SVD.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "40d2e5f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import array\n",
    "from numpy import diag\n",
    "from numpy import zeros\n",
    "from scipy.linalg import svd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d20cd72",
   "metadata": {},
   "source": [
    "### ساخت ماتریس"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "668d6673",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4  5  6  7  8  9 10]\n",
      " [11 12 13 14 15 16 17 18 19 20]\n",
      " [21 22 23 24 25 26 27 28 29 30]]\n"
     ]
    }
   ],
   "source": [
    "A = array([\n",
    "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10],\n",
    "[11, 12, 13, 14, 15, 16, 17, 18, 19, 20],\n",
    "[21, 22, 23, 24, 25, 26, 27, 28, 29, 30]\n",
    "])\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8225d2f7",
   "metadata": {},
   "source": [
    "#### فاکتور سازی"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "09c94848",
   "metadata": {},
   "outputs": [],
   "source": [
    "U, s, V = svd(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a57e7cd4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "Sigma = zeros((A.shape[0], A.shape[1]))\n",
    "print(Sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ee1c48a",
   "metadata": {},
   "source": [
    "ساخت ماتریس قطری n * n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "eb45c333",
   "metadata": {},
   "outputs": [],
   "source": [
    "Sigma[:A.shape[0], :A.shape[0]] = diag(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e5cb0e9",
   "metadata": {},
   "source": [
    "ساخت فاکتور"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5fb2cb3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_elements = 2\n",
    "Sigma = Sigma[:, :n_elements]\n",
    "V = V[:n_elements, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "06a380ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]\n",
      " [11. 12. 13. 14. 15. 16. 17. 18. 19. 20.]\n",
      " [21. 22. 23. 24. 25. 26. 27. 28. 29. 30.]]\n"
     ]
    }
   ],
   "source": [
    "B = U.dot(Sigma.dot(V))\n",
    "print(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9137e7e6",
   "metadata": {},
   "source": [
    "پیاده سازی  کاهش ابعاد"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fda71cc5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-18.52157747  -6.47697214]\n",
      " [-49.81310011  -1.91182038]\n",
      " [-81.10462276   2.65333138]]\n"
     ]
    }
   ],
   "source": [
    "T = U.dot(Sigma)\n",
    "print(T) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9d07d600",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "636cf908",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "86005285",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "      <th>J</th>\n",
       "      <th>K</th>\n",
       "      <th>L</th>\n",
       "      <th>M</th>\n",
       "      <th>N</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A      B     C     D     E    F     G     H     I     J     K     L     M  \\\n",
       "0  1  14.23  1.71  2.43  15.6  127  2.80  3.06  0.28  2.29  5.64  1.04  3.92   \n",
       "1  1  13.20  1.78  2.14  11.2  100  2.65  2.76  0.26  1.28  4.38  1.05  3.40   \n",
       "2  1  13.16  2.36  2.67  18.6  101  2.80  3.24  0.30  2.81  5.68  1.03  3.17   \n",
       "3  1  14.37  1.95  2.50  16.8  113  3.85  3.49  0.24  2.18  7.80  0.86  3.45   \n",
       "4  1  13.24  2.59  2.87  21.0  118  2.80  2.69  0.39  1.82  4.32  1.04  2.93   \n",
       "\n",
       "      N  \n",
