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Created March 28, 2014 17:20
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{
"metadata": {
"name": "MKL"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Multiple Kernel Learning"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook is about multiple kernel learning in shogun. We will see how to construct a combined kernel, determine optimal kernel weights using MKL and use them for [classification](http://en.wikipedia.org/wiki/Statistical_classification)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# import all shogun classes\n",
"from modshogun import *"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Introduction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<em>Multiple kernel learning</em> is about using a combined kernel i.e. a kernel consisting of a linear combination of arbitrary kernels over different domains. The coefficients or weights of the linear combination can be learned as well.\n",
"\n",
"[Kernel based methods](http://en.wikipedia.org/wiki/Kernel_methods) such as support vector machines (SVMs) employ a so-called kernel function $k(x_{i},x_{j})$ which intuitively computes the similarity between two examples $x_{i}$ and $x_{j}$. </br>\n",
"Selecting the kernel function\n",
"$k()$ and its parameters is an important issue in training. Kernels designed by humans usually capture one aspect of data. Choosing one kernel means to select exactly one such aspect. Which means combining such ascpects is often better than selecting.\n",
"\n",
"In shogun the [CMKL](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKL.html) is the base class for MKL. We can do classifications: [binary](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLClassification.html), [one-class](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLOneClass.html), [multiclass](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLMulticlass.html) and regression too: [regression](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLRegression.html)"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Mathematical formulation (skip if just you want code examples)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"</br>So in a svm, defined as:\n",
"$$f({\\bf x})=\\text{sign} \\left(\\sum_{i=0}^{N-1} \\alpha_i k({\\bf x}, {\\bf x_i})+b\\right)$$</brr>\n",
"\n",
"\n",
"One could make a combination of kernels like:\n",
"$${\\bf k}(x_i,x_j)=\\sum_{k=0}^{K} \\beta_k {\\bf k_k}(x_i, x_j)$$\n",
"where $\\beta_k > 0$ and $\\sum_{k=0}^{K} \\beta_k = 1$\n",
"\n",
"In MKL $\\alpha_i$,$\\beta$ and bias are determined by solving the following optimization program\n",
"\n",
"$$\\mbox{min} \\hspace{4mm} \\gamma-\\sum_{i=1}^N\\alpha_i$$\n",
"$$ \\mbox{w.r.t.} \\hspace{4mm} \\gamma\\in R, \\alpha\\in R^N \\nonumber$$\n",
"$$\\mbox {s.t.} \\hspace{4mm} {\\bf 0}\\leq\\alpha\\leq{\\bf 1}C,\\;\\;\\sum_{i=1}^N \\alpha_i y_i=0 \\nonumber$$\n",
"$$ \\frac{1}{2}\\sum_{i,j=1}^N \\alpha_i \\alpha_j y_i y_j \\forall k=1,\\ldots,K\\nonumber\\\\\n",
"$$\n",
"\n",
"\n",
" here C is a pre-specified regularization parameter\n",
"Within shogun this optimization problem is solved using [semi-infinite programming](http://en.wikipedia.org/wiki/Semi-infinite_programming). For 1-norm MKL using one of the two approaches described in\n",
"[1].\n",
"The first approach (also called the wrapper algorithm) wraps around a single kernel SVMs, alternatingly solving for \u03b1 and \u03b2. It is using a traditional SVM to generate new violated constraints and thus requires a single kernel SVM and any of the SVMs contained in shogun can be used. In the MKL step either a linear program is solved via glpk or cplex or analytically or a newton (for norms>1) step is performed.\n",
"\n",
"The second much faster but also more memory demanding approach performing interleaved optimization, is integrated into the chunking-based SVMlight.\n",
