Principal Component Analysis to Reduce the Dimension of the Dataset..ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 187,
   "id": "76ce9576",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "79153f53",
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
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       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
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       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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      ],
      "text/plain": [
       "   Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm      Species\n",
       "0   1            5.1           3.5            1.4           0.2  Iris-setosa\n",
       "1   2            4.9           3.0            1.4           0.2  Iris-setosa\n",
       "2   3            4.7           3.2            1.3           0.2  Iris-setosa\n",
       "3   4            4.6           3.1            1.5           0.2  Iris-setosa\n",
       "4   5            5.0           3.6            1.4           0.2  Iris-setosa"
      ]
     },
     "execution_count": 188,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('iris.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "85467d0b",
   "metadata": {
    "scrolled": true
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   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
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       "      <th>2</th>\n",
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       "      <td>Iris-setosa</td>\n",
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      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm      Species\n",
       "0            5.1           3.5            1.4           0.2  Iris-setosa\n",
       "1            4.9           3.0            1.4           0.2  Iris-setosa\n",
       "2            4.7           3.2            1.3           0.2  Iris-setosa\n",
       "3            4.6           3.1            1.5           0.2  Iris-setosa\n",
       "4            5.0           3.6            1.4           0.2  Iris-setosa"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.drop(['Id'], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "id": "cabff3cf",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Iris-setosa', 'Iris-versicolor', 'Iris-virginica'], dtype=object)"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.unique(df[['Species']].values.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "id": "d0b428b1",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
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      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  Species\n",
       "0            5.1           3.5            1.4           0.2        0\n",
       "1            4.9           3.0            1.4           0.2        0\n",
       "2            4.7           3.2            1.3           0.2        0\n",
       "3            4.6           3.1            1.5           0.2        0\n",
       "4            5.0           3.6            1.4           0.2        0"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_encoded_values = {\"Species\": {\"Iris-setosa\": 0, \"Iris-versicolor\": 1, \"Iris-virginica\" : 2}}\n",
    "df = df.replace(target_encoded_values)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "id": "e36821b0",
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   "outputs": [
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       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  Species\n",
       "0            5.1           3.5            1.4           0.2        0\n",
       "1            4.9           3.0            1.4           0.2        0\n",
       "2            4.7           3.2            1.3           0.2        0\n",
       "3            4.6           3.1            1.5           0.2        0\n",
       "4            5.0           3.6            1.4           0.2        0\n",
       "5            5.4           3.9            1.7           0.4        0\n",
       "6            4.6           3.4            1.4           0.3        0\n",
       "7            5.0           3.4            1.5           0.2        0\n",
       "8            4.4           2.9            1.4           0.2        0\n",
       "9            4.9           3.1            1.5           0.1        0"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "0a110392",
   "metadata": {},
   "outputs": [
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       "      <th>SepalLengthCm</th>\n",
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      "text/plain": [
       "   SepalLengthCm\n",
       "0            5.1\n",
       "1            4.9\n",
       "2            4.7\n",
       "3            4.6\n",
       "4            5.0"
      ]
     },
     "execution_count": 193,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = df.iloc[:, :1]\n",
    "x.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "0616061a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>PetalWidthCm</th>\n",
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       "      <th>0</th>\n",
       "      <td>0.2</td>\n",
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      ],
      "text/plain": [
       "   PetalWidthCm\n",
       "0           0.2\n",
       "1           0.2\n",
       "2           0.2\n",
       "3           0.2\n",
       "4           0.2"
      ]
     },
     "execution_count": 194,
     "metadata": {},
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   ],
   "source": [
    "y = df.iloc[:, 3:4]\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "6803e452",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotVectors(vecs, cols):\n",
