4 Data Processing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Assignment 4 - dimensionality reduction\n",
    "\n",
    "This assignment focuses on two different ways for dimensionality reduction:\n",
    "* feature selection\n",
    "* feature extraction\n",
    "\n",
    "This assignment has weighting $1.5$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Sequential feature selection (50 points)\n",
    "\n",
    "There is a sample code in PML chapter 4 for sequential bardward selection (SBS) and its application to subsequent KNN classifier.\n",
    "\n",
    "Implement sequential forward selection (SFS), and compare it with sequential backward selection by plotting the accuracy versus the number of features.\n",
    "\n",
    "You can start with the sample code provided in the [slides](http://nbviewer.jupyter.org/github/1iyiwei/pyml/blob/master/code/ch04/ch04.ipynb).\n",
    "You can extend the existing SBS class to handle both forward and backward selection, or implement a separate class for SFS.\n",
    "Plot and compare the two accuracy versus number-of-features plots for SFS and SBS.\n",
    "\n",
    "Use the wine dataset as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "wine_data_remote = 'https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data'\n",
    "wine_data_local = '../datasets/wine/wine.data'\n",
    "\n",
    "df_wine = pd.read_csv(wine_data_remote,\n",
    "                      header=None)\n",
    "\n",
    "df_wine.columns = ['Class label', 'Alcohol', 'Malic acid', 'Ash',\n",
    "                   'Alcalinity of ash', 'Magnesium', 'Total phenols',\n",
    "                   'Flavanoids', 'Nonflavanoid phenols', 'Proanthocyanins',\n",
    "                   'Color intensity', 'Hue', 'OD280/OD315 of diluted wines',\n",
    "                   'Proline']\n",
    "\n",
    "#print('Class labels', np.unique(df_wine['Class label']))\n",
    "#df_wine.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn import __version__ as skv\n",
    "from distutils.version import LooseVersion as CheckVersion\n",
    "if CheckVersion(skv) < '0.18':\n",
    "    from sklearn.cross_validation import train_test_split\n",
    "else:\n",
    "    from sklearn.model_selection import train_test_split\n",
    "\n",
    "X, y = df_wine.iloc[:, 1:].values, df_wine.iloc[:, 0].values\n",
    "\n",
    "X_train, X_test, y_train, y_test = \\\n",
    "    train_test_split(X, y, test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "stdsc = StandardScaler()\n",
    "X_train_std = stdsc.fit_transform(X_train)\n",
    "X_test_std = stdsc.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Implement your sequential backward selection class here, either as a separate class or by extending the SBS class that can handle both forward and backward selection (via an input parameter to indicate the direction)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/miracle/anaconda/lib/python3.5/site-packages/sklearn/cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.base import clone\n",
    "from itertools import combinations\n",
    "import numpy as np\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "class SequentialSelection():\n",
    "    def __init__(self, estimator, k_features, scoring=accuracy_score,\n",
    "                 backward = True, test_size=0.25, random_state=1):\n",
    "        self.scoring = scoring\n",
    "        self.estimator = clone(estimator)\n",
    "        self.k_features = k_features\n",
    "        self.backward = backward\n",
    "        self.test_size = test_size\n",
    "        self.random_state = random_state\n",
    "\n",
    "    def fit(self, X, y):\n",
    "        \n",
    "        X_train, X_test, y_train, y_test = \\\n",
    "            train_test_split(X, y, test_size=self.test_size,\n",
    "                             random_state=self.random_state)\n",
    "\n",
    "        dim = X_train.shape[1]\n",
    "        \n",
    "        all_indices = tuple(range(dim))\n",
    "        self.subsets_ = []\n",
    "        self.scores_ = []\n",
    "     \n",
    "        if self.backward: \n",
    "            self.indices_ = all_indices\n",
    "            dims = range(dim, self.k_features-1, -1)\n",
    "        else: # forward\n",
    "            self.indices_ = []\n",
    "            dims = range(1, self.k_features+1, 1)         \n",
    "            \n",
    "        for dim in dims:\n",
    "            scores = []\n",
    "            subsets = []\n",
    "\n",
    "            if self.backward:\n",
    "                p_set = [p for p in combinations(self.indices_, r=dim)]\n",
    "            else:\n",
    "                remaining_indices = set(all_indices).difference(self.indices_)\n",
    "                p_set = [tuple(set(p).union(set(self.indices_))) for p in combinations(remaining_indices, r=1)]\n",
    "            \n",
    "            for p in p_set:\n",
    "                score = self._calc_score(X_train, y_train, \n",
    "                                         X_test, y_test, p)\n",
    "                scores.append(score)\n",
    "                subsets.append(p)\n",
