PCA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Simple Data</h3>\n",
    "Declaring Simplest, Uniform Data, Converted to DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = {\"samad\":[1,2,3,4,5,6,7,8,9,10],\n",
    "        \"misbah\":[1,2,3,4,5,6,7,8,9,10],\n",
    "        \"taha\":[1,2,3,4,5,6,7,8,9,10],\n",
    "        \"hashir\":[1,2,3,4,5,6,7,8,9,10],\n",
    "        \"saqib\":[1,2,3,4,5,6,7,8,9,10]\n",
    "       }\n",
    "df = pd.DataFrame(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
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       "      <th></th>\n",
       "      <th>samad</th>\n",
       "      <th>misbah</th>\n",
       "      <th>taha</th>\n",
       "      <th>hashir</th>\n",
       "      <th>saqib</th>\n",
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       "      <td>1</td>\n",
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       "      <td>2</td>\n",
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       "      <td>2</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   samad  misbah  taha  hashir  saqib\n",
       "0      1       1     1       1      1\n",
       "1      2       2     2       2      2\n",
       "2      3       3     3       3      3\n",
       "3      4       4     4       4      4\n",
       "4      5       5     5       5      5\n",
       "5      6       6     6       6      6\n",
       "6      7       7     7       7      7\n",
       "7      8       8     8       8      8\n",
       "8      9       9     9       9      9\n",
       "9     10      10    10      10     10"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Applying PCA</h3>\n",
    "Reducing 5 dimensions to 3 dimensions (defining principal component names as PC 1, PC 2 etc.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=3)\n",
    "principalComponents = pca.fit_transform(df)\n",
    "principalDf = pd.DataFrame(data = principalComponents,columns = ['PC 1','PC 2','PC 3'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC 1</th>\n",
       "      <th>PC 2</th>\n",
       "      <th>PC 3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>10.062306</td>\n",
       "      <td>9.948776e-16</td>\n",
       "      <td>-2.749356e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7.826238</td>\n",
       "      <td>-1.408494e-16</td>\n",
       "      <td>2.489337e-31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.590170</td>\n",
       "      <td>-2.140940e-16</td>\n",
       "      <td>-3.863646e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.354102</td>\n",
       "      <td>-8.873586e-17</td>\n",
       "      <td>-1.982426e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.118034</td>\n",
       "      <td>-6.267908e-17</td>\n",
       "      <td>-9.406099e-33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-1.118034</td>\n",
       "      <td>6.267908e-17</td>\n",
       "      <td>9.406099e-33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-3.354102</td>\n",
       "      <td>8.873586e-17</td>\n",
       "      <td>1.982426e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-5.590170</td>\n",
       "      <td>2.140940e-16</td>\n",
       "      <td>3.863646e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-7.826238</td>\n",
       "      <td>1.408494e-16</td>\n",
       "      <td>4.066058e-32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-10.062306</td>\n",
       "      <td>4.648103e-16</td>\n",
       "      <td>7.626085e-32</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC 1          PC 2          PC 3\n",
       "0  10.062306  9.948776e-16 -2.749356e-32\n",
       "1   7.826238 -1.408494e-16  2.489337e-31\n",
       "2   5.590170 -2.140940e-16 -3.863646e-32\n",
       "3   3.354102 -8.873586e-17 -1.982426e-32\n",
       "4   1.118034 -6.267908e-17 -9.406099e-33\n",
       "5  -1.118034  6.267908e-17  9.406099e-33\n",
       "6  -3.354102  8.873586e-17  1.982426e-32\n",
       "7  -5.590170  2.140940e-16  3.863646e-32\n",
       "8  -7.826238  1.408494e-16  4.066058e-32\n",
       "9 -10.062306  4.648103e-16  7.626085e-32"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "principalDf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Determine Information %</h3>\n",
    "The information (variance) preserved through PCA seems to be 100% in first column, the rest of the principle components seem to be overkill"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.00000000e+00, 3.29887288e-33, 1.79736710e-64])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Determine Required Principal Components</h3>\n",
    "One great way to determine the number of principal components requrired to optimize this data is use the following syntax, here \".99\" is given as parameter in PCA method to indicate our desired atleast 99% information preservation. It can be for example, .95 for atleast 95% Information preservation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required Principle Components:  1\n"
     ]
    }
   ],
   "source": [
    "pca2 = PCA(.99)\n",
    "pca2.fit(df) # df is our dataFrame which we need optimized\n",
