3_pca_lecture.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_eFEAB9O9PFd"
   },
   "outputs": [],
   "source": [
    "data_dir = './data/'\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.decomposition import PCA\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 336
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 888,
     "status": "ok",
     "timestamp": 1565665958123,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "yyuvAvn19lCV",
    "outputId": "1e55455f-80a1-42c5-e5b8-818d2b3b7090"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.72770452 0.23030523]\n",
      "[[ 0.52237162 -0.26335492  0.58125401  0.56561105]\n",
      " [ 0.37231836  0.92555649  0.02109478  0.06541577]]\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": [
    "# まず具体例\n",
    "iris = pd.read_csv(data_dir+'iris.csv') # csvの読み込み\n",
    "X = iris.drop('class', axis=1) # Xは正解クラスを除く4次元の情報\n",
    "Y = iris['class'] # Yは正解クラス\n",
    "\n",
    "X_scaled = (X-X.mean())/X.std() # Xの正規化\n",
    "\n",
    "# 主成分分析(PCA)\n",
    "pca = PCA(n_components=2) # PCAのパラメータをセット(2次元)\n",
    "pca.fit(X_scaled) # PCAでXを2次元にするルール作り\n",
    "reduced_iris = pca.fit_transform(X_scaled) # 2次元にしたXをゲット\n",
    "\n",
    "# 2次元に圧縮したXをプロット\n",
    "colors = ['blue', 'red', 'Yellow'] # グラフの色\n",
    "uniqueY = pd.unique(Y) # 重複したクラスを削除（クラスのリストを取得）\n",
    "for i in range(len(uniqueY)):\n",
    "    Yi = uniqueY[i]\n",
    "    color = colors[i]\n",
    "    plt.scatter(reduced_iris[np.where(Y == Yi), 0],\n",
    "                             reduced_iris[np.where(Y == Yi), 1],c=color) # Xをプロット\n",
    "plt.xlabel('PC 1') # X軸のラベル\n",
    "plt.ylabel('PC 2') # Y軸のラベル\n",
    "\n",
    "\n",
    "print(pca.explained_variance_ratio_) # 2次元の各主成分の「寄与率」\n",
    "\n",
    "print(pca.components_) # 2次元の各主成分の「中身」\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 322
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1027,
     "status": "ok",
     "timestamp": 1565666079968,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "umzymW5c92FR",
    "outputId": "99d25e17-b2ad-44d4-8a48-cbb60f2ab503"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.68569351 1.27368233]\n",
      " [1.27368233 3.11317942]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x22584472ec8>"
      ]
     },
     "execution_count": 3,
     "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": [
    "# covariance between sepal_length and petal_length in iris data\n",
    "\n",
    "sepal_length = np.array(iris['sepal length'])\n",
    "petal_length = np.array(iris['petal length'])\n",
    "CC = np.cov(sepal_length,petal_length) # 共分散行列\n",
    "print(CC)\n",
    "plt.scatter(sepal_length,petal_length) # 散布図をプロット\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 140
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 607,
     "status": "ok",
     "timestamp": 1565666095014,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "peVvu6O1-HWx",
    "outputId": "cfc8a3a9-8b6d-424c-b9e0-89584e447902"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4. -1.]\n",
      "[[ 0.83205029 -0.70710678]\n",
      " [ 0.5547002   0.70710678]]\n",
      "[[3.32820118]\n",
      " [2.21880078]]\n",
      "[[3.32820118]\n",
      " [2.21880078]]\n"
     ]
    }
   ],
   "source": [
    "# 固有値と固有ベクトル\n",
    "A = np.matrix([[2,3], [2,1]])\n",
    "\n",
    "from numpy import linalg as LA\n",
    "\n",
    "# 固有値と固有ベクトルを算出\n",
    "(eigenvalues, eigenvectors) = LA.eig(A)\n",
    "\n",
    "print(eigenvalues) # 固有値\n",
    "print(eigenvectors) # 固有ベクトル\n",
    "\n",
    "# 本当に合ってるか確認\n",
    "e_vec1 = eigenvectors[:,0] # 第一固有ベクトル\n",
    "e_val1 = eigenvalues[0] # 第一固有値\n",
    "\n",
    "# 固有ベクトルの条件を満たしている(Ae = λe)\n",
    "print(np.dot(A, e_vec1))\n",
    "print(e_val1*e_vec1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "KfP6UYG7-LjL"
   },
   "outputs": [],
   "source": [
    "# sepal_length　と petal_length の共分散行列の固有値\n",
    "# Read iris dataset\n",
    "iris = pd.read_csv(data_dir+'iris.csv')\n",
    "X = iris.drop(['sepal width','petal width','class'], axis=1)\n",
    "\n",
    "# Normalize the data\n",
    "# 正規化なし\n",
    "#X_scaled = (X-X.mean())/X.std()\n",
    "X_scaled = (X-X.mean())\n",
    "\n",
    "# Transform input data into an np.array\n",
    "Y = np.array(X_scaled)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 87
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 645,
     "status": "ok",
     "timestamp": 1565666146012,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "7vzgPC6f-TLn",
    "outputId": "073ffdda-eb6e-4601-ca8c-37783b25bdf0"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained variance ratio:  [0.03686636 0.96313364]\n",
      "the 2 principal vectors: \n",
      " [[-0.91920275  0.39378459]\n",
      " [-0.39378459 -0.91920275]]\n"
     ]
    }
   ],
   "source": [
    "# Compute the covariance matrix\n",
    "cov_matrix = np.cov(Y.transpose())\n",
    "\n",
    "# Compute the eigen values and eigen vectors\n",
    "(l,V) = np.linalg.eig(cov_matrix)\n",
    "\n",
