pca_step_by_step.ipynb

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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "np.random.seed(23) \n",
    "\n",
    "mu_vec1 = np.array([0,0,0])\n",
    "cov_mat1 = np.array([[1,0,0],[0,1,0],[0,0,1]])\n",
    "class1_sample = np.random.multivariate_normal(mu_vec1, cov_mat1, 20)\n",
    "\n",
    "df = pd.DataFrame(class1_sample,columns=['feature1','feature2','feature3'])\n",
    "df['target'] = 1\n",
    "\n",
    "mu_vec2 = np.array([1,1,1])\n",
    "cov_mat2 = np.array([[1,0,0],[0,1,0],[0,0,1]])\n",
    "class2_sample = np.random.multivariate_normal(mu_vec2, cov_mat2, 20)\n",
    "\n",
    "df1 = pd.DataFrame(class2_sample,columns=['feature1','feature2','feature3'])\n",
    "\n",
    "df1['target'] = 0\n",
    "\n",
    "df = df.append(df1,ignore_index=True)\n",
    "\n",
    "df = df.sample(40)"
   ]
  },
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       "      <th>feature1</th>\n",
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       "      <th>2</th>\n",
       "      <td>-0.367548</td>\n",
       "      <td>-1.137460</td>\n",
       "      <td>-1.322148</td>\n",
       "      <td>1</td>\n",
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       "      <th>34</th>\n",
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       "    feature1  feature2  feature3  target\n",
       "2  -0.367548 -1.137460 -1.322148       1\n",
       "34  0.177061 -0.598109  1.226512       0\n",
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    "df.head()"
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       "</body>\n",
       "</html>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.express as px\n",
    "#y_train_trf = y_train.astype(str)\n",
    "fig = px.scatter_3d(df, x=df['feature1'], y=df['feature2'], z=df['feature3'],\n",
    "              color=df['target'].astype('str'))\n",
    "fig.update_traces(marker=dict(size=12,\n",
    "                              line=dict(width=2,\n",
    "                                        color='DarkSlateGrey')),\n",
    "                  selector=dict(mode='markers'))\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UE2ctlnaFru4"
   },
   "outputs": [],
   "source": [
    "# Step 1 - Apply standard scaling\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "df.iloc[:,0:3] = scaler.fit_transform(df.iloc[:,0:3])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BeISGQwWF0eT",
    "outputId": "a85c1f09-3e4b-44aa-bb16-ea4d26200f59"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance Matrix:\n",
      " [[1.02564103 0.20478114 0.080118  ]\n",
      " [0.20478114 1.02564103 0.19838882]\n",
      " [0.080118   0.19838882 1.02564103]]\n"
     ]
    }
   ],
   "source": [
    "# Step 2 - Find Covariance Matrix\n",
    "covariance_matrix = np.cov([df.iloc[:,0],df.iloc[:,1],df.iloc[:,2]])\n",
    "print('Covariance Matrix:\\n', covariance_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "1yBuCLitF6j2"
   },
   "outputs": [],
   "source": [
    "# Step 3 - Finding EV and EVs\n",
    "eigen_values, eigen_vectors = np.linalg.eig(covariance_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "921nxikdGdIH",
    "outputId": "25dfec75-0b27-439d-e5e9-f56aa6893af3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.3536065 , 0.94557084, 0.77774573])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "wZGzT4RrGlMx",
    "outputId": "bf13292e-609e-428f-f394-e227238f0cdd"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.53875915, -0.69363291,  0.47813384],\n",
       "       [-0.65608325, -0.01057596, -0.75461442],\n",
       "       [-0.52848211,  0.72025103,  0.44938304]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigen_vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 411
    },
    "id": "65wi1AT8Gl1n",
    "outputId": "cf2d4eab-7a23-430b-b774-a206e58d8ee1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "from matplotlib.patches import FancyArrowPatch\n",
    "\n",
    "\n",
    "class Arrow3D(FancyArrowPatch):\n",
    "    def __init__(self, xs, ys, zs, *args, **kwargs):\n",
    "        FancyArrowPatch.__init__(self, (0,0), (0,0), *args, **kwargs)\n",
    "        self._verts3d = xs, ys, zs\n",
    "\n",
    "    def draw(self, renderer):\n",
    "        xs3d, ys3d, zs3d = self._verts3d\n",
    "        xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n",
    "        self.set_positions((xs[0],ys[0]),(xs[1],ys[1]))\n",
    "        FancyArrowPatch.draw(self, renderer)\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "ax.plot(df['feature1'], df['feature2'], df['feature3'], 'o', markersize=8, color='blue', alpha=0.2)\n",
    "ax.plot([df['feature1'].mean()], [df['feature2'].mean()], [df['feature3'].mean()], 'o', markersize=10, color='red', alpha=0.5)\n",
    "for v in eigen_vectors.T:\n",
    "    a = Arrow3D([df['feature1'].mean(), v[0]], [df['feature2'].mean(), v[1]], [df['feature3'].mean(), v[2]], mutation_scale=20, lw=3, arrowstyle=\"-|>\", color=\"r\")\n",
    "    ax.add_artist(a)\n",
    "ax.set_xlabel('x_values')\n",
    "ax.set_ylabel('y_values')\n",
    "ax.set_zlabel('z_values')\n",
    "\n",
    "plt.title('Eigenvectors')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "ze3SWMhyGrov",
    "outputId": "f53f0e5e-3f6f-465d-e5c3-defdd25d6cb8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.53875915, -0.69363291,  0.47813384],\n",
       "       [-0.65608325, -0.01057596, -0.75461442]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc = eigen_vectors[0:2]\n",
    "pc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 206
    },
    "id": "POnfqMLAG5ai",
    "outputId": "b6810af8-2f37-48a0-dda5-2756aa953dee"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"df-6a046239-3f9d-4612-ac47-8706bf5a97b1\">\n",
       "    <div class=\"colab-df-container\">\n",
       "      <div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.599433</td>\n",
       "      <td>1.795862</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.056919</td>\n",
       "      <td>-0.212737</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.271876</td>\n",
       "      <td>0.498222</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.621586</td>\n",
       "      <td>0.023110</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.567286</td>\n",
       "      <td>1.730967</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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       "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6a046239-3f9d-4612-ac47-8706bf5a97b1')\"\n",
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      ],
      "text/plain": [
       "        PC1       PC2  target\n",
       "0  0.599433  1.795862       1\n",
       "1  1.056919 -0.212737       0\n",
       "2 -0.271876  0.498222       1\n",
       "3 -0.621586  0.023110       1\n",
       "4  1.567286  1.730967       1"
      ]
     },
     "execution_count": 13,
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     "output_type": "execute_result"
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   ],
   "source": [
    "transformed_df = np.dot(df.iloc[:,0:3],pc.T)\n",
    "# 40,3 - 3,2\n",
    "new_df = pd.DataFrame(transformed_df,columns=['PC1','PC2'])\n",
    "new_df['target'] = df['target'].values\n",
    "new_df.head()"
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    "new_df['target'] = new_df['target'].astype('str')\n",
    "fig = px.scatter(x=new_df['PC1'],\n",
    "                 y=new_df['PC2'],\n",
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    "                  selector=dict(mode='markers'))\n",
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