    "    plt.figure()\n",
    "    plt.axvline(x=0, color='#A9A9A9', zorder=0)\n",
    "    plt.axhline(y=0, color='#A9A9A9', zorder=0)\n",
    "    for i in range(len(vecs)):\n",
    "        x = np.concatenate([[0,0],vecs[i]])\n",
    "        plt.quiver([x[0]],\n",
    "                   [x[1]],\n",
    "                   [x[2]],\n",
    "                   [x[3]],\n",
    "                   angles='xy', scale_units='xy', scale=1, color=cols[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13788643",
   "metadata": {},
   "source": [
    "# 1. Principal Component Analysis using Correlation Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c39444a",
   "metadata": {},
   "source": [
    "## Performing the PCA on Two Features"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d11be9bc",
   "metadata": {},
   "source": [
    "### 1. Standardization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "310b0e69",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.array(x).flatten()\n",
    "y = np.array(y).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "dd110eb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = (x - np.mean(x))/(np.std(x))\n",
    "y = (y - np.mean(y))/(np.std(y))\n",
    "vecs = []\n",
    "for i in range(len(x)):\n",
    "    vecs.append((x[i], y[i]))\n",
    "for items in vecs:\n",
    "    vec = np.array(items)\n",
    "    plt.scatter(vec[0], vec[1], c='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85df93e7",
   "metadata": {},
   "source": [
    "### 2. Co-Variance Matrix for the variables X and Y "
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "78bc8592",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "4495c45d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         0.81795363]\n",
      " [0.81795363 1.        ]]\n"
     ]
    }
   ],
   "source": [
    "covXX = 0\n",
    "covYY = 0\n",
    "covXY = 0\n",
    "covYX = 0\n",
    "for i in range(len(x)):\n",
    "    covXX += (x[i] - np.mean(x))*(x[i] - np.mean(x))\n",
    "    covXY += (x[i] - np.mean(x))*(y[i] - np.mean(y))\n",
    "    covYX += (y[i] - np.mean(y))*(x[i] - np.mean(x))\n",
    "    covYY += (y[i] - np.mean(y))*(y[i] - np.mean(y))\n",
    "covXX = covXX/len(x)\n",
    "covXY = covXY/len(x)\n",
    "covYX = covYX/len(x)\n",
    "covYY = covYY/len(x)\n",
    "\n",
    "covMatrix = np.array([[covXX,covXY],[covYX,covYY]])\n",
    "\n",
    "print(covMatrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "5188f4aa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.18204637 1.81795363] \n",
      "\n",
      "[[-0.70710678 -0.70710678]\n",
      " [ 0.70710678 -0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "eig_val, eig_vec = np.linalg.eig(covMatrix)\n",
    "print(eig_val, \"\\n\")\n",
    "print(eig_vec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "2f54fa99",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0, 1.0)"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotVectors([eig_vec[0].flatten(), eig_vec[1].flatten()], cols=['red', 'orange'])\n",
    "plt.ylim(-1, 1)\n",
    "plt.xlim(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "6c24b9cf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "90.8976816684582 9.102318331541802\n"
     ]
    }
   ],
   "source": [
    "pca1 = eig_val[1] / (eig_val[0] + eig_val[1])\n",
    "pca2 = eig_val[0] / (eig_val[0] + eig_val[1])\n",
    "print(pca1*100, pca2*100)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e185c55",
   "metadata": {},
   "source": [
    "Since the data in the second eigen vector consists more significance than the first vector, we create a new vector with the second vector as it's first component and the first vector as it's second."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "65d6bde5",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 2) (2, 150)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ds = np.array(vecs)\n",
    "print(eig_vec.shape, ds.T.shape)\n",
    "PCA_DS = np.matmul(eig_vec, ds.T)\n",
    "PCA_DS = PCA_DS.T\n",
    "for vec in vecs:\n",
    "    plt.scatter(vec[0], vec[1], color='blue')\n",
    "for array in PCA_DS:\n",
    "    plt.scatter(PCA_DS[:, 0], PCA_DS[:, 1], color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "id": "7b2f9a24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.830155e+00</td>\n",
       "      <td>5.543664e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.543664e-16</td>\n",
       "      <td>1.832682e-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              0             1\n",
       "0  1.830155e+00  5.543664e-16\n",
       "1  5.543664e-16  1.832682e-01"
      ]
     },
     "execution_count": 203,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA_DS = pd.DataFrame(PCA_DS)\n",
    "PCA_DS.cov()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e0138a8",
   "metadata": {},
   "source": [
    "# Performing PCA on the whole Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d192768",
   "metadata": {},
   "source": [
    "### 1. Standardizing the Whole Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "id": "c20b57e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm\n",
       "0            5.1           3.5            1.4           0.2\n",
       "1            4.9           3.0            1.4           0.2\n",
       "2            4.7           3.2            1.3           0.2\n",
       "3            4.6           3.1            1.5           0.2\n",
       "4            5.0           3.6            1.4           0.2"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = df.iloc[:, 0:4]\n",
    "features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "73bd1f98",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.897674</td>\n",
