CanonicalBiplot.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.utils.extmath import randomized_svd\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "y = list(iris.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#wine = pd.read_csv('/Users/victor/Documents/DataLab/2018/wine.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#wine.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standardize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Y_ = wine.iloc[:,:3]\n",
    "#X = wine.iloc[:,3:].as_matrix()\n",
    "medias = X.mean(axis=0)\n",
    "desv = X.std(axis=0)\n",
    "dim = X.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_st = (X-medias)/desv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Groups"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#GroupNames = list(Y_.Group.unique())\n",
    "GroupNames = list(y)\n",
    "g = len(set(GroupNames))\n",
    "n = X_st.shape[0]\n",
    "m = X_st.shape[1]\n",
    "r = np.min(np.array([g - 1, m]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Factor2Binary(y,Name = None):\n",
    "    if Name == None:\n",
    "        Name = \"C\"\n",
    "    #ncat = len(y.unique())\n",
    "    ncat = len(list(set(y)))\n",
    "    n = len(y)\n",
    "    #Z = pd.DataFrame(0, index=np.arange(len(y)), columns=y.unique())\n",
    "    Z = pd.DataFrame(0, index=np.arange(len(y)), columns=list(set(y)))\n",
    "    for col in Z.columns:\n",
    "        for i in range (0,n):\n",
    "            if y[i] == col:\n",
    "                Z[col].iloc[i] = 1\n",
    "    return Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def matrixsqrt(M,dim,tol=np.finfo(float).eps,inv=True):\n",
    "    U, Sigma, VT = randomized_svd(M, n_components=dim, n_iter=5, random_state=None)\n",
    "    nz = Sigma > tol\n",
    "    if inv==True:\n",
    "        S12 = U.dot(np.diag(1/np.sqrt(Sigma[nz]))).dot(VT[nz,:])\n",
    "    else:\n",
    "        S12 = U.dot(np.diag(np.sqrt(Sigma[nz]))).dot(VT[nz,:])\n",
    "    return S12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Groups to Binary\n",
    "Z = Factor2Binary(y)\n",
    "ng = Z.sum(axis=0)\n",
    "S11 = (Z.T).dot(Z)\n",
    "Xb = np.linalg.inv(S11).dot(Z.T).dot(X_st)\n",
    "B = (Xb.T).dot(S11).dot(Xb)\n",
    "S = (X_st.T).dot(X_st) - B\n",
    "Y = np.power(S11,0.5).dot(Xb).dot(matrixsqrt(S,dim,inv=True))\n",
    "\n",
    "U, Sigma, VT = randomized_svd(Y, n_components=dim, n_iter=5, random_state=None)\n",
    "\n",
    "#Variable_Coord\n",
    "H = matrixsqrt(S,dim,inv=False).dot(np.transpose(VT[0:r,:]))\n",
    "#Canonical_Weights\n",
    "B = matrixsqrt(S,dim,inv=True).dot(np.transpose(VT[0:r,:]))\n",
    "\n",
    "#Group_Coord\n",
    "J = Xb.dot(B)\n",
    "\n",
    "#Individual_Coord\n",
    "V = X_st.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sct = np.diag((V.T).dot(V))\n",
    "sce = np.diag((J.T).dot(S11).dot(J))\n",
    "scr = sct -sce\n",
    "fs = (sce/(g - 1))/(scr/(n - g))\n",
    "\n",
    "#eigenvectors\n",
    "vprop = Sigma[:r]\n",
    "#Inertia\n",
    "iner = (np.power(vprop,2)/(np.power(vprop,2).sum()))*100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lamb = np.power(vprop,2)\n",
    "pill = 1/(1 + lamb)\n",
    "pillai = np.linalg.det(np.diag(pill))\n",
    "glh = g - 1\n",
    "gle = n - g\n",
    "t = np.sqrt((np.power(glh,2) * np.power(m,2) - 4)/(np.power(m,2) + np.power(glh,2) - 5))\n",
    "w = gle + glh - 0.5 * (m + glh + 1)\n",
    "df1 = m * glh\n",
    "df2 = w * t - 0.5 * (m * glh - 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Wilksf = (1 - np.power(pillai,1/t))/(np.power(pillai,1/t)) * (df2/df1)\n",
    "Wilksp = stats.f.pdf(Wilksf, df1, df2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "198.71102958937774"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Wilksf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "falfau = stats.t.ppf(1 - (0.025), (n - g))\n",
    "falfab = stats.t.ppf(1 - (0.025/(g * m)), (n - g))\n",
    "falfam = np.sqrt(stats.f.ppf(1 - 0.05, m, (n - g - m + 1)) * (((n - g) * m)/(n - g - m + 1)))\n",
    "falfac = 2.447747"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.97623330888 2.91079647977 3.15291719981 2.447747\n"
     ]
    }
   ],
   "source": [
    "print(falfau,falfab,falfam,falfac)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "UnivRad = falfau * np.diag(np.linalg.inv(np.sqrt(S11)))/np.sqrt(n - g)\n",
    "BonfRad = falfab * np.diag(np.linalg.inv(np.sqrt(S11)))/np.sqrt(n - g)\n",
    "MultRad = falfam * np.diag(np.linalg.inv(np.sqrt(S11)))/np.sqrt(n - g)\n",
    "ChisRad = falfac * np.diag(np.linalg.inv(np.sqrt(S11)))/np.sqrt(n - g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import matplotlib.pyplot as plt\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.68147207, -2.37207307],\n",
       "       [ 1.10980422, -8.280941  ],\n",
       "       [-2.09120788, -0.49394306],\n",
       "       [-2.06567372, -2.41638351]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1IAAAM7CAYAAABA3aGVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f262b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circle1 = plt.Circle(J[0,0:2], BonfRad[0], color='b',alpha=0.4)\n",
    "circle2 = plt.Circle(J[1,0:2], BonfRad[1], color='b',alpha=0.4)\n",
    "circle3 = plt.Circle(J[2,0:2], BonfRad[2], color='b',alpha=0.4)\n",
    "#circle4 = plt.Circle(J[3,0:2], BonfRad[3], color='b',alpha=0.4)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10,10))\n",
    "\n",
    "ax.set_xlim([-2, 2])\n",
    "ax.set_ylim([-2, 2])\n",
    "\n",
    "ax.add_artist(circle1)\n",
    "ax.add_artist(circle2)\n",
    "ax.add_artist(circle3)\n",
    "#ax.add_artist(circle4)\n",
    "\n",
    "\n",
    "#ax1.scatter(J[:,0],J[:,1])\n",
    "#ax1.scatter(V[:,0],V[:,1],c='red')\n",
    "for i in range(0,H.shape[0]):\n",
    "    ax.arrow(0,0,H[i,0],H[i,1],width=0.005)\n",
    "#ax.scatter(H[:,0],H[:,1],c='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}