mc1.ipynb

{
 "metadata": {
  "name": "multiclass_reduction"
 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Multiclass Reductions"
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "by Chiyuan Zhang and Sören Sonnenburg"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since binary classification problems are one of the most thoroughly studied\n",
      "problems in machine learning, it is very appealing to consider reducing\n",
      "multiclass problems to binary ones. Then many advanced learning and\n",
      "optimization techniques as well as generalization bound analysis for binary\n",
      "classification can be utilized."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "\n",
      "In `SHOGUN`, the strategies of reducing a multiclass problem to binary\n",
      "classification problems are described by an instance of\n",
      "`CMulticlassStrategy`. A multiclass strategy describes\n",
      "\n",
      "* How to train the multiclass machine as a number of binary machines?\n",
      "    * How many binary machines are needed?\n",
      "    * For each binary machine, what subset of the training samples are used, and how are they colored? In multiclass problems, we use *coloring* to refer partitioning the classes into two groups: $+1$ and $-1$, or black and white, or any other meaningful names.\n",
      "* How to combine the prediction results of binary machines into the final multiclass prediction?\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The user can derive from the virtual class [CMulticlassStrategy](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMulticlassStrategy.html) to\n",
      "implement a customized multiclass strategy. But usually the built-in strategies\n",
      "are enough for general problems. We will describe the built-in *One-vs-Rest*,\n",
      "*One-vs-One* and *Error-Correcting Output Codes* strategies in this tutorial.\n",
      "\n",
      "The basic routine to use a multiclass machine with reduction to binary problems\n",
      "in shogun is to create a generic multiclass machine and then assign a particular\n",
      "multiclass strategy and a base binary machine."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## One-vs-Rest and One-vs-One\n",
      "\n",
      "The *One-vs-Rest* strategy is implemented in\n",
      "`CMulticlassOneVsRestStrategy`. As indicated by the name, this\n",
      "strategy reduce a $K$-class problem to $K$ binary sub-problems. For the $k$-th\n",
      "problem, where $k\\in\\{1,\\ldots,K\\}$, the samples from class $k$ are colored as\n",
      "$+1$, and the samples from other classes are colored as $-1$. The multiclass\n",
      "prediction is given as\n",
      "\n",
      "$$\n",
      "f(x) = \\operatorname*{argmax}_{k\\in\\{1,\\ldots,K\\}}\\; f_k(x)\n",
      "$$\n",
      "\n",
      "where $f_k(x)$ is the prediction of the $k$-th binary machines.\n",
      "\n",
      "The One-vs-Rest strategy is easy to implement yet produces excellent performance\n",
      "in many cases. One interesting paper, [Rifkin, R. M. and Klautau, A. (2004). *In defense of one-vs-all classification*. Journal of Machine\n",
      "Learning Research, 5:101\u2013141](http://jmlr.org/papers/v5/rifkin04a.html), it was shown that the\n",
      "One-vs-Rest strategy can be\n",
      "\n",
      "> as accurate as any other approach, assuming that the underlying binary\n",
      "classifiers are well-tuned regularized classifiers such as support vector\n",
      "machines.\n",
      "\n",
      "Implemented in [CMulticlassOneVsOneStrategy](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMulticlassOneVsOneStrategy.html), the \n",
      "*One-vs-One* strategy is another simple and intuitive \n",
      "strategy: it basically produces one binary problem for each pair of classes. So there will be $\\binom{K}{2}$ binary problems. At prediction time, the \n",
      "output of every binary classifiers are collected to do voting for the $K$ \n",
      "classes. The class with the highest vote becomes the final prediction.\n",
      "\n",
      "Compared with the One-vs-Rest strategy, the One-vs-One strategy is usually more\n",
      "costly to train and evaluate because more binary machines are used.\n",
      "\n",
      "In the following, we demonstrate how to use `SHOGUN`'s One-vs-Rest and \n",
      "One-vs-One multiclass learning strategy on the USPS dataset.  For \n",
      "demonstration, we randomly 200 samples from each class for training and 200 \n",
      "samples from each class for testing.\n",
      "\n",