       "      <td>1.028611</td>\n",
       "      <td>-1.336794</td>\n",
       "      <td>-1.308593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-1.139200</td>\n",
       "      <td>-0.124540</td>\n",
       "      <td>-1.336794</td>\n",
       "      <td>-1.308593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-1.380727</td>\n",
       "      <td>0.336720</td>\n",
       "      <td>-1.393470</td>\n",
       "      <td>-1.308593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.501490</td>\n",
       "      <td>0.106090</td>\n",
       "      <td>-1.280118</td>\n",
       "      <td>-1.308593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.018437</td>\n",
       "      <td>1.259242</td>\n",
       "      <td>-1.336794</td>\n",
       "      <td>-1.308593</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm\n",
       "0      -0.897674      1.028611      -1.336794     -1.308593\n",
       "1      -1.139200     -0.124540      -1.336794     -1.308593\n",
       "2      -1.380727      0.336720      -1.393470     -1.308593\n",
       "3      -1.501490      0.106090      -1.280118     -1.308593\n",
       "4      -1.018437      1.259242      -1.336794     -1.308593"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = (features - features.mean()) / features.std()\n",
    "features.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff26a5c8",
   "metadata": {},
   "source": [
    "### 2. Generating a covariance matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "53616f8d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "               SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm\n",
      "SepalLengthCm       1.000000     -0.109369       0.871754      0.817954\n",
      "SepalWidthCm       -0.109369      1.000000      -0.420516     -0.356544\n",
      "PetalLengthCm       0.871754     -0.420516       1.000000      0.962757\n",
      "PetalWidthCm        0.817954     -0.356544       0.962757      1.000000\n"
     ]
    }
   ],
   "source": [
    "cov_matrix = features.cov()\n",
    "print(cov_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "9c90968a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov_matrix = np.array(cov_matrix)\n",
    "cov_matrix.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "1fcfce89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.         -0.10936925  0.87175416  0.81795363]\n",
      " [-0.10936925  1.         -0.4205161  -0.35654409]\n",
      " [ 0.87175416 -0.4205161   1.          0.9627571 ]\n",
      " [ 0.81795363 -0.35654409  0.9627571   1.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(cov_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c2d42d1",
   "metadata": {},
   "source": [
    "### 3. Finding the Eigen Values and The Eigen Vectors of the Above Co-Variance Matrix "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "id": "bab88d00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The eigen values are given as:\n",
      "[2.91081808 0.92122093 0.14735328 0.02060771]\n",
      "\n",
      "The Eigen Vectors are given as:\n",
      "[[ 0.52237162 -0.37231836 -0.72101681  0.26199559]\n",
      " [-0.26335492 -0.92555649  0.24203288 -0.12413481]\n",
      " [ 0.58125401 -0.02109478  0.14089226 -0.80115427]\n",
      " [ 0.56561105 -0.06541577  0.6338014   0.52354627]]\n",
      "\n",
      "Where each column represents a single eigen vector.\n"
     ]
    }
   ],
   "source": [
    "eig_values, eig_vectors = np.linalg.eig(cov_matrix)\n",
    "print(f'The eigen values are given as:\\n{eig_values}\\n\\nThe Eigen Vectors are given as:\\n{eig_vectors}\\n\\nWhere each column represents a single eigen vector.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a949e12",
   "metadata": {},
   "source": [
    "So, we transpose the matrix, to get the values represented in rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "id": "dea91f16",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.52237162 -0.26335492  0.58125401  0.56561105]\n",
      " [-0.37231836 -0.92555649 -0.02109478 -0.06541577]\n",
      " [-0.72101681  0.24203288  0.14089226  0.6338014 ]\n",
      " [ 0.26199559 -0.12413481 -0.80115427  0.52354627]]\n"
     ]
    }
   ],
   "source": [
    "eig_vectors = eig_vectors.T\n",
    "print(eig_vectors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "id": "bc18fd0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0, 1.0)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotVectors([eig_vectors[0].flatten(), eig_vectors[1].flatten(), eig_vectors[2], eig_vectors[3]], cols=['red', 'orange', 'blue', 'black'])\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "456f0a89",
   "metadata": {},
   "source": [
    "Now we see the significance of each eigen value for the entire dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "771b616b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The significance of PCA0 is: 72.77%\n",
      "The significance of PCA1 is: 23.03%\n",
      "The significance of PCA2 is: 3.68%\n",
      "The significance of PCA3 is: 0.52%\n"
     ]
    }
   ],
   "source": [
    "indices = []\n",
    "for i in range(len(eig_values)):\n",
    "    sig_n = eig_values[i] / np.sum(eig_values) * 100\n",
    "    print(f'The significance of PCA{i} is: {round(sig_n, 2)}%')\n",
    "    if sig_n > 5:\n",
    "        indices.append(i)\n",
    "PCAs = eig_vectors[indices]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10e91d5a",
   "metadata": {},
   "source": [
    "So the component which is less than 5%, we remove the eigen vector of that particular eigen value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "04cd125e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.52237162 -0.26335492  0.58125401  0.56561105]\n",
