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Created March 29, 2014 18:45
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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": "heading",
"level": 4,
"metadata": {},
"source": [
"By Saurabh Mahindre - <a href=\"https://github.com/Saurabh7\">github.com/Saurabh7</a>"
]
},
{
"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> (MKL) 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 it's 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 aspects 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 you just want code examples)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"</br>In a SVM, defined as:\n",
"$$f({\\bf x})=\\text{sign} \\left(\\sum_{i=0}^{N-1} \\alpha_i k({\\bf x}, {\\bf x_i})+b\\right)$$</br>\n",
"where ${\\bf x_i},{i = 1,...,N}$ are labeled training examples ($y_i \\in {\u00b11}$).\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 the multiple kernel learning problem for binary classification one is given $N$ data points ($x_i, y_i$ )\n",
" ($y_i \\in {\u00b11}$), where $x_i$ is translated via $K$ mappings $\\phi_k(x) \\rightarrow R^{D_k} $, $k=1,...,K$ , from the input into $K$ feature spaces $(\\phi_1(x_i),...,\\phi_K(x_i))$ where $D_k$ denotes dimensionality of the $k$-th feature space.\n",
"\n",
"In MKL $\\alpha_i$,$\\beta$ and bias are determined by solving the following optimization program. For details see [1].\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",
"$$ {\\frac{1}{2}\\sum_{i,j=1}^N \\alpha_i \\alpha_j y_i y_j \\leq \\gamma}, \\forall k=1,\\ldots,K\\nonumber\\\\\n",
"$$\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 one of the two approaches described in [1] is used.\n",
"The first approach (also called the wrapper algorithm) wraps around a single kernel SVMs, alternatingly solving for $\\alpha$ and $\\beta$. 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](http://en.wikipedia.org/wiki/GNU_Linear_Programming_Kit) 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](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CSVMLight.html).\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": "heading",
"level": 3,
"metadata": {},
"source": [
"Prediction on toy data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In order to see the prediction capabilities, let us 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",
"#convert to shogun features and generate labels for data\n",
"feats_train=RealFeatures(traindata) \n",
"labels=BinaryLabels(trainlab) "
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"_=jet()\n",
"figure(figsize(18,5))\n",
"subplot(121)\n",
"# plot train data\n",
"_=scatter(traindata[0,:], traindata[1,:], c=trainlab, s=100)\n",
"title('Toy data for classification')\n",
"axis('equal')\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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TCwEvvwxnzmTJDokkL5BrzpI8wWJRPK2J21dLllS2AZUrl7927Nixg/HjP+fE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\n"