    "print(\"Required Principle Components: \",pca2.n_components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Trying less mutually correlated data</h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "data2 = {\"samad\":[1,9,7,4,3,6,7,4,9,0],\n",
    "        \"misbah\":[1,25,3,4,2,56,37,88,19,1],\n",
    "        \"taha\":[10,3,34,41,50,60,70,82,91,10],\n",
    "        \"hashir\":[1,2,2,4,9,46,27,78,19,1],\n",
    "        \"saqib\":[1,2,3,4,5,6,7,8,9,10]\n",
    "       }\n",
    "df2 = pd.DataFrame(data2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
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       "      <td>2</td>\n",
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       "      <th>2</th>\n",
       "      <td>7</td>\n",
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       "      <td>9</td>\n",
       "      <td>5</td>\n",
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       "      <th>5</th>\n",
       "      <td>6</td>\n",
       "      <td>56</td>\n",
       "      <td>60</td>\n",
       "      <td>46</td>\n",
       "      <td>6</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>7</td>\n",
       "      <td>37</td>\n",
       "      <td>70</td>\n",
       "      <td>27</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4</td>\n",
       "      <td>88</td>\n",
       "      <td>82</td>\n",
       "      <td>78</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>9</td>\n",
       "      <td>19</td>\n",
       "      <td>91</td>\n",
       "      <td>19</td>\n",
       "      <td>9</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>10</td>\n",
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      "text/plain": [
       "   samad  misbah  taha  hashir  saqib\n",
       "0      1       1    10       1      1\n",
       "1      9      25     3       2      2\n",
       "2      7       3    34       2      3\n",
       "3      4       4    41       4      4\n",
       "4      3       2    50       9      5\n",
       "5      6      56    60      46      6\n",
       "6      7      37    70      27      7\n",
       "7      4      88    82      78      8\n",
       "8      9      19    91      19      9\n",
       "9      0       1    10       1     10"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Applying PCA</h3>\n",
    "Preserving 99% of data and using the required number of components (found 3) to fit new dataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Required Principle Components:  3\n",
      "Variance (Information Preservation) Ratio:  [0.81238218 0.17403154 0.0108426 ]\n"
     ]
    },
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-44.060586</td>\n",
       "      <td>-11.353987</td>\n",
       "      <td>-4.318756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-33.059303</td>\n",
       "      <td>-29.764600</td>\n",
       "      <td>10.453193</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-28.092372</td>\n",
       "      <td>6.734891</td>\n",
       "      <td>1.249974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-22.333105</td>\n",
       "      <td>11.178207</td>\n",
       "      <td>-0.661465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-15.519887</td>\n",
       "      <td>18.083251</td>\n",
       "      <td>-4.768428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>42.939398</td>\n",
       "      <td>-12.769779</td>\n",
       "      <td>0.181818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>27.096761</td>\n",
       "      <td>10.613268</td>\n",
       "      <td>4.573104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>92.459960</td>\n",
       "      <td>-21.029967</td>\n",
       "      <td>-4.213712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>24.349474</td>\n",
       "      <td>39.333287</td>\n",
       "      <td>3.672950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-43.780340</td>\n",
       "      <td>-11.024570</td>\n",
       "      <td>-6.168678</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1          2\n",
       "0 -44.060586 -11.353987  -4.318756\n",
       "1 -33.059303 -29.764600  10.453193\n",
       "2 -28.092372   6.734891   1.249974\n",
       "3 -22.333105  11.178207  -0.661465\n",
       "4 -15.519887  18.083251  -4.768428\n",
       "5  42.939398 -12.769779   0.181818\n",
       "6  27.096761  10.613268   4.573104\n",
       "7  92.459960 -21.029967  -4.213712\n",
       "8  24.349474  39.333287   3.672950\n",
       "9 -43.780340 -11.024570  -6.168678"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(.99)\n",
    "pca.fit(df2)\n",
    "print(\"Required Principle Components: \",pca.n_components_)\n",
    "\n",
    "pca = PCA(n_components=pca.n_components_)\n",
    "principalComponents = pca.fit_transform(df2)\n",
    "principalDf = pd.DataFrame(principalComponents)\n",
    "print(\"Variance (Information Preservation) Ratio: \",pca.explained_variance_ratio_)\n",
    "principalDf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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