       "0  1065  \n",
       "1  1050  \n",
       "2  1185  \n",
       "3  1480  \n",
       "4   735  "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('C:\\\\ML\\\\dataset\\\\data.txt')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "678bede8",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "      <th>E</th>\n",
       "      <th>F</th>\n",
       "      <th>G</th>\n",
       "      <th>H</th>\n",
       "      <th>I</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       B     C     D     E    F     G     H     I\n",
       "0  14.23  1.71  2.43  15.6  127  2.80  3.06  0.28\n",
       "1  13.20  1.78  2.14  11.2  100  2.65  2.76  0.26\n",
       "2  13.16  2.36  2.67  18.6  101  2.80  3.24  0.30\n",
       "3  14.37  1.95  2.50  16.8  113  3.85  3.49  0.24\n",
       "4  13.24  2.59  2.87  21.0  118  2.80  2.69  0.39"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data2 = data[['B', 'C', 'D', 'E', 'F', 'G', 'H', 'I']]\n",
    "data2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b28ebdcf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.000e+00 1.423e+01 1.710e+00 ... 1.040e+00 3.920e+00 1.065e+03]\n",
      " [1.000e+00 1.320e+01 1.780e+00 ... 1.050e+00 3.400e+00 1.050e+03]\n",
      " [1.000e+00 1.316e+01 2.360e+00 ... 1.030e+00 3.170e+00 1.185e+03]\n",
      " ...\n",
      " [3.000e+00 1.327e+01 4.280e+00 ... 5.900e-01 1.560e+00 8.350e+02]\n",
      " [3.000e+00 1.317e+01 2.590e+00 ... 6.000e-01 1.620e+00 8.400e+02]\n",
      " [3.000e+00 1.413e+01 4.100e+00 ... 6.100e-01 1.600e+00 5.600e+02]]\n"
     ]
    }
   ],
   "source": [
    "A = data.values\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "59ec794e",
   "metadata": {},
   "outputs": [],
   "source": [
    "U, s, V = svd(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "205a0b36",
   "metadata": {},
   "outputs": [],
   "source": [
    "n_elements = 2\n",
    "Sigma = A[:, :n_elements]\n",
    "V = V[:n_elements, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "03ebb275",
   "metadata": {},
   "outputs": [],
   "source": [
    "B= U.dot(Sigma.dot(V))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "8386e33c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.57592213e+01 -1.46823276e+02]\n",
      " [ 4.29539498e+00 -2.87855605e+01]\n",
      " [-4.89339918e-01 -5.78058685e+00]\n",
      " [ 1.06130937e-01 -8.19120702e-01]\n",
      " [-1.78823356e+00 -2.96983294e+01]\n",
      " [ 1.44281551e+00  1.81111845e-01]\n",
      " [ 1.79877595e+00  8.09849555e+00]\n",
      " [-3.51280892e-02 -5.98098525e+00]\n",
      " [-5.29379370e-01 -8.01164377e+00]\n",
      " [-2.05128964e+00 -1.69475087e+01]\n",
      " [ 1.76677976e-02 -6.87752831e+00]\n",
      " [-1.89236069e+00 -1.70945254e+01]\n",
      " [-4.47471092e+00 -3.32689985e+01]\n",
      " [-2.41415066e-01 -1.18411707e+01]\n",
      " [ 4.56488130e-01  6.75709751e+00]\n",
      " [ 8.19650723e-03 -2.72682237e-01]\n",
      " [ 4.19262441e-01  4.78314480e+00]\n",
      " [ 2.60163081e-02  6.64157326e-01]\n",
      " [-2.01484852e-01  4.68566337e-01]\n",
      " [ 6.81093310e-01  4.76128376e+00]\n",
      " [ 1.17636519e+00  7.31862026e+00]\n",
      " [ 1.00895961e+00  7.95861931e+00]\n",
      " [ 9.90942364e-01  8.20560090e+00]\n",
      " [ 7.17211693e-01  5.49011227e+00]\n",
      " [ 7.93082842e-01  5.81157386e+00]\n",
      " [ 7.46958954e-01  4.72189541e+00]\n",
      " [ 3.76519394e-01  5.05167136e+00]\n",
      " [ 3.87114795e-01  5.94234518e+00]\n",
      " [ 2.67590762e-01  1.54356088e+00]\n",
      " [ 1.18072295e+00  1.07060930e+01]\n",
