scikit-learnのPCAは中心化する

PCA_test.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import sklearn\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "普通にPCAをしてみる "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7faa93da5208>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sVKm9ams2qtRWIHl7lfYREWkgBX8RkQZS8AduK7oBEait2alSe9XWbFSprUDC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\npOAvItJACv4iIg2k4C8i0kAK/iIiDfT/+GBdrxlQdTgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa9409cba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_trans = pca.fit_transform(X)\n",
    "\n",
    "plt.scatter(X_trans[:,0], X_trans[:,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "では，データを移動してみる．すべてのデータに同じベクトルを足す．これでPCAしても，結果は同じ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7faa904f97f0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sVKm9ams2qtRWIHl7lfYREWkgBX8RkQZS8AduK7oBEait2alSe9XWbFSprUDC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\npOAvItJACv4iIg2k4C8i0kAK/iIiDfT/+GBdrxlQdTgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7faa93ddb630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = iris.data + np.array([20, -50, 10, -22])\n",
    "y = iris.target\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "X_trans = pca.fit_transform(X)\n",
    "\n",
    "plt.scatter(X_trans[:,0], X_trans[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.6",
   "language": "python",
   "name": "python36"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}