      " [-0.37231836 -0.92555649 -0.02109478 -0.06541577]]\n"
     ]
    }
   ],
   "source": [
    "print(PCAs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12a0b09c",
   "metadata": {},
   "source": [
    "We watch the first two dimensions of the two Eigen Vectors (**Principal Component Vectors**)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "87bc6edb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0, 1.0)"
      ]
     },
     "execution_count": 214,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotVectors([PCAs[0].flatten(), PCAs[1].flatten()], cols=['red', 'orange'])\n",
    "plt.xlim(-1, 1)\n",
    "plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18d98b87",
   "metadata": {},
   "source": [
    "### 4. Now Finally we multiply our Eigen Vectors lists with our Original Feature Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "id": "2179d82b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 4) (150, 4)\n"
     ]
    }
   ],
   "source": [
    "print(PCAs.shape, features.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "id": "b16af697",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n"
     ]
    }
   ],
   "source": [
    "PCA_features = np.matmul(PCAs, features.T)\n",
    "PCA_features = PCA_features.T\n",
    "print(PCA_features.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "d03426d2",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.256981</td>\n",
       "      <td>-0.504015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.079459</td>\n",
       "      <td>0.653216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.360044</td>\n",
       "      <td>0.317414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.296504</td>\n",
       "      <td>0.573447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.380802</td>\n",
       "      <td>-0.672514</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1\n",
       "0 -2.256981 -0.504015\n",
       "1 -2.079459  0.653216\n",
       "2 -2.360044  0.317414\n",
       "3 -2.296504  0.573447\n",
       "4 -2.380802 -0.672514"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA_features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "1d61885a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PC1</th>\n",
       "      <th>PC2</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.256981</td>\n",
       "      <td>-0.504015</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.079459</td>\n",
       "      <td>0.653216</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.360044</td>\n",
       "      <td>0.317414</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.296504</td>\n",
       "      <td>0.573447</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.380802</td>\n",
       "      <td>-0.672514</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC1       PC2  Species\n",
       "0 -2.256981 -0.504015        0\n",
       "1 -2.079459  0.653216        0\n",
       "2 -2.360044  0.317414        0\n",
       "3 -2.296504  0.573447        0\n",
       "4 -2.380802 -0.672514        0"
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA_features = PCA_features.rename(columns={0: \"PC1\", 1:\"PC2\"})\n",
    "PCA_features = pd.concat([PCA_features, df['Species']], axis=1)\n",
    "PCA_features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "id": "1a753d82",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='PC1', ylabel='PC2'>"
      ]
     },
     "execution_count": 219,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.scatterplot(data=PCA_features, x = \"PC1\", y = \"PC2\", palette='icefire', hue=\"Species\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7b2df2b",
   "metadata": {},
   "source": [
    "# Applying Singular Value Decomposition for Finding out the Principle Components"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "9fbdfef8",
   "metadata": {},
   "source": [
    "### Expression for SVD:\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 220,
   "id": "3cd2331d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm\n",
       "0            5.1           3.5            1.4           0.2\n",
       "1            4.9           3.0            1.4           0.2\n",
       "2            4.7           3.2            1.3           0.2\n",
       "3            4.6           3.1            1.5           0.2\n",
       "4            5.0           3.6            1.4           0.2"
      ]
     },
     "execution_count": 220,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = features = df.iloc[:, 0:4]\n",
    "features.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "168b69b9",
   "metadata": {},
   "source": [
    "A'A = V &^2 V' <br>\n",
    "A A'= U &^2 U'\n",
    "#### Finally,\n",
    "### A = U & V'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "id": "667b4c8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 221,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "features = np.array(features)\n",
    "features.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c51fc715",
   "metadata": {},
   "source": [
    "We can see that our feature matrix is a rectangular matrix, now we find out the **A'A**\n",
    "of our features matrix and call it M.\n",
    "We also find **AA'** of the feature matrix and call it N."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "c261e02a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 4) (150, 150)\n"
     ]
    }
   ],
   "source": [
    "M = np.matmul(features.T, features)\n",
    "N = np.matmul(features, features.T)\n",
    "print(M.shape, N.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "id": "3d3bc566",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5223.85 2670.98 3484.25 1127.65]\n",
      " [2670.98 1427.05 1673.91  531.53]\n",
      " [3484.25 1673.91 2583.    868.97]\n",
