{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "cell_id": "f6a27e2085c84834892fb19b1abf31c4",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 664,
    "execution_start": 1660293330892,
    "source_hash": "ee2dcee6",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "数据集大小： 500\n"
     ]
    },
    {
     "data": {
      "image/png": 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ddkMur74aeII26z/qOCCI7fndNNrpTuEfv1KilkfLJlIwWZLZyrbVPfk2qnNF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\nhJBaQVEjhNSK/w8EjaQDPH4zSAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eca7e0fba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 导入数据集\n",
    "data = np.loadtxt('PCA_dataset.csv', delimiter=',')\n",
    "print('数据集大小：', len(data))\n",
    "\n",
    "# 可视化\n",
    "plt.figure()\n",
    "plt.scatter(data[:, 0], data[:, 1], color='blue', s=10)\n",
    "plt.axis('square')\n",
    "plt.ylim(-2, 8)\n",
    "plt.grid()\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "cell_id": "6f97733b0a20476a91144869e008b297",
    "collapsed": true,
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 2,
    "execution_start": 1660293078045,
    "id": "E74EC9FF8CDC4271872000B35DA48AA0",
    "jupyter": {},
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "source_hash": "d4408561",
    "tags": []
   },
   "outputs": [],
   "source": [
    "def pca(X, k):\n",
    "    d, m = X.shape\n",
    "    if d < k:\n",
    "        print('k应该小于特征数')\n",
    "        return X, None\n",
    "\n",
    "    # 中心化\n",
    "    X = X - np.mean(X, axis=0)\n",
    "    # 计算协方差矩阵\n",
    "    cov = X.T @ X\n",
    "    # 计算特征值和特征向量\n",
    "    eig_values, eig_vectors = np.linalg.eig(cov)\n",
    "    # 获取最大的k个特征值的下标\n",
    "    idx = np.argsort(-eig_values)[:k]\n",
    "    # 对应的特征向量\n",
    "    W = eig_vectors[:, idx]\n",
    "    # 降维\n",
    "    X = X @ W\n",
    "    return X, W"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "cell_id": "9330cd1cb3bb414cbc53904bab40eb4a",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 855,
    "execution_start": 1660293382703,
    "source_hash": "1277cc9c",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "变换矩阵：\n",
      " [[ 0.90322448 -0.42916843]\n",
      " [ 0.42916843  0.90322448]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bs87qrpyi43XvlSeeAG65ZW3NDy5LS9mIS0VNAmsldZSvnklR1Lot9CyLKfJo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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eca8f957f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, W = pca(data, 2)\n",
    "print('变换矩阵：\\n', W)\n",
    "\n",
    "# 绘图\n",
    "plt.figure()\n",
    "plt.scatter(X[:, 0], X[:, 1], color='blue', s=10)\n",
    "plt.axis('square')\n",
    "plt.ylim(-5, 5)\n",
    "plt.grid()\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "cell_id": "9ebd28c5c3824975bc68378a5793d108",
    "deepnote_cell_type": "code",
    "deepnote_to_be_reexecuted": false,
    "execution_millis": 253,
    "execution_start": 1660293646968,
    "id": "5094FD114B51443EACDAB2D0C183285D",
    "jupyter": {},
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    },
    "source_hash": "f1a5a4a7",
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sklearn计算的变换矩阵：\n",
      " [[-0.90322448  0.42916843]\n",
      " [-0.42916843 -0.90322448]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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3p2EEC2VWbXsN21mucuL2aXv2ZLdXm5lpn1ArNRpSON5k3jHDNo1A6/QJWW1N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\nFEtCCDHw/wHKxnPxSAVZRQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1eca900a320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# 中心化\n",
    "X = data - np.mean(data, axis=0)\n",
    "pca_res = PCA(n_components=2).fit(X)\n",
    "W = pca_res.components_.T\n",
    "print ('sklearn计算的变换矩阵：\\n', W)\n",
    "X_pca = X @ W\n",
    "\n",
    "# 绘图\n",
    "plt.figure()\n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1], color='blue', s=10)\n",
    "plt.axis('square')\n",
    "plt.ylim(-5, 5)\n",
    "plt.grid()\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "deepnote": {},
  "deepnote_execution_queue": [],
  "deepnote_notebook_id": "1c69d9d8957b4e07a2c94ce4117cb5c4",
  "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}