "Table of Contents",
      "title_sidebar": "Contents",
      "toc_cell": false,
      "toc_position": {},
      "toc_section_display": true,
      "toc_window_display": true
    },
    "colab": {
      "name": "4_Vector_Semantics.ipynb",
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}