    "print(\"Explained variance ratio: \", l/l.sum())\n",
    "print(\"the 2 principal vectors: \\n\", V.transpose())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 70
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 593,
     "status": "ok",
     "timestamp": 1565666161300,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "dl62_x4s-aOj",
    "outputId": "a5a0b5de-cd67-4587-a22e-fb77a2737613"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.96313364 0.03686636]\n",
      "[[ 0.39378459  0.91920275]\n",
      " [-0.91920275  0.39378459]]\n"
     ]
    }
   ],
   "source": [
    "# PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X_scaled)\n",
    "\n",
    "# 先程の結果とPCA関数による結果を比較\n",
    "print(pca.explained_variance_ratio_) # 2次元の各主成分の「寄与率」\n",
    "print(pca.components_) # 2次元の各主成分の「中身」\n",
    "\n",
    "A = pca.components_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 712,
     "status": "ok",
     "timestamp": 1565666179105,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "1HpaXTv9-btX",
    "outputId": "f1eb6f88-5c33-4b6c-e4c5-5b567c5e7b3a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4, 4)"
      ]
     },
     "execution_count": 8,
     "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": [
    "# 第一主成分\n",
    "a = A[0][1]/A[0][0]\n",
    "xx = [min(X_scaled['sepal length']) + 0.01*(max(X_scaled['sepal length'])\n",
    "-min(X_scaled['sepal length']))*i for i in range(101)]\n",
    "yy = [xx[i]*a for i in range(len(xx))]\n",
    "# 第二主成分\n",
    "b = A[1][1]/A[1][0]\n",
    "xx2 = [min(X_scaled['sepal length']) + 0.01*(max(X_scaled['sepal length'])\n",
    "-min(X_scaled['sepal length']))*i for i in range(101)]\n",
    "yy2 = [xx2[i]*b for i in range(len(xx))]\n",
    "# 表示\n",
    "plt.scatter(X_scaled['sepal length'],X_scaled['petal length'])\n",
    "plt.scatter(xx,yy)\n",
    "plt.scatter(xx2,yy2)\n",
    "plt.axis('scaled')\n",
    "plt.xlim([-4,4])\n",
    "plt.ylim([-4,4])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 87
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 764,
     "status": "ok",
     "timestamp": 1565666198232,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "10dDPIw--jH3",
    "outputId": "2bc49567-c9f6-4dfa-8876-dc2d04df5712"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explained variance ratio:  [0.93587708 0.06412292]\n",
      "the 2 principal vectors: \n",
      " [[ 0.70710678  0.70710678]\n",
      " [-0.70710678  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "##### 正規化あり\n",
    "X_scaled = (X-X.mean())/X.std()\n",
    "\n",
    "# Transform input data into an np.array\n",
    "Y = np.array(X_scaled)\n",
    "\n",
    "# Compute the covariance matrix\n",
    "cov_matrix = np.cov(Y.transpose())\n",
    "\n",
    "# Compute the eigen values and eigen vectors\n",
    "(l,V) = np.linalg.eig(cov_matrix)\n",
    "\n",
    "print(\"Explained variance ratio: \", l/l.sum())\n",
    "print(\"the 2 principal vectors: \\n\", V.transpose())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 70
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 601,
     "status": "ok",
     "timestamp": 1565666213796,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "OHvNEjiz-nCp",
    "outputId": "332dc295-7844-49a1-9da5-99599995ba5e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.93587708 0.06412292]\n",
      "[[ 0.70710678  0.70710678]\n",
      " [-0.70710678  0.70710678]]\n"
     ]
    }
   ],
   "source": [
    "# PCA\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X_scaled)\n",
    "\n",
    "# 先程の結果とPCA関数による結果を比較\n",
    "print(pca.explained_variance_ratio_) # 2次元の各主成分の「寄与率」\n",
    "print(pca.components_) # 2次元の各主成分の「中身」\n",
    "\n",
    "A = pca.components_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1002,
     "status": "ok",
     "timestamp": 1565666229573,
     "user": {
      "displayName": "竜馬備瀬",
      "photoUrl": "",
      "userId": "17932567482837919211"
     },
     "user_tz": -540
    },
    "id": "vUCi5gkV-oUb",
    "outputId": "2bf1d230-6624-4c80-9193-109802a4f927"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4, 4)"
      ]
     },
     "execution_count": 11,
     "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": [
    "# 第一主成分\n",
    "a = A[0][1]/A[0][0]\n",
    "xx = [min(X_scaled['sepal length']) + 0.01*(max(X_scaled['sepal length'])\n",
    "-min(X_scaled['sepal length']))*i for i in range(101)]\n",
    "yy = [xx[i]*a for i in range(len(xx))]\n",
    "# 第二主成分\n",
    "b = A[1][1]/A[1][0]\n",
    "xx2 = [min(X_scaled['sepal length']) + 0.01*(max(X_scaled['sepal length'])\n",
    "-min(X_scaled['sepal length']))*i for i in range(101)]\n",
    "yy2 = [xx2[i]*b for i in range(len(xx))]\n",
    "# 表示\n",
    "plt.scatter(X_scaled['sepal length'],X_scaled['petal length'])\n",
    "plt.scatter(xx,yy)\n",
    "plt.scatter(xx2,yy2)\n",
    "plt.axis('scaled')\n",
    "plt.xlim([-4,4])\n",
    "plt.ylim([-4,4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "name": "PCA.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}