KernalPCA(exponential).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "3b(B).ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "7jePkdnoP1ZP",
        "outputId": "db31996c-f8bc-4280-ebce-753f6715252c",
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": "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",
              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 73
        }
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy.linalg import eigh\n",
        "import matplotlib.pyplot as plt\n",
        "from google.colab import files\n",
        "uploaded=files.upload()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-0c33ee36-8677-423a-aac8-e09001fa2bdd\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-0c33ee36-8677-423a-aac8-e09001fa2bdd\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving Dataset3.csv to Dataset3 (1).csv\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U1P_E1sbYut8",
        "outputId": "33667ea6-402f-4d8d-d719-f0cca8be81a0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "source": [
        "import io\n",
        "data=pd.read_csv(io.BytesIO(uploaded['Dataset3.csv']),header=None)\n",
        "data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>0.14300</td>\n",
              "      <td>0.98493</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.30467</td>\n",
              "      <td>0.98562</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.46625</td>\n",
              "      <td>-0.84003</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.94847</td>\n",
              "      <td>0.37222</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.96871</td>\n",
              "      <td>-0.26697</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>4.48210</td>\n",
              "      <td>-7.40030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>-3.49630</td>\n",
              "      <td>8.63860</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>6.10620</td>\n",
              "      <td>-5.98640</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>-7.40940</td>\n",
              "      <td>-5.52050</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>-0.12948</td>\n",
              "      <td>-8.80360</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           0        1\n",
              "0    0.14300  0.98493\n",
              "1   -0.30467  0.98562\n",
              "2    0.46625 -0.84003\n",
              "3    0.94847  0.37222\n",
              "4   -0.96871 -0.26697\n",
              "..       ...      ...\n",
              "995  4.48210 -7.40030\n",
              "996 -3.49630  8.63860\n",
              "997  6.10620 -5.98640\n",
              "998 -7.40940 -5.52050\n",
              "999 -0.12948 -8.80360\n",
              "\n",
              "[1000 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 101
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "17McZ-1cYwX0",
        "outputId": "b1845f61-bcc5-4f17-bcdc-1576d9044496",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        }
      },
      "source": [
        "df=data.values.tolist()\n",
        "avg = np.full(data.shape,np.mean(data,axis=0))\n",
        "df=np.subtract(df,avg)\n",
        "sd = np.full(data.shape,np.std(df, axis = 0))\n",
        "df=np.divide(df,sd)\n",
        "df"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.03721355,  0.23990329],\n",
              "       [-0.07928601,  0.24007136],\n",
              "       [ 0.12133462, -0.20460953],\n",
              "       ...,\n",
              "       [ 1.58904894, -1.45813149],\n",
              "       [-1.92818785, -1.34465036],\n",
              "       [-0.03369538, -2.14432818]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 185
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3GqLMNn3Y0za",
        "outputId": "726118b0-e9c1-4db8-922a-8d81b4dac0cd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 514
        }
      },
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "plt.scatter(*zip(*df))\n",
        "plt.title('Scatter plot')\n",
        "plt.xlabel('Variable_1')\n",
        "plt.ylabel('Variable_2')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GnIHmvYS1B9n",
        "outputId": "86cb71b7-26f6-4f51-8be8-baecda7de150",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print (df.shape)\n",
        "X=df.T"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(1000, 2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ar4zMN3cOoBE"
      },
      "source": [
        "d,n=X.shape\n",
        "s=1.0\n",
        "g=2*s*s\n",
        "K = [[0 for i in range(n)] for j in range(n)]\n",
        "for i in range (0,n):\n",
        "  for j in range (0,n):\n",
        "    diff=X[:,i]-X[:,j]\n",
        "    dist = (diff[0]*diff[0]+diff[1]*diff[1])\n",
        "    K[i][j]=np.exp(-dist/g)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_MkIpM5bw1Sy",
        "outputId": "ee600083-98bf-45c5-dee7-008577f33293",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "I=np.identity(n)\n",
        "One_n=np.full_like(I,(1/n))\n",
        "M=I-One_n\n",
        "Kc=np.matmul(M,np.matmul(K,M))\n",
        "np.shape(Kc)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000, 1000)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 189
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vHgvow87wTwE",
        "outputId": "c5ff5a75-8453-420d-c32e-b57f7a7124d5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        }
      },
      "source": [
        "e_val, e_vec = eigh(Kc)\n",
        "id=np.argsort(e_val)[::-1]\n",
        "e_val=e_val[id]\n",
        "e_vec=e_vec[:,id]\n",
        "k=2\n",
        "Alpha_pc = np.column_stack([e_vec[:, i]\n",
        "                           for i in range(k)]) \n",
        "np.shape(Alpha_pc)\n",
        "Alpha_pc"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.04058419, -0.00937113],\n",
              "       [-0.04079713, -0.00213413],\n",
              "       [-0.03873797,  0.00194867],\n",
              "       ...,\n",
              "       [ 0.03820798, -0.01003174],\n",
              "       [ 0.04421458,  0.04031023],\n",
              "       [ 0.04065194,  0.02722035]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 190
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ubr6LRpoxAe9",
        "outputId": "e8c87690-d6f8-4960-d333-b4cd45c5e0ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        }
      },
      "source": [
        "for i in range (k):\n",
        " print (e_val[i])\n",
        "Alpha_scaled=np.column_stack([np.divide(Alpha_pc[:,i],np.sqrt(n*e_val[i])) for i in range(k)])\n",
        "Alpha_scaled"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "149.84718840436986\n",
            "116.2376247762836\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-1.04841336e-04, -2.74864546e-05],\n",
              "       [-1.05391424e-04, -6.25962216e-06],\n",
              "       [-1.00072001e-04,  5.71564785e-06],\n",
              "       ...,\n",
              "       [ 9.87028810e-05, -2.94240908e-05],\n",
              "       [ 1.14219750e-04,  1.18233870e-04],\n",
              "       [ 1.05016356e-04,  7.98399794e-05]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 191
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1haVktCplF6q",
        "outputId": "c68abfd8-97f7-4fe6-a82b-93963d6de749",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#Projection in PC_1\n",
        "Z_1=[]\n",
        "for i in range(n):\n",
        "  sum=0.0\n",
        "  for j in range (n):\n",
        "    sum=sum+Alpha_scaled[j][0]*K[i][j]\n",
        "  Z_1.append(sum)\n",
        "np.shape(Z_1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 192
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q6AlPcmM4xcB",
        "outputId": "d26ed6a5-0621-405b-ba06-a3a7aa5be8c8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "#Projection in PC_1\n",
        "Z_2=[]\n",
        "for i in range(n):\n",
        "  sum=0.0\n",
        "  for j in range (n):\n",
        "    sum=sum+Alpha_scaled[j][1]*K[i][j]\n",
        "  Z_2.append(sum)\n",
        "np.shape(Z_2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1000,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 193
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MfeD4dbP48Vw",
        "outputId": "2eae8ec0-0bd5-4779-8a00-6f0c8ca4865f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "plt.title('Scatter Plot on top 2 Pricipal components [s=1.0]')\n",
        "plt.xlabel('Pricipal Component 1')\n",
        "plt.ylabel('Principal Component 2')\n",
        "plt.scatter(Z_1,Z_2)\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}