      " [-3.26852826e-02  1.30137343e+00]\n",
      " [ 3.14183628e-01  4.42402265e+00]\n",
      " [ 5.15707445e-01  5.42359259e+00]\n",
      " [ 4.76120975e-01  3.68633462e+00]\n",
      " [ 4.42173300e-01  4.04271110e+00]\n",
      " [ 7.29653142e-01  5.72182366e+00]\n",
      " [ 1.31814309e-01  2.09187826e-01]\n",
      " [-7.29743053e-02  4.59156594e-01]\n",
      " [-1.84640371e-02  6.58715603e-01]\n",
      " [ 1.16721955e+00  9.21024428e+00]\n",
      " [ 1.12163735e+00  8.29967665e+00]\n",
      " [ 4.66133130e-01  7.11862810e+00]\n",
      " [ 3.33743459e-01  3.30271235e+00]\n",
      " [ 7.70082420e-01  7.74314483e+00]\n",
      " [ 9.77881766e-01  8.20655025e+00]\n",
      " [ 7.85830551e-01  8.72139914e+00]\n",
      " [ 5.55944661e-01  7.14739153e+00]\n",
      " [ 7.37524168e-01  6.75830622e+00]\n",
      " [ 6.44022772e-01  6.81098158e+00]\n",
      " [ 7.10547598e-01  6.16732077e+00]\n",
      " [ 6.59038482e-01  6.29461958e+00]\n",
      " [ 6.06581431e-01  5.71502435e+00]\n",
      " [ 9.05395909e-02  1.47802526e+00]\n",
      " [ 4.22282162e-01  4.81371072e+00]\n",
      " [ 1.00134674e+00  7.93831430e+00]\n",
      " [ 9.43932174e-01  7.86813712e+00]\n",
      " [ 9.93510533e-01  7.96115483e+00]\n",
      " [-6.85225581e-02  7.42462154e-01]\n",
      " [ 1.11780892e-01  2.18057823e+00]\n",
      " [-6.58546395e-01 -5.48968355e+00]\n",
      " [-8.89596300e-01 -7.73693798e+00]\n",
      " [-4.12132200e-01 -4.49791048e+00]\n",
      " [-6.64886559e-01 -6.52442473e+00]\n",
      " [-1.43069651e+00 -1.48050647e+01]\n",
      " [-9.43222077e-01 -1.16032997e+01]\n",
      " [-6.56165449e-01 -7.04511074e+00]\n",
      " [-3.48085648e-01 -4.17801762e+00]\n",
      " [ 3.47683825e-02 -2.52512629e+00]\n",
      " [-6.47828076e-01 -5.08233783e+00]\n",
      " [ 1.38382427e+00  6.61040002e+00]\n",
      " [ 4.94383161e-01  4.94416831e+00]\n",
      " [-1.19085181e+00 -1.25943466e+01]\n",
      " [-1.12117250e-01 -2.17420889e+00]\n",
      " [-3.36427243e-01 -6.03617129e+00]\n",
      " [-6.15467737e-01 -6.56618490e+00]\n",
      " [-4.12288265e-01 -5.97870288e+00]\n",
      " [-3.42563152e-01 -5.19582441e+00]\n",
      " [ 3.02013583e-01  1.10914173e+00]\n",
      " [ 1.08237830e+00  7.11421490e+00]\n",
      " [-3.87798536e-01 -3.68893110e+00]\n",
      " [-7.67999279e-01 -1.02649453e+01]\n",
      " [-2.14738303e-01 -2.86161584e+00]\n",
      " [-6.55993135e-01 -6.63674391e+00]\n",
      " [ 3.90520346e-01  5.75670529e+00]\n",
      " [ 5.43831220e-01  2.24085992e+00]\n",
      " [-9.84602968e-02 -4.08936519e+00]\n",
      " [-5.96908470e-01 -6.35270468e+00]\n",
      " [-2.76618300e-01 -5.29479700e+00]\n",
      " [-2.29996003e-02 -1.41559730e-01]\n",
      " [-1.26469962e-01 -9.67055086e-01]\n",
      " [-2.85845258e-02 -5.19153973e-02]\n",
      " [ 5.79684456e-01  3.30258154e+00]\n",
      " [ 2.94350313e-01  3.54911684e+00]\n",
      " [-2.11801544e-01 -3.85881167e+00]\n",
      " [-1.02591113e+00 -1.24045787e+01]\n",
      " [ 1.09392113e+00  6.87114512e+00]\n",
      " [ 4.07788149e-01 -2.10980031e-01]\n",
      " [-8.04032198e-01 -8.42577498e+00]\n",
      " [-1.34931506e+00 -1.21362901e+01]\n",
      " [-8.05066256e-01 -7.03572807e+00]\n",
      " [-3.61688263e-01 -4.45596594e+00]\n",
      " [ 3.93261849e-01  2.34122433e+00]\n",
      " [ 2.56056307e-01  5.85228988e-01]\n",
      " [-3.92983201e-01 -3.39539013e+00]\n",
      " [ 4.07891299e-01  2.60674934e+00]\n",
      " [ 1.09892290e+00  8.75668917e+00]\n",
      " [ 4.82732981e-01  2.89010737e+00]\n",
      " [ 5.05220529e-01  4.54358318e+00]\n",