"\n"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Using a Combined kernel:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Shogun provides an easy way to make combination of kernels using the [CombinedKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CCombinedKernel.html) class, to which we can append any [Kernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CKernel.html) from the many options shogun provides. It is especially useful to combine kernels working on different domains and to combine kernels looking at independent features and requires [CombinedFeatures](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CCombinedFeatures.html) to be used. Similarly the CombinedFeatures is used to combine a number of feature objects into a single CombinedFeatures object"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernel = CombinedKernel()"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To see the preiction capabilities, lets generate some data using the [GMM](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGMM.html) class. The data is sampled by setting means ([GMM notebook](http://www.shogun-toolbox.org/static/notebook/current/GMM.html)) such that it sufficiently covers X-Y grid and is not too easy to classify."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"num=30;\n",
"num_components=4\n",
"means=zeros((num_components, 2))\n",
"means[0]=[-1,1]\n",
"means[1]=[2,-1.5]\n",
"means[2]=[-1,-3]\n",
"means[3]=[2,1]\n",
"\n",
"covs=array([[1.0,0.0],[0.0,1.0]])\n",
"\n",
"gmm=GMM(num_components)\n",
"[gmm.set_nth_mean(means[i], i) for i in range(num_components)]\n",
"[gmm.set_nth_cov(covs,i) for i in range(num_components)]\n",
"gmm.set_coef(array([1.0,0.0,0.0,0.0]))\n",
"xntr=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,1.0,0.0,0.0]))\n",
"xntr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xnte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,1.0,0.0]))\n",
"xptr=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte=array([gmm.sample() for i in xrange(5000)]).T\n",
"gmm.set_coef(array([0.0,0.0,0.0,1.0]))\n",
"xptr1=array([gmm.sample() for i in xrange(num)]).T\n",
"xpte1=array([gmm.sample() for i in xrange(5000)]).T\n",
"traindata=concatenate((xntr,xntr1,xptr,xptr1), axis=1)\n",
"trainlab=concatenate((-ones(2*num), ones(2*num)))\n",
"\n",
"testdata=concatenate((xnte,xnte1,xpte,xpte1), axis=1)\n",
"testlab=concatenate((-ones(10000), ones(10000)))\n",
"\n",
"feats_train=RealFeatures(traindata) #convert to shogun features\n",
"labels=BinaryLabels(trainlab) #generate labels for data"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"_=jet()\n",
"figure(figsize(18,5))\n",
"subplot(121)\n",
"_=scatter(traindata[0,:], traindata[1,:], c=trainlab, s=100) # plot train data\n",
"colors=[\"blue\",\"blue\",\"red\",\"red\"]\n",
"# a tool for visualisation\n",
"from matplotlib.patches import Ellipse\n",
"def get_gaussian_ellipse_artist(mean, cov, nstd=1.96, color=\"red\", linewidth=3):\n",
" vals, vecs = eigh(cov)\n",
" order = vals.argsort()[::-1]\n",
" vals, vecs = vals[order], vecs[:, order] \n",
" theta = numpy.degrees(arctan2(*vecs[:, 0][::-1]))\n",
" width, height = 2 * nstd * sqrt(vals)\n",
" e = Ellipse(xy=mean, width=width, height=height, angle=theta, \\\n",
" edgecolor=color, fill=False, linewidth=linewidth)\n",
" \n",
" return e\n",
"for i in range(num_components):\n",
" gca().add_artist(get_gaussian_ellipse_artist(means[i], covs, color=colors[i]))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
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gDeIk0CExkSunT7NlyxaGD4d165IWR4qJEVnxFi1Ku2iNGjWiQ/eerFYq+QZY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XykyRW3aJEw7S3MrVu3qFGjDnFxr8OzqV+ngXPASxl88j+02mXcvx+e4m+aEY8ePWL58uWcO/cv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\nJBKJRFKAkYpaIpFIJJICzP8DrGr6J3JJ4h4AAAAASUVORK5CYII=\n"
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Generating Kernel weights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just to help us visualize lets use two gaussian kernels ([CGaussianKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGaussianKernel.html)) with considerably different widths. We need to append them to the Combined kernel. To generate the optimal weights (i.e $\\beta$s in the above equation), training of [MKL](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLClassification.html) is required. This generates the weights as seen in this example."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"width0=0.5\n",