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Generating Kernel weights"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Just to help us visualize let's use two gaussian kernels ([CGaussianKernel](http://www.shogun-toolbox.org/doc/en/latest/classshogun_1_1CGaussianKernel.html)) with considerably different widths. As required in MKL, 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",
"#combine kernels\n",
"kernel.append_kernel(kernel0) \n",
"kernel.append_kernel(kernel1)\n",
"kernel.init(feats_train, feats_train)\n",
"\n",
"mkl = MKLClassification()\n",
"#set the norm, weights sum to 1.\n",
"mkl.set_mkl_norm(1) \n",
"mkl.set_C(1, 1)\n",
"mkl.set_kernel(kernel)\n",
"mkl.set_labels(labels)\n",
"\n",
"#train to get weights\n",
"mkl.train() \n",
"\n",
"w=kernel.get_subkernel_weights()\n",
"print w"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[ 0.98377736 0.01622264]\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Binary classification using MKL"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now with the data ready and training done, we can do the binary classification. The weights generated can be intuitively understood. We will see that on plotting individual subkernels outputs and outputs of the MKL classification. To apply on test features, we need to reinitialize the kernel with `kernel.init` and pass the test features. After that it's 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",
"#Generate X-Y grid test data\n",
"grid=RealFeatures(array((ravel(x), ravel(y))))\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",
"#initailize with test grid\n",
"kernelt.init(feats_train, grid)\n",
"\n",
"mkl.set_kernel(kernelt)\n",
"#prediction\n",
"grid_out=mkl.apply() \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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7N8X9VCQSs9+hIEflZnsfRFeBEG0R4iRn+z5yfltL1KDexjaLrkChwpcvVnI1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SAAAg\nAElEQVRBoVKvRGwjc7O6fIJL1yuhQ3wm34iFrlQKDXrtxge9yxE8R4/d6LpXqvKpeZgyGaZMTqe0\nJJkPXmvknTtX8vDpjUw4NpHJJybR7/D0IGNDRm2I61TayDKBVNzpKtjlmnb1y6XPp39nxbQb8G3c\njKtrdou+2143QlYbRbyGZLRFa/2CmlCbeJ+QZ5GIGTR7v8g0u53CuY+jFxSgKdAUjas34u7Vdfd3\n8ZqSiReKvzmZ+1+FJlW5FswIZKlQHWYh60eksFREtFCgTOS1SDxs/GoDm77a2Or2YUMEGhiaruv6\nvhqoFj/59ddfpR4MTdN4W58eounuPw4GA6O2sontqyrZ+FstG5fVsmFZ4LO+xkePIbEUDo2jx9BY\n+g1107VvVNBDTSVN9WAyMHwO4UEjMTDEuAMxVRJkaaGB7yWbPMx9q4IvX69gy1oPhxydzLhjkxkx\nJQlvXJKhHzMGRgWt96PSRmWsWr8bzRZ8HFUUQUXIHgbGInutF+KTxbGEysDY2zltCfFakMWo6LpO\n04YiGhauouGX5dR/u5imTSV0X/I6trhAn6KBESepaiLG3sgKDMZTE/Q9iXJDGzNKvdLft0KsS1uK\nELa1jRjHI7v3q6Qam7l+Ae7R7qKVx2vIoGkavG1irNlaWOfY6m031MVPLIQGdVVetv1et2dZW8vW\nVbVsXVVHXaWXvF7RdOkfS7dBsRw7OZmuA2LJyrcHxUvIjAcL7YusLi5OuTqDU67OYONmG9++t5MP\nntzGfWeupc/YZEbNzGD0zHRSc9W0/zsaonGxvyj769PEnzgVV6+CkPYbSdh02Pl41m4mamgfoob1\nIeW6M4mdNBJb9IFxzi1Y2Bv263VetfiJ01OLza5hs2EFBO4Dfr9OQ2UjVaVNVGzftXio3NbIji0e\ndmzxULrFw44tjXg9Otnd3eR0d5PdPYp+A5xMm51Glz5RpOc6ibK1NB50oEapzoixjYLQVqNEIEvw\nPLgkNcs0Fe9oiNx+0gtdWOmyG70lPoEicTskHh138LoYu+yNr/Xy9fH5MQy43M6Fl6dRU5XC3M+9\nfP1+Ea/eupq8Hi4mHpvA6FnZdOmz5624XOJ5EN8uzbrBjbU/ZPSQiiBV27FrbFt2JluOuJCcuc9h\n75EZ1EY160iE+JaqkiWhkjGiUh9ERp/1+PDv2BP2KMAGtvHTMjHYSMO1TnvJ27TuWVTJNGltm0iA\nynmVXdFGtE6bRIRnvLMJbakWPzkudj66X8fvB00DzaZht4PNrqHZNGzNf9v29vfuRf4/u2PP/+1C\n+z3/C25ns2st2krGsWnN8wv0iRZYF/g0Gkq6Htg/3a/j94Hfp+P36TR5dJoa/Xg9fpoadTz1Phpq\n/TTW+Wio9VFf46O20kdthZf6ai9RcXaS0p