      " [ 5.90483574e-01  3.60148048e+00]\n",
      " [-8.97629417e-02 -2.27767986e+00]\n",
      " [ 6.12625785e-01  6.17658117e+00]\n",
      " [-6.41543892e-01 -6.13949201e+00]\n",
      " [-3.78832836e-01 -5.00316540e+00]\n",
      " [-8.57548045e-01 -9.34338736e+00]\n",
      " [-3.45241892e-01 -4.75530187e+00]\n",
      " [-1.07232241e+00 -1.19365302e+01]\n",
      " [ 5.00202207e-01  2.69428981e+00]\n",
      " [ 2.23925616e-01 -9.09003853e-01]\n",
      " [ 1.39518085e-01  2.91043273e+00]\n",
      " [ 4.52544168e-01  4.96554812e+00]\n",
      " [ 2.43043132e-02 -8.44036981e-01]\n",
      " [-4.86053838e-01 -9.01863396e+00]\n",
      " [ 2.21644729e-01  1.39642635e+00]\n",
      " [ 4.74242684e-02  2.89848326e+00]\n",
      " [ 3.41633179e-01  2.96827631e+00]\n",
      " [-1.75168443e-01 -2.52125878e+00]\n",
      " [-1.76946828e-01 -2.09011563e+00]\n",
      " [-1.85105133e-01 -1.99997601e+00]\n",
      " [-1.54998557e-02 -8.14598448e-01]\n",
      " [-1.39368610e-01  1.11868977e+00]\n",
      " [-7.73087980e-01 -8.18807654e+00]\n",
      " [-7.67371237e-01 -7.31862853e+00]\n",
      " [-5.69991916e-01 -5.40852964e+00]\n",
      " [-1.24990123e+00 -1.07892471e+01]\n",
      " [-3.69897470e-01 -1.86664272e+00]\n",
      " [ 1.10230530e-02  1.07448995e+00]\n",
      " [-7.79015032e-01 -3.29551501e+00]\n",
      " [-4.48220213e-01 -1.70686982e+00]\n",
      " [-1.36327948e-01  7.22189761e-01]\n",
      " [-5.88354721e-01 -5.19040536e+00]\n",
      " [ 5.48597564e-02  3.12085701e-01]\n",
      " [ 2.38353116e-01  2.38987412e+00]\n",
      " [-4.57674232e-01 -3.97257518e+00]\n",
      " [-6.58583855e-01 -3.50867851e+00]\n",
      " [ 4.75970231e-01  3.30117521e+00]\n",
      " [ 1.83309318e-01  4.63045294e+00]\n",
      " [-2.94273392e-01  6.86834902e-01]\n",
      " [-5.84543053e-03  1.62999769e+00]\n",
      " [ 4.85156894e-02  1.55499886e+00]\n",
      " [-2.44752447e-03 -9.55632732e-01]\n",
      " [-1.74288983e-01 -3.76689250e+00]\n",
      " [ 2.26102352e-01 -1.16728176e+00]\n",
      " [-5.62462759e-01 -7.00600373e+00]\n",
      " [ 7.87570344e-01  7.72653899e+00]\n",
      " [ 6.52161996e-01  5.10668023e+00]\n",
      " [ 2.87178191e-01  5.93763519e+00]\n",
      " [ 2.77242268e-01  3.60329184e+00]\n",
      " [ 7.22518981e-02  2.14799652e+00]\n",
      " [ 8.47760368e-01  6.36313977e+00]\n",
      " [ 4.40441165e-01  3.14631064e+00]\n",
      " [-5.05693139e-01 -3.11901041e+00]\n",
      " [-4.54103361e-01 -3.72962469e+00]\n",
      " [ 7.69602215e-02  1.59247732e-01]\n",
      " [-2.98042784e-03  5.69548772e-01]\n",
      " [ 2.05815467e-01  1.41291262e+00]\n",
      " [ 1.39351294e-01  2.86160197e+00]\n",
      " [ 7.25398744e-02 -7.30338111e-01]\n",
      " [ 7.67327642e-02  7.18908532e-02]\n",
      " [ 2.93530076e-01  1.66234945e+00]\n",
      " [-2.24837069e-01 -2.99360015e+00]\n",
      " [-5.11079192e-03 -6.64740373e-01]\n",
      " [ 2.27735837e-01  7.28308919e-01]\n",
      " [ 2.98236949e-01  2.73345725e+00]\n",
      " [ 1.00015400e-01  3.87100438e+00]\n",
      " [-8.91727078e-02  6.97112964e-01]\n",
      " [ 7.20259068e-01  6.32014667e+00]\n",
      " [ 8.49071767e-01  6.93622696e+00]\n",
      " [ 7.55635499e-02  1.91515503e+00]]\n"
     ]
    }
   ],
   "source": [
    "T = U.dot(Sigma)\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e4ef22d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(178, 2)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "72e7e008",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5686204d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "        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>فاکتور1</th>\n",