"kernel0=GaussianKernel(feats_train, feats_train, width0)\n",
"\n",
"width1=25\n",
"kernel1=GaussianKernel(feats_train, feats_train, width1)\n",
"\n",
"kernel.append_kernel(kernel0) #combine kernels\n",
"kernel.append_kernel(kernel1)\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLClassification()\n",
"mkl.set_mkl_norm(1) #set the norm, weights sum to 1.\n",
"mkl.set_C(1, 1)\n",
"mkl.set_kernel(kernel)\n",
"mkl.set_labels(labels)\n",
"\n",
"mkl.train() #train to get weights\n",
"\n",
"w=kernel.get_subkernel_weights()\n",
"print w"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.94960839 0.05039161]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Prediction using MKL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The weights generated can be intuitively understood too. We will see that on plotting individual subkernels outputs and and outputs of the MKL classification. To apply on test features, we can reinitialize the kernel with `kernel.init` and pass the test features. After that its just a matter of doing `mkl.apply` to generate outputs. "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size=100\n",
"x1=linspace(-5, 5, size)\n",
"x2=linspace(-5, 5, size)\n",
"x, y=meshgrid(x1, x2)\n",
"grid=RealFeatures(array((ravel(x), ravel(y)))) # generate X-Y grid test data\n",
"\n",
"kernel0t=GaussianKernel(feats_train, grid, width0)\n",
"kernel1t=GaussianKernel(feats_train, grid, width1)\n",
"\n",
"kernelt=CombinedKernel()\n",
"kernelt.append_kernel(kernel0t)\n",
"kernelt.append_kernel(kernel1t)\n",
"kernelt.init(feats_train, grid) #initailize with test grid\n",
"\n",
"mkl.set_kernel(kernelt)\n",
"grid_out=mkl.apply() #prediction\n",
"\n",
"z=grid_out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(10,5))\n",
"title(\"Classification using MKL\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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6sUv+UIkGsRwxYnW/ANKGYcDLD0LeRLjrSbj9Csk+svFV2sgIB8eXzTYkJSUx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\nEEIIIYThpIMhhBBCCMP9HyAh872+IvE+AAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To justify the weights, lets train and compare two subkernels with the MKL classification output. Training MKL classifier with a single kernel appended to a combined kernel makes no sense and is just like normal single kernel based classification, but lets do it for comparison."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"z=grid_out.get_labels().reshape((size, size))\n",
"\n",
"figure(figsize=(20,5)) # MKL\n",
"subplot(131, title=\"Multiple Kernels combined\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker0=CombinedKernel()\n",
"comb_ker0.append_kernel(kernel0)\n",
"comb_ker0.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker0)\n",
"mkl.train()\n",
"comb_ker0t=CombinedKernel()\n",
"comb_ker0t.append_kernel(kernel0)\n",
"comb_ker0t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker0t)\n",
"out0=mkl.apply()\n",
"\n",
"z=out0.get_labels().reshape((size, size)) #subkernel 1\n",
"subplot(132, title=\"Kernel 1\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n",
"comb_ker1=CombinedKernel()\n",
"comb_ker1.append_kernel(kernel1)\n",
"comb_ker1.init(feats_train, feats_train)\n",
"mkl.set_kernel(comb_ker1)\n",
"mkl.train()\n",
"comb_ker1t=CombinedKernel()\n",
"comb_ker1t.append_kernel(kernel1)\n",
"comb_ker1t.init(feats_train, grid)\n",
"mkl.set_kernel(comb_ker1t)\n",
"out1=mkl.apply()\n",
"\n",
"z=out1.get_labels().reshape((size, size)) #subkernel 2\n",
"subplot(133, title=\"kernel 2\")\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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gRvz8sc53eQdTCoqmAlKBG/Dztyi/szhHeUIkAQ3FfJGwxnYgkggczROOhi0i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\n"