      "The [CLibLinear](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CLibLinear.html) is used as the base binary classifier in a [CLinearMulticlassMachine](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CLinearMulticlassMachine.html), with One-vs-Rest and One-vs-One strategies. The running time and performance (on my machine) is reported below:"
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "-------------------------------------------------\n",
      "Strategy       Training Time  Test Time  Accuracy\n",
      "-------------  -------------  ---------  --------\n",
      "One-vs-Rest    12.68           0.27       92.00%\n",
      "One-vs-One     11.54           1.50       93.90%\n",
      "-------------------------------------------------\n",
      "Table: Comparison of One-vs-Rest and One-vs-One multiclass reduction strategy on the USPS dataset."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "First we load the data and initialize random splitting:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "\n",
      "from numpy    import random\n",
      "from scipy.io import loadmat\n",
      "\n",
      "mat  = loadmat('../../../data/multiclass/usps.mat')\n",
      "Xall = mat['data']\n",
      "\n",
      "#normalize examples to have norm one\n",
      "Xall = Xall / np.sqrt(sum(Xall**2,0))\n",
      "Yall = mat['label'].squeeze()\n",
      "\n",
      "# map from 1..10 to 0..9, since shogun\n",
      "# requires multiclass labels to be\n",
      "# 0, 1, ..., K-1\n",
      "Yall = Yall - 1\n",
      "\n",
      "N_train_per_class = 200\n",
      "N_test_per_class = 200\n",
      "N_class = 10\n",
      "\n",
      "# to make the results reproducable\n",
      "random.seed(0)\n",
      "\n",
      "# index for subsampling\n",
      "index = np.zeros((N_train_per_class+N_test_per_class, N_class), 'i')\n",
      "for k in range(N_class):\n",
      "        Ik = (Yall == k).nonzero()[0] # index for samples of class k\n",
      "        I_subsample = random.permutation(len(Ik))[:N_train_per_class+N_test_per_class]\n",
      "        index[:, k] = Ik[I_subsample]\n",
      "\n",
      "idx_train = index[:N_train_per_class, :].reshape(N_train_per_class*N_class)\n",
      "idx_test  = index[N_train_per_class:, :].reshape(N_test_per_class*N_class)\n",
      "\n",
      "random.shuffle(idx_train)\n",
      "random.shuffle(idx_test)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "import SHOGUN components and convert features into SHOGUN format:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from modshogun import RealFeatures, MulticlassLabels\n",
      "from modshogun import LibLinear, L2R_L2LOSS_SVC, LinearMulticlassMachine\n",
      "from modshogun import MulticlassOneVsOneStrategy, MulticlassOneVsRestStrategy\n",
      "from modshogun import MulticlassAccuracy\n",
      "\n",
      "import time\n",
      "\n",
      "feats_train = RealFeatures(Xall[:, idx_train])\n",
      "feats_test  = RealFeatures(Xall[:, idx_test])\n",
      "\n",
      "lab_train = MulticlassLabels(Yall[idx_train].astype('d'))\n",
      "lab_test  = MulticlassLabels(Yall[idx_test].astype('d'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "define a helper function to train and evaluate multiclass machine given a strategy:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def evaluate(strategy, C):\n",
      "        bin_machine = LibLinear()\n",
      "        bin_machine.set_bias_enabled(True)\n",
      "        bin_machine.set_C(C, C)\n",
      "\n",
      "        mc_machine = LinearMulticlassMachine(strategy, feats_train, bin_machine, lab_train)\n",
      "\n",
      "        t_begin = time.clock()\n",
      "        mc_machine.train()\n",
      "        t_train = time.clock() - t_begin\n",
      "\n",
      "        t_begin = time.clock()\n",
      "        pred_test = mc_machine.apply_multiclass(feats_test)\n",
      "        t_test = time.clock() - t_begin\n",
      "\n",
      "        evaluator = MulticlassAccuracy()\n",
      "        acc = evaluator.evaluate(pred_test, lab_test)\n",
      "\n",
      "        print \"training time: %.4f\" % t_train\n",
      "        print \"testing time:  %.4f\" % t_test\n",
      "        print \"accuracy:      %.4f\" % acc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Test on One-vs-Rest and One-vs-One strategies."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"\\nOne-vs-Rest\"\n",
      "print \"=\"*60\n",
      "evaluate(MulticlassOneVsRestStrategy(), 5.0)\n",
      "\n",
      "print \"\\nOne-vs-One\"\n",
      "print \"=\"*60\n",
