etc.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pylab as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# For Data Hackers Question\n",
    "\n",
    "This is just a pathological case that I think you should think about when you do SVD. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11426c630>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pS18K/OrBXX+a1JX1uq7kGbXu9XqdylP741nDutfrdSpP7esaHs9HPepRNDH2PviIuAS4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114197048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([1,10, 1+4, 10+4], [1, 10, 1-4, 10-4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = np.random.multivariate_normal([1,1], [[1,0], [0,1]], size=30)\n",
    "b = np.random.multivariate_normal([10,10], [[1,0], [0,1]], size=30)\n",
    "c = np.random.multivariate_normal([1+4,1-4], [[1,0], [0,1]], size=30)\n",
    "d = np.random.multivariate_normal([10+4,10-4], [[1,0], [0,1]], size=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = np.vstack([a,b,c,d])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1143ad588>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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A25U+Y3cHiYjIGbc1+J8KIToApACcArDN9R4REZEnan4nKxER1QbvZCUiCigm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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11427f748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:,1], X[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import TruncatedSVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "svd = TruncatedSVD(n_components=1)\n",
    "X_new = svd.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x11407d128>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1140ab048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X_new, X_new * 0)"
   ]
  }
 ],
 "metadata": {
  "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": "3.4.1"
  },
  "latex_envs": {
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 0
  },
  "toc": {
   "toc_cell": false,
   "toc_number_sections": true,
   "toc_threshold": 6,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}