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see the multiple kernel output seems just about right. Kernel 1 gives a sort of overfiting output while the kernel 2 seems not so accurate. The kernel weights are hence so adjusted to get a refined output. We can have a look at the errors by these subkernels to have more food for thought. Most of the times, the MKL error is lesser as it incorporates aspects of both kernels. One of them is strict while other is lenient, MKL finds a balance between those."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"kernelt.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(kernelt)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :MKL\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"\n",
"comb_ker0t.init(feats_train,RealFeatures(testdata)) \n",
"mkl.set_kernel(comb_ker0t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :Subkernel1\"% (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n",
"\n",
"comb_ker1t.init(feats_train, RealFeatures(testdata))\n",
"mkl.set_kernel(comb_ker1t)\n",
"out=mkl.apply()\n",
"\n",
"evaluator=ErrorRateMeasure()\n",
"print \"Test error is %2.2f%% :subkernel2\" % (100*evaluator.evaluate(out,BinaryLabels(testlab)))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Test error is 11.74% :MKL\n",
"Test error is 22.09% :Subkernel1"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Test error is 14.50% :subkernel2"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"MKL for knowledge discovery:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MKL can recover information about the problem at hand. Let us see this with a binary classification problem. The task is to separate two concentric classes shaped like circles. By varying the distance between the boundary of the circles we can control the separability of the problem. Starting with an almost non-separable scenario, the data quickly becomes separable as the distance between the circles increases."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def circle(x, radius, neg):\n",
" y=sqrt(square(radius)-square(x))\n",
" if neg:\n",
" return[x, -y]\n",
" else:\n",
" return [x,y]\n",
" \n",
"def get_circle(radius):\n",
" neg=False\n",
" range0=linspace(-radius,radius,100)\n",
" pos_a=array([circle(i, radius, neg) for i in range0]).T\n",
" neg=True\n",
" neg_a=array([circle(i, radius, neg) for i in range0]).T\n",
" c=concatenate((neg_a,pos_a), axis=1)\n",
" return c\n",
"\n",
"def get_data(r1, r2):\n",
" c1=get_circle(r1)\n",
" c2=get_circle(r2)\n",
" c=concatenate((c1, c2), axis=1)\n",
" feats_tr=RealFeatures(c)\n",
" return c, feats_tr\n",
"\n",
"l=concatenate((-ones(200),ones(200)))\n",
"lab=BinaryLabels(l)\n",
"\n",
"c, feats_tr=get_data(2,4) #get 2 circles with radius 2 and 4\n",
"c1, feats_tr1=get_data(2,3)\n",
"_=gray()\n",
"figure(figsize=(10,5))\n",
"title(\"Different separations\")\n",
"subplot(121)\n",
"p=scatter(c[0,:], c[1,:], c=lab)\n",
"subplot(122)\n",
"q=scatter(c1[0,:], c1[1,:], c=lab)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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UrFkz9ke7npw8eZLU1NRIV1eX1q9fTwMHDqSysjLy8vIiT09P6tu3L/H5fDp3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0nK5W1KSkrC/PnzYWBgAB0dHbi6uuLAgQNITEzE3LlzkZqaiu7du0NaWhpRUVFwcnKCtDR/hn9d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\nEOzfvx/e3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XHQ0NCAnZ1dl/mahI4kdG35q3oQHByM4OBghISEYPny5YiOju7Q8YG3V49e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\ngWKMMcYYa6f/A05wr0GMGwMfAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are the type of circles we want to distinguish between. We can try classification with a constant separation between the circles first."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def train_mkl(circles, feats_tr):\n",
" kernel0=GaussianKernel(feats_tr, feats_tr, 1) # four kernels with different widths \n",
" kernel1=GaussianKernel(feats_tr, feats_tr, 5)\n",
" kernel2=GaussianKernel(feats_tr, feats_tr, 7)\n",
" kernel3=GaussianKernel(feats_tr, feats_tr, 10)\n",
" kernel = CombinedKernel()\n",
" kernel.append_kernel(kernel0)\n",