      "evaluate(MulticlassOneVsOneStrategy(), 2.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "LibLinear also has a true multiclass SVM implemenentation - so it is worthwhile to compare training time and accuracy with the above reduction schemes:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from modshogun import MulticlassLibLinear\n",
      "mcsvm = MulticlassLibLinear(5.0, feats_train, lab_train)\n",
      "mcsvm.set_use_bias(True)\n",
      "\n",
      "t_begin = time.clock()\n",
      "mcsvm.train(feats_train)\n",
      "t_train = time.clock() - t_begin\n",
      "\n",
      "t_begin = time.clock()\n",
      "pred_test = mcsvm.apply_multiclass(feats_test)\n",
      "t_test = time.clock() - t_begin\n",
      "\n",
      "evaluator = MulticlassAccuracy()\n",
      "acc = evaluator.evaluate(pred_test, lab_test)\n",
      "\n",
      "print \"training time: %.4f\" % t_train\n",
      "print \"testing time:  %.4f\" % t_test\n",
      "print \"accuracy:      %.4f\" % acc"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you can see performance of all the three is very much the same though the multiclass svm is a bit faster in training. Usually training time of the true multiclass SVM is much slower than one-vs-rest approach. It should be noted that classification performance of one-vs-one is known to be slightly superior to one-vs-rest since the machines do not have to be properly scaled like in the one-vs-rest approach. However, with larger number of classes one-vs-one quickly becomes prohibitive and so one-vs-rest is the only suitable approach - or other schemes presented below."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Error-Correcting Output Codes\n",
      "\n",
      "*Error-Correcting Output Codes* (ECOC) is a\n",
      "generalization of the One-vs-Rest and One-vs-One strategies. For example, we\n",
      "can represent the One-vs-Rest strategy with the following $K\\times K$ coding \n",
      "matrix, or a codebook:\n",
      "\n",
      "$$\n",
      "    \\begin{bmatrix}\n",
      "    +1 & -1 & -1 & \\ldots & -1 & -1 \\\\\\\\\n",
      "    -1 & +1 & -1 & \\ldots & -1 & -1\\\\\\\\\n",
      "    -1 & -1 & +1 & \\ldots & -1 & -1\\\\\\\\\n",
      "    \\vdots & \\vdots & \\vdots & \\ddots & \\vdots & \\vdots \\\\\\\\\n",
      "    -1 & -1 & -1 & \\ldots & +1 & -1 \\\\\\\\\n",
      "    -1 & -1 & -1 & \\ldots & -1 & +1\n",
      "    \\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Denote the codebook by $B$, there is one column of the codebook associated with\n",
      "each of the $K$ classes. For example, the code for class $1$ is\n",
      "$[+1,-1,-1,\\ldots,-1]$. Each row of the codebook corresponds to a binary\n",
      "coloring of all the $K$ classes. For example, in the first row, the class $1$\n",
      "is colored as $+1$, while the rest of the classes are all colored as $-1$.\n",
      "Associated with each row, there is a binary classifier trained according to the\n",
      "coloring. For example, the binary classifier associated with the first row is\n",
      "trained by treating all the examples of class $1$ as positive examples, and all\n",
      "the examples of the rest of the classes as negative examples.\n",
      "\n",
      "In this special case, there are $K$ rows in the codebook. The number of rows in\n",
      "the codebook is usually called the *code length*. As we can see, this\n",
      "codebook exactly describes how the One-vs-Rest strategy trains the binary\n",
      "sub-machines."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "OvR=-np.ones((10,10))\n",
      "fill_diagonal(OvR, +1)\n",
      "\n",
      "_=gray()\n",
      "_=imshow(OvR, interpolation='nearest')\n",
      "_=gca().set_xticks([])\n",
      "_=gca().set_yticks([])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "A further generalization is to allow $0$-values in the codebook. A $0$ for a\n",
      "class $k$ in a row means we ignore (the examples of) class $k$ when training\n",
      "the binary classifiers associated with this row. With this generalization, we\n",
      "can also easily describes the One-vs-One strategy with a $\\binom{K}{2}\\times K$\n",
      "codebook:\n",
      "\n",
      "$$\n",
      "\\begin{bmatrix}\n",
      "+1     & -1     & 0      & \\ldots & 0      & 0 \\\\\\\\\n",
      "+1     & 0      & -1     & \\ldots & 0      & 0 \\\\\\\\\n",
      "\\vdots & \\vdots & \\vdots & \\ddots & \\vdots & 0 \\\\\\\\\n",
      "+1     & 0      & 0      & \\ldots & -1     & 0 \\\\\\\\\n",
      "0      & +1     & -1     & \\ldots & 0      & 0 \\\\\\\\\n",