       "      <th>فاکتور 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-25.759221</td>\n",
       "      <td>-146.823276</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.295395</td>\n",
       "      <td>-28.785560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.489340</td>\n",
       "      <td>-5.780587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.106131</td>\n",
       "      <td>-0.819121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.788234</td>\n",
       "      <td>-29.698329</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     فاکتور1    فاکتور 2\n",
       "0 -25.759221 -146.823276\n",
       "1   4.295395  -28.785560\n",
       "2  -0.489340   -5.780587\n",
       "3   0.106131   -0.819121\n",
       "4  -1.788234  -29.698329"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_svd = pd.DataFrame(T, columns= ['فاکتور1', 'فاکتور 2'])\n",
    "data_svd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "231e3216",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>A</th>\n",
       "      <th>فاکتور1</th>\n",
       "      <th>فاکتور 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>-25.759221</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>4.295395</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>-0.489340</td>\n",
       "      <td>-5.780587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.106131</td>\n",
       "      <td>-0.819121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>-1.788234</td>\n",
       "      <td>-29.698329</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A    فاکتور1    فاکتور 2\n",
       "0  1 -25.759221 -146.823276\n",
       "1  1   4.295395  -28.785560\n",
       "2  1  -0.489340   -5.780587\n",
       "3  1   0.106131   -0.819121\n",
       "4  1  -1.788234  -29.698329"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_final = data[['A']]\n",
    "data_final = data_final.join(data_svd)\n",
    "data_final.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "37b43441",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_final.to_csv('C:\\\\ML\\\\dataset\\\\کاهش ابعاد دیتاست.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "4e809237",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>A</th>\n",
       "      <th>فاکتور1</th>\n",
       "      <th>فاکتور 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>-25.759221</td>\n",
       "      <td>-146.823276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4.295395</td>\n",
       "      <td>-28.785560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>-0.489340</td>\n",
       "      <td>-5.780587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0.106131</td>\n",
       "      <td>-0.819121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>-1.788234</td>\n",
       "      <td>-29.698329</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  A    فاکتور1    فاکتور 2\n",
       "0           0  1 -25.759221 -146.823276\n",
       "1           1  1   4.295395  -28.785560\n",
       "2           2  1  -0.489340   -5.780587\n",
       "3           3  1   0.106131   -0.819121\n",
       "4           4  1  -1.788234  -29.698329"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_final_file = pd.read_csv('C:\\\\ML\\\\dataset\\\\کاهش ابعاد دیتاست.csv')\n",
    "data_final_file.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "24ad4a55",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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