    "\n",
    "            best = np.argmax(scores)\n",
    "            self.indices_ = subsets[best]\n",
    "            self.subsets_.append(self.indices_)\n",
    "            self.scores_.append(scores[best])\n",
    "            \n",
    "        self.k_score_ = self.scores_[-1]\n",
    "\n",
    "        return self\n",
    "\n",
    "    def transform(self, X):\n",
    "        return X[:, self.indices_]\n",
    "\n",
    "    def _calc_score(self, X_train, y_train, X_test, y_test, indices):\n",
    "        self.estimator.fit(X_train[:, indices], y_train)\n",
    "        y_pred = self.estimator.predict(X_test[:, indices])\n",
    "        score = self.scoring(y_test, y_pred)\n",
    "        return score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Apply your sequential forward/backward selection code to the KNN classifier with the wine data set, and plot the accuracy versus number-of-features curves for both.\n",
    "Describe the similarities and differences you can find, e.g. \n",
    "* do the two methods agree on the optimal number of features?\n",
    "* do the two methods have similar accuracy scores for each number of features?\n",
    "* etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## Answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "SBS and SFS give similar plots for accuracy versus the feature size, they agree on the accuracy score for 5 to 9 features based on the parameters setting used in the code.\n",
    "\n",
    "SFS reaches a higher accuracy score than SBS with a smaller feature size. We could see from the figure that SFS has a higher accuracy of 1 with a featue size of 3 while SBS gives an accuracy of 0.96. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
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bWwHW/H6uWkTk9gWMBm7NLE8Axnfa59ckxahjeSZJE1/nc00CTl/PdaJW5s+P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\nXHFTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116fecf98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kdgMeA04C1gLzgbMiYklmn+uB5yJikqQDgQeAo4H1XR2bOUepipSZWRl1p0jl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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116febc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "knn = KNeighborsClassifier(n_neighbors=2)\n",
    "\n",
    "# selecting features\n",
    "for backward in [True, False]:\n",
    "    if backward:\n",
    "        k_features = 1\n",
    "    else:\n",
    "        k_features = X_train_std.shape[1]\n",
    "        \n",
    "    ss = SequentialSelection(knn, k_features=k_features, backward=backward)\n",
    "    ss.fit(X_train_std, y_train)\n",
    "\n",
    "    # plotting performance of feature subsets\n",
    "    k_feat = [len(k) for k in ss.subsets_]\n",
    "\n",
    "    plt.plot(k_feat, ss.scores_, marker='o')\n",
    "    plt.ylim([0.7, 1.1])\n",
    "    plt.ylabel('Accuracy')\n",
    "    plt.xlabel('Number of features')\n",
    "    if backward:\n",
    "        plt.title('backward')\n",
    "    else:\n",
    "        plt.title('forward')\n",
    "    plt.grid()\n",
    "    plt.tight_layout()\n",
    "    # plt.savefig('./sbs.png', dpi=300)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# PCA versus LDA (50 points)\n",
    "\n",
    "We have learned two different methods for feature extraction, PCA (unsupervised) and LDA (supervised).\n",
    "\n",
    "Under what circumstances would PCA and LDA produce very different results? \n",
    "\n",
    "Provide one example dataset in 2D, analyze it via PCA and LDA, and plot it with the PCA and LDA components.\n",
    "\n",
    "You can use code from the scikit-learn library."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "One simple case is several very tall and narrow clusters stacked horizontally.\n",
    "PCA/LDA and will favor the vertical/horizontal direction, respectively.\n",
    "\n",
    "To avoid curing via standardization, just having enough classes so that the total/individual set is sufficiently isotropic/anisotropic.\n",
    "\n",
    "The difference could be explained: \n",
    "\n",
    "PCA: \n",
    "(1) unsupervised (no class label information) \n",
    "(2) project data into dimensions that maximize variance.\n",
    "\n",
    "LDA:\n",
    "(1) supervised (with class label information) \n",
    "(2) project data into dimensions to (a) maximize inter-class spread, (b) minimize intra-class spread"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Write code to produce your own dataset in 2D.\n",
    "You are free to design relative characteristics like the number of class, the number of samples for each class, as long as your dataset could be analyzed via PCA and LDA."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# visualize the data set\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_dataset(X, y, xlabel=\"\", ylabel=\"\"):\n",
    "    num_class = np.unique(y).size\n",
    "    \n",
    "    colors = ['red', 'blue', 'green', 'black']\n",
    "    markers = ['^', 'o', 's', 'd']\n",
    "    \n",
    "    if num_class <= 1:\n",
    "        plt.scatter(X[:, 0], X[:, 1])\n",
    "        pass\n",