      " [1127.65  531.53  868.97  302.3 ]]\n"
     ]
    }
   ],
   "source": [
    "print(M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "1c866a0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[40.26 37.49 37.03 ... 51.33 51.54 48.09]\n",
      " [37.49 35.01 34.49 ... 48.53 48.6  45.41]\n",
      " [37.03 34.49 34.06 ... 47.31 47.5  44.32]\n",
      " ...\n",
      " [51.33 48.53 47.31 ... 82.29 83.18 77.47]\n",
      " [51.54 48.6  47.5  ... 83.18 84.45 78.46]\n",
      " [48.09 45.41 44.32 ... 77.47 78.46 73.06]]\n"
     ]
    }
   ],
   "source": [
    "print(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "id": "cd3cc2d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "lam_M, V = np.linalg.eig(M)\n",
    "lam_N, U = np.linalg.eig(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "id": "64cd205f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9.20653060e+03 3.14103073e+02 1.20360193e+01 3.53031167e+00]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(4,)"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(lam_M)\n",
    "lam_M.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "id": "0e89d8de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.75116805  0.37978837  0.51315094  0.16787934]\n",
      " [ 0.28583096  0.54488976 -0.70889874 -0.34475845]\n",
      " [ 0.49942378 -0.67502499 -0.05471983 -0.54029889]\n",
      " [ 0.32345496 -0.32124324 -0.48077482  0.74902286]]\n"
     ]
    }
   ],
   "source": [
    "V = V.T\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "id": "fbb5fa68",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The significance of PCA0 is: 96.54%\n",
      "The significance of PCA1 is: 3.29%\n",
      "The significance of PCA2 is: 0.13%\n",
      "The significance of PCA3 is: 0.04%\n"
     ]
    }
   ],
   "source": [
    "indices = []\n",
    "for i in range(len(lam_M)):\n",
    "    sig_n = lam_M[i] / np.sum(lam_M) * 100\n",
    "    print(f'The significance of PCA{i} is: {round(sig_n, 2)}%')\n",
    "    if sig_n > 2:\n",
    "        indices.append(i)\n",
    "PCAs = V[indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "id": "46f807bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.75116805  0.28583096  0.49942378  0.32345496]\n",
      " [ 0.37978837  0.54488976 -0.67502499 -0.32124324]]\n"
     ]
    }
   ],
   "source": [
    "print(PCAs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 257,
   "id": "0c6b63fa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for vectors in PCAs:\n",
    "    plotVectors([vectors], cols=['red'])\n",
    "    plt.xlim(-1, 1)\n",
    "    plt.ylim(-1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "id": "ccdcf0d7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 4) (150, 4)\n"
     ]
    }
   ],
   "source": [
    "print(PCAs.shape, features.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "id": "301e0e42",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n"
     ]
    }
   ],
   "source": [
    "PCA_features = np.matmul(PCAs, features.T)\n",
    "PCA_features = PCA_features.T\n",
    "print(PCA_features.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 261,
   "id": "2677e4f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PA_1</th>\n",
       "      <th>PA_2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.595250</td>\n",
       "      <td>2.834751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.302101</td>\n",
       "      <td>2.486349</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.159091</td>\n",
       "      <td>2.586871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.155276</td>\n",
       "      <td>2.359399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.548716</td>\n",
       "      <td>2.851261</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       PA_1      PA_2\n",
       "0  5.595250  2.834751\n",
       "1  5.302101  2.486349\n",
       "2  5.159091  2.586871\n",
       "3  5.155276  2.359399\n",
       "4  5.548716  2.851261"
      ]
     },
     "execution_count": 261,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA_features = pd.DataFrame(PCA_features, columns = ['PA_1', 'PA_2'])\n",
    "PCA_features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 262,
   "id": "e4fe43f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PA_1</th>\n",
       "      <th>PA_2</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.595250</td>\n",
       "      <td>2.834751</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.302101</td>\n",
       "      <td>2.486349</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.159091</td>\n",
       "      <td>2.586871</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.155276</td>\n",
       "      <td>2.359399</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.548716</td>\n",
       "      <td>2.851261</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       PA_1      PA_2  Species\n",
       "0  5.595250  2.834751        0\n",
       "1  5.302101  2.486349        0\n",
       "2  5.159091  2.586871        0\n",
       "3  5.155276  2.359399        0\n",
       "4  5.548716  2.851261        0"
      ]
     },
     "execution_count": 262,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PCA_features = pd.concat([PCA_features, df['Species']], axis=1)\n",
    "PCA_features.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 264,
   "id": "a6929f04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='PA_1', ylabel='PA_2'>"
      ]
     },
     "execution_count": 264,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(data=PCA_features, x = \"PA_1\", y = \"PA_2\", palette='icefire', hue=\"Species\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e265805",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}