      "\\vdots & \\vdots & \\vdots &        & \\vdots & \\vdots \\\\\\\\\n",
      "0      & 0      & 0      & \\ldots & +1     & -1\n",
      "\\end{bmatrix}\n",
      "$$\n",
      "\n",
      "Here each of the $\\binom{K}{2}$ rows describes a binary classifier trained with\n",
      "a pair of classes. The resultant binary classifiers will be identical as those\n",
      "described by a One-vs-One strategy.\n",
      "\n",
      "Since $0$ is allowed in the codebook to ignore some classes, this kind of\n",
      "codebooks are usually called *sparse codebook*, while the codebooks with\n",
      "only $+1$ and $-1$ are usually called *dense codebook*.\n",
      "\n",
      "In general case, we can specify any code length and fill the codebook\n",
      "arbitrarily. However, some rules should be followed:\n",
      "\n",
      "* Each row must describe a *valid* binary coloring. In other words, both $+1$ and $-1$ should appear at least once in each row. Or else a binary classifier cannot be obtained for this row.\n",
      "* It is good to avoid duplicated rows. There is generally no harm to have duplicated rows, but the resultant binary classifiers are completely identical provided the training algorithm for the binary classifiers are deterministic. So this can be a waste of computational resource.\n",
      "* Negative rows are also duplicated. Simply inversing the sign of a code row does not produce a \"new\" code row. Because the resultant binary classifier will simply be the negative classifier associated with the original row."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Though you can certainly generate your own codebook, it is usually easier to\n",
      "use the `SHOGUN` built-in procedures to generate codebook automatically. There\n",
      "are various codebook generators (called *encoders*) in `SHOGUN`. However,\n",
      "before describing those encoders in details, let us notice that a codebook \n",
      "only describes how the sub-machines are trained. But we still need a\n",
      "way to specify how the binary classification results of the sub-machines can be\n",
      "combined to get a multiclass classification result.\n",
      "\n",
      "Review the codebook again: corresponding to each class, there is a column. We\n",
      "call the codebook column the (binary) *code* for that class. For a new\n",
      "sample $x$, by applying the binary classifiers associated with each row\n",
      "successively, we get a prediction vector of the same length as the\n",
      "*code*. Deciding the multiclass label from the prediction vector (called\n",
      "*decoding*) can be done by minimizing the *distance* between the\n",
      "codes and the prediction vector. Different *decoders* define different \n",
      "choices of distance functions. For this reason, it is usually good to make the\n",
      "mutual distance between codes of different classes large. In this way, even\n",
      "though several binary classifiers make wrong predictions, the distance of\n",
      "the resultant prediction vector to the code of the *true* class is likely\n",
      "to be still smaller than the distance to other classes. So correct results can\n",
      "still be obtained even when some of the binary classifiers make mistakes. This\n",
      "is the reason for the name *Error-Correcting Output Codes*.\n",
      "\n",
      "In `SHOGUN`, encoding schemes are described by subclasses of\n",
      "[CECOCEncoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCEncoder.html), while decoding schemes are described by subclasses\n",
      "of [CECOCDecoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCDecoder.html). Theoretically, any combinations of\n",
      "encoder-decoder pairs can be used. Here we will introduce several common\n",
      "encoder/decoders in shogun."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* [CECOCRandomDenseEncoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCRandomDenseEncoder.html): This encoder generate random dense ($+1$/$-1$) codebooks and choose the one with the largest *minimum mutual distance* among the classes. The recommended code length for this encoder is $10\\log K$. \n",
      "* [CECOCRandomSparseEncoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCRandomSparseEncoder.html): This is similar to the random dense encoder, except that sparse ($+1$/$-1$/$0$) codebooks are generated. The recommended code length for this encoder is $15\\log K$.\n",