" kernel.append_kernel(kernel1)\n",
" kernel.append_kernel(kernel2)\n",
" kernel.append_kernel(kernel3)\n",
" \n",
" kernel.init(feats_tr, feats_tr)\n",
" mkl = MKLClassification()\n",
" mkl.set_mkl_norm(1)\n",
" mkl.set_C(1, 1)\n",
" mkl.set_kernel(kernel)\n",
" mkl.set_labels(lab)\n",
" \n",
" mkl.train()\n",
" \n",
" w=kernel.get_subkernel_weights()\n",
" return w, mkl\n",
"\n",
"def test_mkl(mkl, grid):\n",
" kernel0t=GaussianKernel(feats_tr, grid, 1)\n",
" kernel1t=GaussianKernel(feats_tr, grid, 5)\n",
" kernel2t=GaussianKernel(feats_tr, grid, 7)\n",
" kernel3t=GaussianKernel(feats_tr, grid, 10)\n",
" kernelt = CombinedKernel()\n",
" kernelt.append_kernel(kernel0t)\n",
" kernelt.append_kernel(kernel1t)\n",
" kernelt.append_kernel(kernel2t)\n",
" kernelt.append_kernel(kernel3t)\n",
" kernelt.init(feats_tr, grid)\n",
" mkl.set_kernel(kernelt)\n",
" out=mkl.apply()\n",
" return out\n",
"\n",
"size=50\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))))\n",
"\n",
"\n",
"w, mkl=train_mkl(c, feats_tr)\n",
"print w\n",
"out=test_mkl(mkl,grid)\n",
"\n",
"z=out.get_values().reshape((size, size))\n",
"\n",
"figure(figsize=(5,5))\n",
"c=pcolor(x, y, z)\n",
"_=contour(x, y, z, linewidths=1, colors='black', hold=True)\n",
"_=colorbar(c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 3.70179551e-05 6.14303709e-01 3.83958304e-01 1.70096833e-03]\n"
]
},
{
"output_type": "display_data",
"png": 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8GX5+fgqz50BpaSlWrFiBbdu2kRbX19fXY8WKFbCwsMC8efMID1V9fT0iIiJw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\ndoQQWfg/hd7ZQYGHl5AAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So MKL classifier classifies them as expected. Now lets vary the separation and see how it affects the weights.The choice of the kernel width of the Gaussian kernel used for classification is expected to depend on the separation distance of the learning problem: An increased distance between the circles will correspond to a larger optimal kernel width. This effect should be visible in the results of the MKL, where we used MKL-SVMs with four kernels with different widths (1,5,7,10). "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"range1=linspace(5.5,7.5,50)\n",
"x=linspace(1.5,3.5,50)\n",
"temp=[]\n",
"\n",
"for i in range1:\n",
" c, feats=get_data(4,i) #vary separation between circles\n",
" w, mkl=train_mkl(c, feats)\n",
" temp.append(w)\n",
"y=array([temp[i] for i in range(0,50)]).T\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figure(figsize=(20,5))\n",
"_=plot(x, y[0,:], color='k', linewidth=2)\n",
"_=plot(x, y[1,:], color='r', linewidth=2)\n",
"_=plot(x, y[2,:], color='g', linewidth=2)\n",
"_=plot(x, y[3,:], color='y', linewidth=2)\n",
"title(\"Comparison between kernel widths and weights\")\n",
"ylabel(\"Weight\")\n",
"xlabel(\"Distance between circles\")\n",
"_=legend([\"1\",\"5\",\"7\",\"10\"])\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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WNXRviB7BPdAzuCcaV3/8KAl7K3t0CuiETgGdAAC5mlycuH0CB2P15dLRm0dx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\nljl2xAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the above plot we see the obtained kernel weightings for the four kernels. Every line shows one weighting. The courses of the kernel weightings reflect the development of the learning problem: as long as the problem is difficult the best separation can be obtained when using the kernel with smallest width. The low width kernel looses importance when the distance between the circle increases and larger kernel widths obtain a larger weight in MKL. Increasing the distance between the circles, kernels with greater widths are used. "
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Multiclass classification using MKL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"MKL can be used for multiclass classification using the [MKLMulticlass](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CMKLMulticlass.html) class. It is based on the GMNPSVM Multiclass SVM. Its termination criterion is set by `set_mkl_epsilon(float64_t eps )` and the maximal number of MKL iterations is set by `set_max_num_mkliters(int32_t maxnum)`.\n",