    "    else:\n",
    "        for k in range(num_class):\n",
    "            plt.scatter(X[y == k, 0], X[y == k, 1], color=colors[k], marker=markers[k], alpha=0.5)\n",
    "         \n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel(ylabel)\n",
    "    plt.tight_layout()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "def blobs(num_samples_per_class, dimension, num_class, cluster_std, center_spacing):\n",
    "    cluster_scale = num_class*center_spacing\n",
    "\n",
    "    class_centers = np.zeros((num_class, 2))\n",
    "    for k in range(num_class):\n",
    "        class_centers[k, 0] = center_spacing*(k-num_class*0.5)\n",
    "\n",
    "    X, y = make_blobs(n_samples = num_samples_per_class*num_class, \n",
    "                      n_features = dimension, centers = class_centers,\n",
    "                      cluster_std=cluster_std)\n",
    "\n",
    "    X[:, 1] *= cluster_scale\n",
    "    \n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def slices(num_samples_per_class, dimension, num_class, aspect_ratio=1.0):\n",
    "    num_rows = num_class*num_samples_per_class\n",
    "    num_cols = dimension\n",
    "    \n",
    "    y = np.zeros(num_rows)\n",
    "    X = np.random.uniform(low=0, high=1, size=(num_rows, num_cols))\n",
    "        \n",
    "    for k in range(num_class):\n",
    "        row_lo = k*num_samples_per_class\n",
    "        row_hi = (k+1)*num_samples_per_class\n",
    "        y[row_lo:row_hi].fill(k)\n",
    "        X[row_lo:row_hi, 0] = (X[row_lo:row_hi, 0]+k)*aspect_ratio/num_class\n",
    "            \n",
    "    y = y.astype(int)        \n",
    "    return X, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(300, 2)\n",
      "[0 1 2]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "num_samples_per_class = 100\n",
    "dimension = 2\n",
    "cluster_std = 1\n",
    "center_spacing = 5*cluster_std\n",
    "\n",
    "aspect_ratio = 0.8\n",
    "\n",
    "num_class = 3\n",
    "\n",
    "# You guys could try different dataset using blobs or slices and adjusting the angle below\n",
    "\n",
    "#X, y = blobs(num_samples_per_class, dimension, num_class, cluster_std, center_spacing)\n",
    "X, y = slices(num_samples_per_class, dimension, num_class, aspect_ratio)\n",
    "\n",
    "print(X.shape)\n",
    "print(np.unique(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    " class RotationMatrix():\n",
    "    # angle in degree\n",
    "    def __init__(self, angle=0):\n",
    "        theta = (angle/180.0)*np.pi\n",
    "        self.matrix = np.array([[np.cos(theta), -np.sin(theta)], \n",
    "                                [np.sin(theta), np.cos(theta)]])\n",
    "    def rot(self, X):\n",
    "        return X.dot(self.matrix.transpose())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "angle = 0\n",
    "\n",
    "if angle != 0:\n",
    "    rmat = RotationMatrix(angle)\n",
    "    X = rmat.rot(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "if False:\n",
    "    sc = StandardScaler()\n",
    "    X = sc.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Plot your data set, with different classes in different marker colors and/or shapes.\n",
    "\n",
    "You can write your own plot code or use existing library plot code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
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L9WdtNFe4NJkmGWtScXMlAkoKBSoqIsCsWfphGhPrfFxeK1Swhbhpuu7CGiZGRoCf/ERn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\nCLESChQhhBAr+f+Ux13tBTmEcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119c64320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dataset(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Apply your dataset through PCA and LDA, and plot the projected data using the same plot code.\n",
    "Explain the differences you notice, and how you manage to construct your dataset to achieve such differences.\n",
    "\n",
    "You can use the PCA and LDA code from the scikit-learn library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA()\n",
    "X_pca = pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Pb8+bWrbMrlw4dqx9XLYsM2/Kh3GlVpcGb7ZO1Hvfm02706BepuF118GCBe4m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\nUhRFUbzl/wN5m1oWCF8YmQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11957e978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dataset(X_pca, y, xlabel='PC 1', ylabel='PC 2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "lda = LDA(n_components=dimension)\n",
    "X_lda = lda.fit_transform(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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r7xw8o0eHgOUlhdioSGWrw6ct4rQS0tFuKIO1m1R45GKMqt/42vao1rikQ3s0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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a4b1630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dataset(X_lda, y, xlabel = \"LD 1\", ylabel = \"LD 2\")"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "celltoolbar": "Slideshow",
  "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": "3.5.2"
  },
  "name": "_merged"
 },
 "nbformat": 4,
 "nbformat_minor": 0
}