      "* [CECOCOVREncoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCOVREncoder.html), [CECOCOVOEncoder](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CECOCOVOEncoder.html): These two encoders mimic the One-vs-Rest and One-vs-One strategies respectively. They are implemented mainly for demonstrative purpose.  When suitable decoders are used, the results will be equivalent to the corresponding strategies, respectively."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using ECOC Strategy in `SHOGUN` is similar to ordinary one-vs-rest or one-vs-one. You need to choose an encoder and a decoder, and then construct a `ECOCStrategy`, as demonstrated below:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from modshogun import ECOCStrategy, ECOCRandomDenseEncoder, ECOCLLBDecoder\n",
      "\n",
      "print \"\\nRandom Dense Encoder + Margin Loss based Decoder\"\n",
      "print \"=\"*60\n",
      "evaluate(ECOCStrategy(ECOCRandomDenseEncoder(), ECOCLLBDecoder()))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Using a kernel multiclass machine"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Expanding on the idea of creating a generic multiclass machine and then assigning a particular multiclass strategy and a base binary machine, one can also use the [KernelMulticlassMachine](http://www.shogun-toolbox.org/doc/en/current/classshogun_1_1CKernelMulticlassMachine.html) with a kernel of choice.\n",
      "\n",
      "Here we will use a [GaussianKernel](http://www.shogun-toolbox.org/doc/en/3.0.0/classshogun_1_1CGaussianKernel.html) with LibSVM as the classifer.\n",
      "All we have to do is define a new helper evaluate function with the features defined as in the above examples."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def evaluate_multiclass_kernel(strategy):\n",
      "    from modshogun import KernelMulticlassMachine, LibSVM, GaussianKernel\n",
      "    width=2.1\n",
      "    epsilon=1e-5\n",
      "    \n",
      "    kernel=GaussianKernel(feats_train, feats_train, width)\n",
      "    \n",
      "    classifier = LibSVM()\n",
      "    classifier.set_epsilon(epsilon)\n",
      "\n",
      "    mc_machine = KernelMulticlassMachine(strategy, kernel, classifier, lab_train)\n",
      "\n",
      "    t_begin = time.clock()\n",
      "    mc_machine.train()\n",
      "    t_train = time.clock() - t_begin\n",
      "\n",
      "    t_begin = time.clock()\n",
      "    pred_test = mc_machine.apply_multiclass(feats_test)\n",
      "    t_test = time.clock() - t_begin\n",
      "\n",
      "    evaluator = MulticlassAccuracy()\n",
      "    acc = evaluator.evaluate(pred_test, lab_test)\n",
      "\n",
      "    print \"training time: %.4f\" % t_train\n",
      "    print \"testing time:  %.4f\" % t_test\n",
      "    print \"accuracy:      %.4f\" % acc\n",
      "\n",
      "print \"\\nOne-vs-Rest\"\n",
      "print \"=\"*60\n",
      "evaluate_multiclass_kernel(MulticlassOneVsRestStrategy())\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So we have seen that we can classify multiclass samples using a base binary machine. If we dwell on this a bit more, we can easily spot the intuition behind this.\n",
      "\n",
      "The MulticlassOneVsRestStrategy classifies one class against the rest of the classes. This is done for each and every class by training a separate classifier for it.So we will have total k classifiers where k is the number of classes.\n",
      "\n",
      "Just to see this in action lets create some data using the gaussian mixture model class (GMM) from which we sample the data points.Four different classes are created and plotted."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from modshogun import *\n",
      "from numpy import *\n",
      "\n",
      "num=1000;\n",
      "dist=1.0;\n",
      "\n",
      "gmm=GMM(4)\n",
      "gmm.set_nth_mean(array([-dist*4,-dist]),0)\n",
      "gmm.set_nth_mean(array([-dist*4,dist*4]),1)\n",
      "gmm.set_nth_mean(array([dist*4,dist*4]),2)\n",
      "gmm.set_nth_mean(array([dist*4,-dist]),3)\n",
      "gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),0)\n",
      "gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),1)\n",
      "gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),2)\n",
      "gmm.set_nth_cov(array([[1.0,0.0],[0.0,1.0]]),3)\n",
      "\n",
      "gmm.set_coef(array([1.0,0.0,0.0,0.0]))\n",
      "x0=array([gmm.sample() for i in xrange(num)]).T\n",
      "x0t=array([gmm.sample() for i in xrange(num)]).T\n",
      "\n",
      "gmm.set_coef(array([0.0,1.0,0.0,0.0]))\n",
      "x1=array([gmm.sample() for i in xrange(num)]).T\n",
      "x1t=array([gmm.sample() for i in xrange(num)]).T\n",