"\n",
"To see this in action let us compare it to the normal [GMNPSVM](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGMNPSVM.html) example as in the [KNN notebook](http://www.shogun-toolbox.org/static/notebook/current/KNN.html#Comparison-to-Multiclass-Support-Vector-Machines), just to see how MKL fares in object recognition. We use the USPS digit recognition dataset."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.io import loadmat, savemat\n",
"from numpy import random\n",
"from os import path\n",
"\n",
"mat = loadmat('../../../data/multiclass/usps.mat')\n",
"Xall = mat['data']\n",
"Yall = np.array(mat['label'].squeeze(), dtype=np.double)\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",
"random.seed(0)\n",
"\n",
"subset = random.permutation(len(Yall))\n",
"\n",
"Xtrain = Xall[:, subset[:5000]]\n",
"Ytrain = Yall[subset[:5000]]\n",
"\n",
"Nsplit = 2\n",
"all_ks = range(1, 21)\n",
"\n",
"print Xall.shape\n",
"print Xtrain.shape"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(256, 9298)\n",
"(256, 5000)\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_example(dat, lab):\n",
" for i in xrange(5):\n",
" ax=subplot(1,5,i+1)\n",
" title(int(lab[i]))\n",
" ax.imshow(dat[:,i].reshape((16,16)), interpolation='nearest')\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])\n",
" \n",
" \n",
"_=figure(figsize=(17,6))\n",
"gray()\n",
"plot_example(Xtrain, Ytrain)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAA8MAAAC/CAYAAADafQ4RAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We combine a Gaussian kernel and a [PolyKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CPolyKernel.html)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"labels = MulticlassLabels(Ytrain)\n",
"feats = RealFeatures(Xtrain) #training features\n",
"Xrem=Xall[:,subset[6000:]]\n",
"Yrem=Yall[subset[6000:]]\n",
"\n",
"feats_rem=RealFeatures(Xrem) #test features not used in training\n",
"labels_rem=MulticlassLabels(Yrem)\n",
"\n",
"kernel = CombinedKernel()\n",
"feats_train = CombinedFeatures()\n",
"feats_test = CombinedFeatures()\n",
"\n",
"\n",
"subkernel = GaussianKernel(10,80) #append gaussian kernel\n",
"feats_train.append_feature_obj(feats)\n",
"feats_test.append_feature_obj(feats_rem)\n",
"kernel.append_kernel(subkernel)\n",
"\n",
"feats = RealFeatures(Xtrain)\n",
"subkernel = PolyKernel(10,2) #append PolyKernel\n",
"feats_train.append_feature_obj(feats)\n",
"feats_test.append_feature_obj(feats_rem)\n",
"kernel.append_kernel(subkernel)\n",
"\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLMulticlass(1.2, kernel, labels)\n",
"\n",
"mkl.set_epsilon(1e-2)\n",
"mkl.set_mkl_epsilon(0.001)\n",
"mkl.set_mkl_norm(2)\n",
"\n",
"mkl.train()\n",
"\n",
"kernel.init(feats_train, feats_test) #initialize with test features\n",
"\n",
"out = mkl.apply()\n",
"evaluator = MulticlassAccuracy()\n",
"accuracy = evaluator.evaluate(out, labels_rem)\n",
"print \"Accuracy = %2.2f%%\" % (100*accuracy)\n",
"\n",
"idx=np.where(out.get_labels() != Yrem)[0]\n",
"Xbad=Xrem[:,idx]\n",
"Ybad=Yrem[idx]\n",
"_=figure(figsize=(17,6))\n",
"gray()\n",
"plot_example(Xbad, Ybad)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Accuracy = 97.70%\n"
]
},
{
"output_type": "display_data",
"png": 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}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The misclassifed examples are surely pretty tough to predict. As seen MKL seems to work a shade better in this case. One could try out this with more and different type of kernels too."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"References:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[1] Soeren Sonnenburg, Gunnar Raetsch, Christin Schaefer, and Bernhard Schoelkopf. Large Scale Multiple Kernel Learning. Journal of Machine Learning Research, 7:1531-1565, July 2006.\n",
"\n",
"[2] Kernel Methods for Object Recognition , Christoph H. Lampert"
]
}
],
"metadata": {}
}
]
}
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