      "\n",
      "gmm.set_coef(array([0.0,0.0,1.0,0.0]))\n",
      "x2=array([gmm.sample() for i in xrange(num)]).T\n",
      "x2t=array([gmm.sample() for i in xrange(num)]).T\n",
      "\n",
      "gmm.set_coef(array([0.0,0.0,0.0,1.0]))\n",
      "x3=array([gmm.sample() for i in xrange(num)]).T\n",
      "x3t=array([gmm.sample() for i in xrange(num)]).T\n",
      "\n",
      "\n",
      "traindata=concatenate((x0,x1,x2,x3), axis=1)\n",
      "testdata=concatenate((x0t,x1t,x2t,x3t), axis=1)\n",
      "\n",
      "l0 = array([0.0 for i in xrange(num)])\n",
      "l1 = array([1.0 for i in xrange(num)])\n",
      "l2 = array([2.0 for i in xrange(num)])\n",
      "l3 = array([3.0 for i in xrange(num)])\n",
      "\n",
      "trainlab=concatenate((l0,l1,l2,l3))\n",
      "testlab=concatenate((l0,l1,l2,l3))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "_=scatter(traindata[0,:], traindata[1,:], c=trainlab, s=100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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t18XK20djX4ysVh4Z2kc54dW/RZInQfr8oAuU7m5IwxrI6AFIMk9k2XRlr1zz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cebEfHjI4ALJEkSwPbtG6lSpUoi5/v3w927dymYJw+9/4+98w6Tosra+K9nenoiOWfJShQBSSIY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\nhHDZaJSJ0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mw6ciTCEb9NOmmEOWhy0fPPP8OTT/6FyZMnk52dTZUqVXC73Qwd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\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have the data ready , lets convert it to shogun format features."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "feats_tr=RealFeatures(traindata)\n",
      "labels=MulticlassLabels(trainlab)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The [KernelMulticlassMachine](http://www.shogun-toolbox.org/doc/en/current/classshogun_1_1CKernelMulticlassMachine.html) is used with LibSVM as the classifer just as in the above example.\n",
      "\n",
      "Now we have four different classes, so as explained above we will have four classifiers which in shogun terms are submachines.\n",
      "\n",
      "We can see the outputs of two of the four individual submachines(specified by the index) and of the main machine. The plots clearly show how the submachine classify each class as if it is a binary classification problem and this provides the base for the whole multiclass classification."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from modshogun import KernelMulticlassMachine, LibSVM, GaussianKernel\n",
      "\n",
      "width=2.1\n",
      "epsilon=1e-5\n",
      "   \n",
      "kernel=GaussianKernel(feats_tr, feats_tr, width)\n",
      "    \n",
      "classifier = LibSVM()\n",
      "classifier.set_epsilon(epsilon)\n",
      "\n",
      "mc_machine = KernelMulticlassMachine(MulticlassOneVsRestStrategy(), kernel, classifier, labels)\n",
      "\n",
      "mc_machine.train()\n",
      "\n",
      "size=100\n",
      "x1=linspace(-10, 10, size)\n",
      "x2=linspace(-10, 10, size)\n",
      "x, y=meshgrid(x1, x2)\n",
      "grid=RealFeatures(array((ravel(x), ravel(y)))) #test features\n",
      "\n",
      "out = mc_machine.apply_multiclass(grid) #main output\n",
      "z=out.get_labels().reshape((size, size))\n",
      "\n",
      "sub_out0 = mc_machine.get_submachine_outputs(0) #first submachine\n",
      "sub_out1 = mc_machine.get_submachine_outputs(1) #second submachine\n",
      "\n",
      "z0=sub_out0.get_labels().reshape((size, size))\n",
      "z1=sub_out1.get_labels().reshape((size, size))\n",
      "\n",
      "figure(figsize=(20,5))\n",
      "subplot(131)\n",
      "c0=pcolor(x, y, z0)\n",
      "_=contour(x, y, z0, linewidths=1, colors='black', hold=True)\n",
      "_=colorbar(c0)\n",
      "\n",
      "subplot(132)\n",
      "c1=pcolor(x, y, z1)\n",
      "_=contour(x, y, z1, linewidths=1, colors='black', hold=True)\n",
      "_=colorbar(c1)\n",
      "\n",
      "subplot(133)\n",
      "c2=pcolor(x, y, z)\n",
      "_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
      "_=colorbar(c2)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "-c:11: RuntimeWarning: \u001b[1;34m[WARN]\u001b[0m In file /home/saurabh/l/shogun/src/shogun/multiclass/MulticlassStrategy.cpp line 45: MulticlassStrategy::CMulticlassStrategy(): register parameters!\n",
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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1jBkzBr/fH/mORUQk9pQTIt5QWgJbPoe0dDJa2y5GPCUKOZGens5dd91Fbm4u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\ncwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}