0kZQSWxHQnqZkOeg6LZewxKaTnucjMtZOY5giaQyT+\nwC2YR1yCjcnHJzL5+ES8TToL59cy790qrp28nKQMB5NPS+eI09KwZbfe14GMhHNnoTc1UTT5XLr9\n9FKnrL3R0riwYME0IvAR0GoMxn4PoGnM00cBwQ9hn2/Pw9jn09H9gYeyz6ej+Xz4/bse0oH/7/rb\n3+IB7tv16ZW028v/d/29ayyxbctxdD+72+h6YP66v/lvvx6wllrAZttlALHbUHG5bThcGi63ht2p\nERVjIyrWRlSMjehYOzGxOgnJDuKS7MTE21pUEt0D8c1I9mai8qYkvkVL2zQKMRiNxrd6h7iZrKK6\n+DInu/jbMyhJxZRWoVZl/QjrdIkUhBgD0igp817vbp3Tr/DF8cvXDXz4UjVz3q1lwNg4TrgijdFT\n43cbnGUEB1GXYgyqLiNN+G5sI24nbgPG2I2W33Wvl50vf0HUGccFUSd7q4OyL+y45C6c8VFk/O1P\nu9epaKuYjcEQIa+m2rqHx8ybrWw+4m9etl+iV0wWo6ISp6ESYyUee7OaJPsbXNyWNtJqwIY2rZ9n\n1fncpD3cvjEYL5gY648dHIMRSmhawHOBXcPh3Hu7g+lt/GDaVwv7D7tdY9Th0Yw6PJqbHvPzwZs+\nHru2iCdscPr1GUw+MTlQvj0SYLOx46l3ScBF0h9n7FdXSTecy9ZhJ5B6y3nY4603fgsWDIjALJID\nNwHfgoWDHDGxNo46K4X/LOnNJffl8MGzOzmh5wrmvFjcbm9O+4Jms5H/6JVsv/4R6r5ZuF99Obvm\nkPn4DWAyq8iChU6Pzia0pQpZznbwJA78t3iznggzVVBlgZeiW1NaBbVO0LOQBV7WCitk8U3idrI2\n4m6E8mI2c9WqbBMiGkWT9CNku+KQBJTGxgWnEDbG1hjaxMSIacSNoMGM6TBjehILv2/klkt+54dX\nN3Hz07lk5svdGWbSMGuklISovSAECY8qpOsLt7Jp9rVk/uUc0i6ZDZI4bxU3dOIpbS/wJQvOlOsY\niG1EmWn1iqfBCF5nVo5epfKwSInIaBQVasOokRKaH29He2vN36OD919Go3T0vgGWB8OCBQvhxdAx\nbp5f0IPB42I4Y9ha3n16Z4d7MxKmHULP756m7F/vseOh1zp0LhYsdFpEoAfDMjAsWOhkcDg1zrkl\ng6fmduO9Z8q5c8Zi6qo69vXG3SOPnt8/Q8pZRym113Udz+oN4Z2UBQudCRFoYLQLRSKLQm6JULng\nVNCedIyZKGq5y1JwQ/sk+e2NQg68SHWAkdqQtRHXyTJERO+sCkViFrIr1Gy2Rzi2UYU4Z9lYVcFf\n3ZJYRndiMG3iSpG45ZvHGjEA3v4uhRsva+TWw3/igf8WkpwRoEzEjAeZ+qio0inLShBpFJlbfjct\nEGuHWDse4YLRdZ3fj7sJ7/ad+KvrAktFNY6cNHovehGbS07zqFCFajoPrdOSMpjRzzCrO2GUCm9d\nxVRGo6jI2qtUUzWjlRFKqFVTbXsbFUQspd/ZdDAsWLAQ2XA6Na77Zxee/UsRlxy6ioc+70lWV1lJ\n9Q6Ez0fKRbOwxUVji4/BHh+LKyEKe2qiJcxnwYIqItDusQwMCxY6OTRN4/y7cklIcXDFpNU8Ob83\n5HT0rPZAcziInzYmaF3EviVasBCpiMAgz3aiSPadRRLOinqh6dfcmVO5SRqqGyrIboeM/jDbjzhF\n2eExc8gURKz2uk6EWj2ijoNsH0THgkzuQTg/CV4jTeDLLgv6vqvA1oVXudHq47juyFXc93Us8cl7\nJlGtUDxLJvwlZp+oZIOYFaQSf4dmXfeh6kcF0SGqhKyUJWagSFrvR+X4tLeIVrggm494vUbanA90\nWEGeFiwcRDj/piTGTo3mLzOW42mwNCUsWOg0OFiDPC10Tvj9sGUnrNoCm8tgRzXsqAp8ltdAky+g\ni7RrcTkgPmrPkhgDWQmQnQQ5SZCdCjnJgXYWwgNN07jm/lQuP6WKf5yzhhtf7mXFOViw0BkQZoPh\n1ltv5YMPPkDTNFJTU3n++efJz8/f5zbtUoukWE/cZxszfGvIaBVfiPrxSiLRFVQH7cJmhjofoCZs\nJVIZRo0mNYpkL0JbHi8s2gzfrYUF62BFCazZDonR0DsDuiRDetyeJcUNTjvYNbDbwO4M9FHdGFiq\nGqCyHkqqobgSiqqguAq2VUNmPBSkQLdU6JYB3dP2LFkJYFMpZdGeFImZS0g2P9GwklEkYsmQFGMT\nXYivKEox1hlZW5/LxRPXMn5GAufcmkURxqppxUKgxjYyDW3EGiZi5gkYqRWZqJdKtVIRKtSGDCpZ\nJOEbq3VKQkZ/qFAkZjJEZJkm4r6qUCSRSC2o0HXh7Odi7fn2rUVyrYmxHlCvRVJdXU18fOD3/dhj\nj7F48WKeffbZfW5jvStakELXYdFGeOdH+GoVLNwEhRkwtgcc2ReuPhx6ZUBCNGqFzBTjJrw+2FIB\n68ual3L4fDn8XgrrdkB1A3RNhS6p0CUl8HfX1IDhkZEAmQmQHk+g5k0I4PVBRR2U10F5bfPftYHv\nFc1LdT3Ue6DOA/VN0NAUEKt02JuNKw1i3ZCVGPDU5CVDfhoMyoOYDkrocEfb+Pv73Thv9Gq69nbT\n98ROXpbVgoXOjjDbeLuMC4CamhrS0ozFD0W0T5CnrxUdDMnbf2tQ8Q7IxwrPNprKyVUJhgyVB0PF\nOyF4OXQdfl4Bby2EtxYF1s3uD7dNhFH5kBDV3HDXvjY1L2aDPMWrzxFYVeCEgiw4PAvDm35NI2ys\nhk3lsKkCNuyETzdDSbP3Y1s1lNcH5poQBfHu5iUKHLbAYm9e0AJelSYfeHyBv2saA0ZMjSfw2eCF\nxChIjgksSVGQHB1YkpqXvCSIdu5ZojTQaaaG9MBndWPAW7N+M3zzG2ysgJXbYVA2TOgBE7rDoX0C\n82zTMZQYUprg+YhPNAZwJtnLScqGpz5I47ypm7mzSzz9Dgn2PtQLnodGQxSqEbLAQrFUgEfST6je\nNlVg5m07nMGiZqolq3geZOeio6ugHohQ0dOICLRDTMWf//xnXnrpJWJiYvjhhx9abd8uFEmld98+\nbcvAaIEOMDB2VMGL38H/zYemJjhpGMweAkPyQJMlAIn7GkIDwwAVKkH47vVBRX0zHdOwh5bx+gIP\n/F2f2MBlD8R8OO3g0iDOHWyUxDjB1jIUWmW/FPe9thF+3ARf/x5YFm6Fk4fDpRNgQA5yikRkGzMk\nbQSKpKqL8fdXZN/jsZj3cR1/Pr+Ch7/uT27hHsGtIgWKRCzXLqdIgkW8LANj3/1YBkZoEK5rSrXf\ndqdILlYYa+tXUPTVnu8/3xE0xylTplBSUmLY7J577mHGjD0Vke+77z5WrVrFc889t+95WQZGaLY5\nEA2MHxfDPz6Dz5fBscPg3AkwPgeCYv5k/US4gaEMsW+z59BMG8mci+rhme/g6W+hMB1umwWT+gqN\nwmBgADz7jJ2X79nKA3P6kdM94EaxDIx9b2MZGJGNg87AOM/EWM+qx2C0xKZNm/jDH/7AsmXL9tmu\nXSiSljLWKg/rkD3QZQjVA0JlGzMP4nYwML5ZA3d9BCuL4NpJ8MzsQLAmgEEOQRYsKu6XTE5cBe1p\nYJi90sN1vUjmk+OA28bDzWPgjaVw7rNwVH948NgWmTXidlViL0Bc8Nf4SuODJj4l+MSedH42Dm8K\nV09YyqOfFdC9fxRJVAS1kVcmDd552YMvXjAozAZ5qmhlqNz8VdqEKlhUJWBSNATMVlQOncGjsu/h\n88ernOeORMQaV2Ge1po1a+jZsycA77//PkOHDm11m8g+kxZCinmr4I4PYUMp3HwUnDnISgmNRDjt\ncNoQOHoY/PFlmPAovHk25CeHd9zZF6cSE2/nkskbePDDLqSNDO94FixYCCHCHINx0003sWrVKux2\nOz169OCpp55qdRvr8XIQYNlmuOolWF8CtxwNp40GpwO5l8NCxCAxGt45B/7+Pxj1IHx6EQyWpKWG\nEtNPTyI2wcZVR23kkn/FMuY4GQdjwYKFiEOYDYy33nqrzdu0D0XS8kEWKpezSpuOplHCRZGoyHfX\nws5a+Mt78MbP8JcZcOEZgbfj3duHqpqqyn6ZpTFUaBOzcuJmEM4qsWJogj0gtXvjeOiRAEc+CZ9d\nCYPzWrSJwgiB1tIqjU3EzJJk+544iZnHQNcPUrjqjFV8/8omrnwkj/QceUVTMV5AVjlZpERkdIjo\nFpfRGOK6UPVjlqs3QzeoaFOoVFMNlTZFe1ayVoU4J7OUyQGT/REqRGA1VUsqvBOiyQuPzYE+twS+\nr7gLLpvUbFxYOCBxwiB49Bg4+gkokRgMocaQQ9z8Z0kfuvSO4szBK3n7yVJ8vvYJWLNgwULngGVg\ndDJ8vQKG3AQfLoY518Djp0FqXOvbWYh8nDgYzhkLZzwX0CwJN9zRNi78azZPfFXIF6+Wc+WwBXz+\nf0XUVUXeW68FCwc9fCaWMKNd0lT131tpFK70wFBRJGYpEzMUiWzOChRJaSlc/xZ8sRwePhlm9RbS\nTQHEN9/2pEhkCFUWidm+VRCuZ6lMs0qkOyQ6GN44GPMwXDAGzh+LVCrckLoqK80uZJyWphut0NIW\nMuC6rvPpJxrvP7uTX+bWcuiMeI4+K5neh2dhs+250GQVV8XqqTKXtwptIQp9ydqIdIxMHExlLJWs\nFpUSB2YyRMzSHypZJB0JM3LwELqskvamSC7QXmrfNNUZJsb60FyaqiqsIM8DHE1e+NdcuOs9OHUU\nLL+rWQ3SCuDslHDY4blT4fDHApLtXcIc9LkLmqYx/qh4xh8VT/kOL5+/Wsmj15WwfetWBoyPZ+D4\nePqPiydnSBROl+UYtWCh3RGBjkXLwDiA8b/f4PKXIDcZvrgKBu27sJ2FToIB2XDFRLjsLfjghvYf\nPzndwUlXpHLSFams2+Ri2TdVLP2mmk+f38HWtcvJLIgmuzCa7MIYcgqjSekWT3K2m6QsNwnpLouY\ntWAhHIjAIM/2oUhWtFhhNvsjXNkn4VRvDBNFsnETXPs2/LIJHjweZg4GTdTdkXkwRNEsFYpEJWPF\nLEUi4kDIIlGBiidWlv0hevP3IRXe6IXBD8PfToSZot6NSJHIvBwCReKVZKNWJATTJiqVUitrHWxe\n52HLWg+b1zaxea2HLRt8lBY3UVbcRE2lj+QMJ6lZTpIyHCRnOEjJdJKU6SIt10VajpO0XBfJOVG4\no4MPpEh3yAS7xPmI9Exgu9AIf4kIlbCVWRqlI2GWfmhP2iScFIms73ZX8jzcxFhzLYrEQjPWb4d7\nPoR3foI/TYIXz4JoldLlFjod3A548lg4+1U4ol+gWmskIDrWRq9BUfQatMeCamkYNHn87CjRKd/e\nRPl27+7PHVs8rFhQS+lWDzu2eigrbiIhxUFuYRS5PaPJ7RlFbr8ECofHk5rjCtxQLViwsAcWRWLB\nDDaWwt3vw9s/wyWTYfUdVmaIBZhUCOMK4b7/wl3HdvRs1OB02cjsYiezixj4GfwG2OS3UbrVw9Y1\nDWxZ08DWNfUseqqINb9UY7NpFA6Po/vwJPodmkzfcUm4Y6wcbAsHOSLQwGgfiuTnVhqZydoIJ42i\nQm2o9GuGImn+7vfD3JXw9Dz4YhlcPBGuntxsWKjUIpHVEDFTcdVsbZRwClKJ68JZEE2EynPM7JxF\no1GhmuoWHwy+F366HrqnNa9MFbaRUSQKbXRhrLpYY/CExx3sOpFREqI7W0ZJiAaGLPvDgwtd19m2\nxcuKXxpY/LOXxV/XsPrXOnoNi2H4pHj6T06j35gE7A6teRtjPyKNIpuPSml6FYSqPkhr/YYSoar5\nYnYbM7SJ2UyTUNEmEUGRjDAx1s8WRXJQoaQSnv8GnpkHcVFw4WHwr5MhyZj9Z8ECeclwzWS46m14\n7wJJanIng6ZpZOU7ycp3MvrYwI+ivtbH0m9r+eV/VTz1p9/ZtqGR4UcmMXZmKoOnZxGbaN3mLBwE\niKywHKC9PBjftFgRqrLmoepHhlB5MFTm7IV1O+DdRfDeIlhWBLMGw4XjYVTX5geG6CEwKyduxoMh\n08FQ8XKE04OhEuSp0o+Z545Zb4m4nSzIU/RYyDwY4rrUQMDnqH/AZYc2a2MkCG3EEu+ydbI24lgq\n2h2SffcK2/lkbezB3hHRMwJGz0O9UAZ+V5vtRV7mf1zL3Pdq+GV+PYPGxzFxVjLjZyaSnO5UKh+v\not1hBioBnGr9tL5NOAMv27OybajmY3Z8s/20uwdjoImxlloejE6HshqYvwa+Xg1fLodtVYFMkD9P\nh0k9wC0v+2DBghRuB7z2x0DV1XHdoZ9oYBxkyMhxMPv8RGafn0hJVQzff1LJvHcqePyazfQaFsOY\n4zIYfXQK2d1lVp4FCwcoIjAGwzIwwgyvD1YUw8/r4affA4bFxjIY0wMm9oJ/ngqju8HuF7gIvEgs\nRD76ZsF9M+DE5+DbWyHRotQAiE2wc8TJKRxxcgqN9X4WfF7F3PeqeeXuzSSkOhgzM5XRs7IpHB4f\npEhqwYKF/Uf7UCRzWqwwGwwpIpz9mKRRdtYGKI5lRbBsKyzeEljykmFEFxieH3jDHJYfUGQE1DQl\nxLFU5LtDpYOhElAqm4+ZcyGDigkcKtrC7PgqY4leeBndIFISskyhfdAfug5XfAALS+DjiwPl3sU2\nex1LhY5RoZnMUlri8ZA4F7zCfOpijcGZ1fZgrY5qyUGsJwa/X+e3nxr46r1q/vdeLZWlXoYeFsfQ\nw+MZPimBrN7xQamwKpLjKuho/Ypw0RahDAxtT9qkU1EkhSbGWhteisQyMNpoYPj9sKUcVhcFPBMr\nS5o/i6GmEQbk7FkGZcPQvBY3ehksA2PfsAyMYLQSX+H3w5Wfwjfr4LNLIT3e2EY61kFmYAT1Qwzb\nt3j4dW41v/6vml/+V42nQafnsFh6DImhcEgsXYYkk9ktWAZ9fw0MXdeprfRRucNDVZmXmp1NVJU1\nUb3TS12Vl8Y6Pw21PhpqfTQ1+NFsGja7hs0GNrtGdLydxHQnCWlOEtNdJGc6yekZQ2La3jlWy8Aw\nNycz/bS7gdHNxFjrLQNDjjAbGI1NsHpbwHBYUdT8WQyrSwIZHT0zA27pvtnQJxv6pEN+shDFrzK+\nZWDsG5aBEQyFAE49Bv7yMbzyM7z8RzhkiMJYB7mB0RK6rrN1C6xdVMu6RXWsWVjL2kV1lG5pJD7V\nSUYXN+ldokjOdhMVZycq1o47JvAJ4PX48Tbp+Jp0PA1+aiuaqKnwUlvhpbY8YERUlQYWV7SNxLSA\nkRCf4iQ+xUFcipPYRAfuGBtRsYF+nW4NXQfdD36fjt+nU1flo7K5n8odHspLPGxdXY/doVEwKJYe\nQ+LoNy6RIZOTd2fSWAaGuTmZ6afdDYx8E2Nt7gwGxictVuxHtsU+v8ug8LCuqwsYDsubl9+aP7eU\nQ7c06JMVMB76ZgWW3hmQEC2ZYziNIhXdCXGd2ewPM3oaKvOJRAMjVP2oPEAVKqUaHrJmPQ/N272z\nBC55By6aCDcdKQQPi9vJ4h1DJckeIgPDMGfJ8WkU1lXHGA0MUfJcVgFWlmni8+nsLGli2yYP2zd7\n2F7ko6HWT0Nd82etHzRwOLXA4tJwuW3EJdmJS3IQn2wnNtFOYpqTxDQHCakO3FFGbZH9eejpemCO\n6xbXsnphPUvmVfLbt9V0HxzLiCOTGDY9nZ7D4/aphKpSbVaE7IFv9gHfkZklZo99RBgY2SbGKrYM\nDHmbNj7Q/X5Ysw0WbwzERyzdCku3wNYK6JUB/bIDS/+cgCHRIx1cDmM/e52jZWDse51lYASjHQwM\ngKJKuOT9QN2am6bBOWMhyinZzjIwhHWtp7KGq7ZFqPrd9RBurPexbH4VP39Wzg8flqPZNCafmcnk\nM7NIzzNXzn5vYwVvZxkY7WpgpJkYq9QyMORt9vHA8vlhVTH8tAZ+3RhYFm2GtDgYkg8Dc2FgHgzI\nhZ4pLQIu9wbLwGh7P5aBEYwOMjB2tVmwHu74GH7aCGeOhj9OggF5LSg9y8AQ1nUeAyNonW5n5Y/V\nzHmhhK/f2M6gw5KYfW0+fcfsOXCWgdF2RISBkWxirPLOYGC802KFWeNhH0ZIUQV8vw5+XAcLNsCv\nmyAjHkY2Z24My4eh+ZAsS90LlbckDPu11zZm5btDJcalEu8hjhXK9NtQxUWICKeIlpkHqEzPQkVO\nfB8CWWtL4ekF8OZSqPXAYYWBZWI/6JUJzpb7EiohMhEqBpgsRkVFHEw4Zl5REh2oTgg2HmRVYkX5\n8P9v78zjo6ruBf6drATCDmFJIETWhJAQ6CPoU6ti4JWKWIQPLoitaBeVtgSjlpaWvgIpWylIX59V\nRNFK21erqI15RCT4hGoqS9jxgaFNgKCAECIJIUv/OBNIzpxkTi535k4m5/v53M9kbs4593fv3OV3\nf9tRKSHyQ8XqQ9bbuFb7qcZpKGNFeQ15L53iT0uP0z8xipk/j2dYekcPme1SAnSPhV0Kjue4/i3G\n9W3Xy/5VMDpa2NYFo2A0WldbK1wcWw/CtiNCsSi/JOpKjB0AYwbAV+KhW4cmxpExCkbz64yC4X2c\nVqRgNNz+P87C1iOQfwTe/xSKv4DenWBAd7H07SrijTq1g47uJTJMKCFhoeIzPBTCQq5+DwuH9hGi\nzH2HCAjXtXoYBaPJca3286Zg1FN1qZZN606xYXEJA5Lb88AvrmPw6KvHxCgYrUTBiLKwrYo2rmDU\n1cGB47B5L+Qfgq2HoUdHuHmwmEny+oHizcvlan6cJjEKRvPrjILhfZxWqmDIbS7XiODmY2fEcuIC\nXKiEsgooqxR/V1VDda1oe7lafFbXupcaqKqBiiqh9H95SRSQ6xwFfbu4l64Q2w2G9YWR/WFwb7eL\n0igYTY5rtZ+uglFP1aVactee4tWFxaRP6s43F19Hp+7hRsFoLQpGmIVtVQeDgrGhwQqNh+zJM/Du\nQcg7IEpptwuHcUPh1qFwyxBxo7Icz+CrOU105NEZWzWOTjyDTgyGjmJg11wkcj/Fsbhsk9KhfEuW\nsWq695WCoaMY6LRRpbLqKBh2pfE2Q12dmCfliwo4eQFOlIml5ALsL4XCE2J9Ui9hdZyQKK7zju0U\n+wCe+6pSwCzMEnuhs2e668XQxkqInNoKng8eq8W4dBQVzz6eP5iVB7Oqzblzdbz003+w9Y+n+dai\neG5/KNajyqkv4zQCbQ6TVqNguCxsq67lCsaKFSvIysri9OnTdOummqr5KgFRKrymFgo+hbd2wzt7\n4dhpuG0YZCTBzybBwBjsfQM2GAw+x+USLwd9wqFPJxgV6/5Hg7vOhUrYWwp/K4E178MD6+Hf4uGO\nUTDjeohp4/OqOEF0lzAeWz2QCd/qxTOPHuWdtZ/x/WeHkJCi0mYNAYMfdJni4mLy8vKIj4/Xau8f\nC8a6Bivcb7JV1bD5IPxlJ7y5G3p1gkkpMHE4pDcspS31u4Ivs1F8ZeXwpTxWMk1UGSI2WTkuS+NU\nK/brsg+rJodrvHSEaajXHtYRHTeKjvtDp9CWVSuHjrvBigtJhRXFv5kskvIqeIGBp2MAABQ+SURB\nVK8IXj8CbxyAu5PhhzdCcm/0XCTyC5XCRSK3kS0aABc7NK5PURHpacGQLRayWwWsuVF0XBJ2ZW14\n21ZtbR1vrz3NunnHuDszlmlZcYSGuWyTWS2j97G9bUt3e750YfndgmFJw2iZBWPatGnMnz+fyZMn\ns2PHjsCyYFRUQW4hvLYTcvZAUl+YMgp+NB6u69mgobFWGAxtkugIuHMo3DkKlpbDsx9BxvMwojc8\nORHGDZOq5Rp8SkiIi4mP9Gb0+C78atb/s+2NM2S9NITYYca01NbYuHEjcXFxpKSkaPe5ZgVDxx+T\ntx9e3g5v7oJR8TB1NCybCn26uBsYhcJgMEj0jIafjIOsr8IfCuGxP0B8N/jtfaIQnsF/9IpvR/am\nZN7+71Iyb9zDvfMHMPn7sc1WBDUEIvnuRU1GRgalpaUe6xctWkR2djabNm26sk7H8nFNLpLi4mIe\neeQRDh8+3KS5xOVyMbo/PDAWpo+G3iqTbqC5P6wEcNo1sZrVLBIrmSZ2ZYgotlUhtVG5Q2S3iV1B\nn7roBIfKbhSV68WjjcolIbuv7XKR6ASU6rhIrGLlN7MYBHs5GlZvg+wtQvGY/TWRpdIIjSBPjzaK\nl3HZbSK7TACqIhsLfUnhIpELdNnl/vDnOPL340cqWHj/ETr3COeJdYPpEhNhOejUnwGt/s40CSYX\nyb59+xg3bhzt2wtXYUlJCbGxsRQUFBATE9NkP8+rpgVkZmaydOlSr+0+ngc/uA16q3ymBoPBoEF4\nKMy9GbY/Cq/thZtXwNHPnZaq7RE7KIqVH6SQkNKB76XtZue755wWyQDAZQuLHsnJyZw6dYqioiKK\nioqIi4tj586dzSoXcA0KhhV/jMFgMFwrQ3rC1u/A1DQYuwQ2H3JaorZHWHgIs7IHkPXSEJY9+Akv\n/vhTaqr987ZuaIpqC4s1dF1jzdqD7PLHLHjj6t+3JIjSxI1oje6PQKuDYWVKdx03ioY8sjsEoEJq\no3J/yKv09Wl7qNC4vsKlNqoLRna1RCnGjZJ/H5X7Q0bnvFP9hjpFvWSs1rzQOcflsXVk9jJuCDDn\nehgVA9Oeh+emweRkxTgq95C8TrHvLuk3bU+tYiBpR1TbktCr++DpavEnLan7MOr2Lvx210h+OeMT\n5t2+mx9tGEr3Ptcmv44rI1TjxJP3I0zRR95WqOKi03WbHM4v5ZP8U1ptfYP/7qCffvqpVjtLMRgt\n8ce4XC7qVjVYESzxFcGgYFiMr5D72aVgXAI+B0qA4+7PUuACIqP2onvTlxC7W+3+VB3mEIQyUP8Z\nirj/twOi3J/RQBeEm76r+zMOiHe3AQinMVoKhuJBE6Uz2ZmVVFarVUNl/Klg6Ex2piq5IMdKuGMp\nPi6GSWth6R3wwHh1m0bIcRkq1620rk7xe8lxGXJMBnjGZegoGKp0V52qmFZiHlTjyNvXGqemjlcX\nFpPzu1Ke/v1QUm/pbCneQ1dGnXGcLsbl/xiMMxZ6dvepjJYiWur9MfUkJCRo5cQaDA35DNjlXnYD\nhYjnTCziQR8HDAQ6Ip437d2fEYgTt15xCAFkg12NtFQjFJNKoML99wXgC8RlecT9WexeuiAUjWHA\nKPeSYOveG+ziK/3gve9BxrPQqQdMHuW0RG2P0FAXD/ysP0k3dCT73kNMmRPLlKx4k2XiV/xtA/aO\nLbHkXk+i6ib+rkfnDT3QrRNOy2zXlO4abWSLhWytAE/3Q/2pXwK8A+QARUAqkALMBJJQB/17w+7L\nqhah/PwTOAr8L7AEYUFJA24GbgP6utvLbhSVtUbOolFWEZD76WRc6bgbVJYquwpt6aBjwZD3XcfK\n0WC/EqPhtekwaR0kdYXB9YZUlSVEPh4qC490XGWXCUBkmOw2UfwYksw1ipuAXLArgiqPNqEeZcl9\nh7wtHeotAaMzurK6YCS/uPsgh/7+JXNeGEr7jk2fXDquDhU6VgV5bJWVQXabqCwasttEtW2r+2Ev\nQapg6PpjDG2TcuDP7uUfwHggExhNYxdEoJRDCQF6u5d/b7D+M4SVZQvwjPv/44A7gKF+ltHgSXoc\n/OfXYcrz8OFc6KARE2Gwn5h+kax4P4U1s4uYk76T+a8nEzfUsxKqwW4C5Q56lWtKUzUYmqIaeA+Y\nDYwB3gd+CHwE/BK4Cc/4hkAnBvgasBTYBsxHWDW+CXwD+CNqY4HBf3znRkjuA4s3eW9r8B0R7UL4\nwXNDuWtOHE/ctIu/51iJDzC0DN+lqVrFP3ORLG6wwqpLwkqgY7C4P6wcH6tTulsI4GzoDjkDrHcv\nfYC7gImoXQLy6a2rf+tcFnbp8rKJrymlaBvwF2AH8HXgfhpbNeT3tyiF7bCj5BJRFuzSmWdEbmN1\nGnoZX85Iq1NkTA7GbKKIVvEXMHIp7Hsa+qgCZ3TGkdtozO5arfgtLkV6DwS1MiurXYGgquJgdhTj\naijP/u1lLJx2iDu/H8e0J/s1cqn7cip4f85kq2KW61U/B3l+YqHnEJ/KaCwYhmumDuE6eBIRn3AS\neBHhEpmBtbiK1kQY8FVgFfAawtIxCxFX8i56iRYG++jXFR4aCz/PdVoSA8DwGzqx+qNUPvjz5yy5\n7yCVF80V4Rv8VwdDF6NgGCzzZR28VAsZwGOI7I/3ES6EwY5K5hy9gMcR7qFpwG+B/wDWoZ681uAb\nnhoHG3ZCuSqQ2eB3esZFsuz9kYSEunjy5t2cPu7LMNW2SuC5SPwzm6pTWSSqm0trdH/o1LjQaSMH\nCGjMIVKmCCr4BHgZYaEYDWQBY7maKlqGSAVtiOpU1tGf/ekOUSFfIKptNXUR3Y4IAt0F/AFYjggI\nvQ9IUmWanG/83aN2BhAl/WZKN4pOloRsCdZpo0LeeZ2XU50sEh2auZ56tIMbBsDbO+CedC/9dDKu\nNFw/qiY1cqbJJc+NyW4TVbEnGVWmiZUCXariU76ifVQoT788iD8uKWFO+g5++pdEBo/p6rWfjqtD\n55ipxtHJ/rCzGJdvMUGehlbMLuC7wGT3943Ac8D1eNahMAhciBoaKxExGtEI18lMRPpr4CWWBQ/T\nR8KfCpyWwtAQl8vFPU/3Y/Z/DWT+HQfI3+Bk5ctgw1gw9GYCbY21MvxpUbGpxoXKOnFBtmAAm4CX\nEFU2ZyBiLTo0+L9srUCxTrVbTlsndLBiwVC1iUIU7/o28CDClfQ7RCbKN4CpwAB5HI0aJEorh2TV\nCLdamlvHyiFj1TrhgzvRbYNg3jt47ptdlkWNNhHyb9jOs+R4TU1jgSJDPa0TOg4FK7UYrNS8sIOb\n7uxC7OZEfjzpMMcPlTPjZ/0JCbH+mmK1vLiOdcRKrQxnCAQZGmMsGAYlVcCriJoVrwAPA3nAQ+hN\no2FomkjgTsRxXYt4eExHWDV+j6i3Ybh2+nWBL6vgjAl+CUiuG9GB1R+lsjPvHNn3HjbBn9dM4Fkw\njIJhaEQlIgPkJkTFzeUIRSMD69NVGJpmEPAUIij0AUTJ9InAvQirkVE2rONywfC+cOCE05IYmqJr\nrwiWvjeC0HAXT3x1L2dLVbElBj0CL4vEPy6ShvY9qy4AXwVD+tLVYmUcnX3XqHFxWeH+kOtXNHSH\nVCMCEX+FKNm9AlHCuwIxZ0dDyuRxNURW6cqBFn+gqnGhU6sjSrHOG6p9v9G9VAF/Q7imliDmQBnn\nXuTsHMtuFGlH5HLngJ5LRMecJd9lVJqqvE6njcbdq2dHOGul+pnOtatxL5FLjIcq2kRKAZuXIj2D\nNcNCvb/dW3F3qEqXW6ElM7DKRLQL4amXh/DqwmJ+MLaQn/81hfjhzZ9YVtxBVkt8W5mV1RkC7Y7q\nLwXDELDUIYINsxGlr9cAyY5KZIhA1NW4HaFsfAxsBr6FeJ7fAtyKyOAxNE90JJSbjMiAx+Vycf/8\n/vS+rh1P3bqbrJcTGT0h2Cvo2E3gxWAYBaMNcxARZHgOWIB4cMnWCoOzRAA3uJcfI1KEtwDLEJOx\n1ae9pjolYIATFQ4XjdW91TDu/hh6xndg0bT9zFgwgInf6eu9k8FNW7VgeKuDYZfbQjYX+zOLxJ9u\nHY0MEdUMp/UukUpE1cnfI4pCTUNYny/g6f5QKRyyS+SiRht/1qrQRWcuFJ02dl3WOsdsoHt5GChF\nxMl8G5Ghcg9irpTucieNYlPhOtkfVicP0ykVblcbicpqaOftR7To/vA4riorudQvVMOSHqrwo4Rq\ndLTi7rCa/eBZG8K+AM2UGzvwq/8bwU8m7uezoovMXDzQI8PESvaHCl/NyuoMgadgmCDPNsbfEJkh\nR4HXEQ+lQPAeGlpOb4RykYuYVG4LIk5jISY4tJ7ySuEmMbQuYgdF8evtqez7oIyl9x+kqtIzvdcg\nE3hBnkbBaCPU1ImMkNnAPEQNhp7OimSwiVDEHDBrEHOh1CEmXPvASaEChLJK6KgTrGoIODr3CGfJ\nu8nU1dYxL6OQsjOB94ZuaB7/u0h86bbwlavFabeOxiyoctGshpkEZ4BH3cO8hlAsLuLpDgHvGSOq\ndVazSHRQWbflk1Y1ttwv0IKNrB4Pb/16Ak8gFI45iLol38Wz0qqcNXJZcf4qy5B7w+rMrfI6lVKg\n8yNKbT4rg16qqXxbik6FNY17m6qUlEdyjFxeHM9iXKrjbMXdYdW07y+XQFg7mLdhCC/86Bhzb9jJ\nwpwk+g7Uy9vyVYlxqwW7fE/gKWDGghHkFAITEJkh6zBWi7bCGETa8VvAXFDOXNEWKLVLwTA4RkiI\ni4eXJDBlTl8yb9zDoY9MKLoa4yIx+JGPERkGCxDZIoH2Fm/wLX0R1UKPIYJB2xrVNXC+ArpHOy2J\nwQ7u+G4f5jw/mPl37OfDt047LU4AEniVPP3zzGloUfJnYSt/zjPizwwRRZtqafvbEAGAKxA1FSrw\ndGXozCFitY0VF4lOxoaKYFWcrM57Ird/CGHNmNxgvewSkc8f0Pw9dNwfsvVY5XqR19lQaOvzcujW\nAULlHbFyL9GxgKvG0ejnz2JcOuZ+zz7WClTp0FLXQvrXu/GLvw5nwV0H+fyfl5j0WOw1yWNlDhOr\ns7L6nsCrg2EsGAryz3tvE8gU1AnlYjlCuQhEipwWoA3wd/dnBnAAKHFQFic4dcE/7pH8j32/jbZO\nYYOb8rAxHVn+QRpvPnOc5544Sm1tnYOSBRK+tWAsWLCAuLg40tLSSEtLIzc312sf/7/82TVzoY5V\nwaLlIf8c3BLdfBt/yiO/bV5WjFPhbnMS+CawCEinsXVBx/Ig17Swy4IhcxTo56WNLlZPYrmf6o1d\nJ1jUShtfUr+tXYgCXZFAH+AsEFffRhIyzEIApXKdqo0csGlXHQwvVo7zVdDZSh130KsB4m6TXwC3\njGxCHp3j2kZqZajH1pNnX/4XjG5wU467Lpxfbx/BgskHWT7jAD9cl0hEZMvfl63UygjcIE/fWjBc\nLheZmZlkZmZq9zEWjCCiCvgeQsG42VlRDAFEHaLqZ7zTgviZi1XQwdTACFo6dQsne9Nwqipr+enE\nPXx5PvBcBP7F9zEYdXUtsxYZBSOI2AJ0Ax5zWhBDQHERGAZ0dloQPxMVAUmm0nRQExkVyk/+Zxj9\nEzvwfNZRp8VxGJ2skSPAuw2WlvHMM8+QmprKrFmzOHfunNf2rrqWqiQtxOVSZX4bDAaDwRDc+Pjx\negWrz9muXbty9uzZK98zMjIoLS31aLdo0SLGjh1Lz56i0MH8+fM5efIka9eubV4uXysYBoPBYDAY\ngodjx44xadIk9u7d22w74yIxGAwGg8HQLCdPnrzy9+uvv86IESO89jEWDIPBYDAYDM0yc+ZMdu/e\njcvlIiEhgWeffZZevXo128dYMJphxYoVhISENPJRGewjKyuLxMREUlNTmTJlCufPt/ICJAFEbm4u\nw4YNY/DgwSxZssRpcYKO4uJibr31VoYPH05ycjKrV692WqSgpaamhrS0NCZNmuS0KG2a9evXs2fP\nHgoLC3njjTe8KhdgFIwmKS4uJi8vj/j4tpbc5z/Gjx/P/v37KSwsZMiQIWRnZzstUlBQU1PD448/\nTm5uLgcOHGDDhg0cPHjQabGCivDwcFauXMn+/fv58MMP+c1vfmOOsY9YtWoVSUlJJmGgFWIUjCbI\nzMxk6dKlTosR1GRkZBASIk7B9PR0SkraWq1J31BQUMCgQYMYMGAA4eHh3HPPPWzcuNFpsYKK3r17\nM3LkSACio6NJTEzkxIkTDksVfJSUlJCTk8PDDz/st4wMg30YBUPBxo0biYuLIyUlxWlR2gwvvPAC\nEydOdFqMoOD48eP063e1TmpcXBzHjx93UKLg5tixY+zatYv09HSnRQk65syZw7Jly668iBhaF8E6\nT5RXmsv3zc7OZtOmTVfWGc3ZOk0d58WLF1/xqS5atIiIiAjuu+8+f4sXlBhTsv8oLy9n6tSprFq1\niuhoM22rnbz99tvExMSQlpZGfn6+0+IYLNBmFYy8vDzl+n379lFUVERqaiogTHSjR4+moKCAmJgY\nf4oYFDR1nOt58cUXycnJYfPmzX6SKPiJjY2luLj4yvfi4mLi4uKa6WGwwuXLl7n77ruZMWMGd911\nl9PiBB3bt2/nzTffJCcnh8rKSsrKypg5cybr1693WjSDJiZN1QsJCQns2LGDbt26OS1K0JGbm8vc\nuXPZunUrPXr0cFqcoKG6upqhQ4eyefNm+vbty5gxY9iwYQOJiYlOixY01NXV8eCDD9K9e3dWrlzp\ntDhBz9atW1m+fDlvvfWW06IYWoBxbHnBmJt9x+zZsykvLycjI4O0tDQeffRRp0UKCsLCwlizZg0T\nJkwgKSmJ6dOnG+XCZrZt28Yrr7zCli1bWjR9tcE65l7c+jAWDIPBYDAYDLZjLBgGg8FgMBhsxygY\nBoPBYDAYbMcoGAaDwWAwGGzHKBgGg8FgMBhsxygYBoPBYDAYbMcoGAaDwWAwGGznX7h9uvmLZ7wn\nAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To justify the weights, let's 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 let's do it for comparison."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"z=grid_out.get_labels().reshape((size, size))\n",
"\n",
"# MKL\n",
"figure(figsize=(20,5))\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",
"# subkernel 1\n",
"z=out0.get_labels().reshape((size, size)) \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",
"# subkernel 2\n",
"z=out1.get_labels().reshape((size, size)) \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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wwJxId/WuJwHtwxBfKB3GFKY0i43UkfKESJTohSnOL8fDPnJJAO7AzRMOxyVx\nz9I8YWnYIuHSDnM3vdjpQKQmdASTCCoEXgx4xIUpqAwisGtTNOgN7AQ+LfdYS0yXKpt8evJdRKqj\nPCESRc7DDP7/HrAUeJL9QDNHY5K4Z2mesDRskXC5EPgG+NLpQEQkiuwCnsOMiWP8DGiBaf0Sra1F\nrsKMTbDfu92GslZDtvjG6QBERCSkXMAlmJsNW/gYGOBsQCJWUiFHROxlaZ9WscuPQC7liziXYoq+\nNujmdABB2u10AGI75QmRKJUC+CYmF3GQpXlChRwRsZeOYBJmB4An8Z1oJmKKOOc5GJGI1IryhEgU\n8uC7PVLibCAi1uYJS8MWEUFHMAmrw8ATmDmTegKruY/ond0plkVr1zWxgvKESBRyYWZNhJVAFprB\nShxkaZ6wNGwREaxtCinR7ximiFMEQFdWcw0qKDghwbuo8b3UkfKESJTqARTiAXJJ4E5Kael0SBKf\nLM0TKuSIBNiCBte0iI5gEibTMJOkwmmgIo5DPJSdXXmq21GkasoTIlGqL3AIM3tVKU8Cd6MZrMQB\nluYJS8MWCZeVwD6ng5Ca0hFMwuRH/9ogB6OIdx5a8RN7MCf2rZwOR+ykPCESxS7BdGT+lBLg/1EP\nuBs3f3c2LIkvluYJS8MWEUFHMImAHGAi9k3bHQteYw/QELgDa1s+i9OUJ0Si3FWYNrBrMR2aczgG\n1Hc0JokrluYJS8MWCQcP5ae61UWDBfQ/ScLgABU78qhbVeS9CqwlGZiATuglCMoTIhYYDpwNLAO+\nZgZwi7MBSTyxNE+okCPi9x98I+jXB851NBapER3BJMR8M1WV6Y1+0SLNA3wFQHegsaOxiPX05yti\nARdwJtAUmKZBDiSyLM0TloYtEmo7gdWA6UBxJ9DAyXCkZnQEkxA6hulIVeR/pCuQ7VQ4cWwfpqSm\ntlASAsoTIiJSHUvzhKVhi4RaPcBcNNwBNHE0FqkxS5tCSnR6E1/5ADRblZO2Ox2AxBLlCRGLmPPx\nw8B+NIOVRIileSLB6QBEosMxwDToPMXZQETEIb4ijpkdaSQq4jhll9MBiIiII1oBZ+HBzGDl5v84\nHZBI1FIhR0TslVSHpRL5+fl07dqVLl268PDDD1e6T0FBAb1796ZHjx70798/tN9DokofwNrbMyIS\nSHlCxDLdvf+WzWAlElaW5gl1rRLBA7wPqEuVdUJwBCspKWHChAksWbKE1NRU+vTpQ3Z2NpmZmf59\n9u3bxx18cpNHAAAgAElEQVR33MFbb71FWloae/bsCf6DJaocAL72rqtVnpOKgS/8WynOBSKxQnlC\nxDJnAqdjsvIRcoC7MGNYioSFpXlCLXIkzm2iG5OBTdQHbnQ6HKmdxDosFaxYsYLOnTuTkZFBcnIy\nI0aMIC8vL2Cf2bNnM2zYMNLS0gBo1apVuL6ROOAwZpDjEgB68RJuJ8OJY8eBlzBlNUgHLnIyHIkN\nyhMilnFhuje3B0xGeIiW3hwtEgaW5gkVciSOvQW8yJeUzVTV0NmApLZC0BRy586dpKen+7fT0tLY\nuXNnwD6bNm3ixx9/5OKLLyYrK4uZM2eG49uIA4qBqfhGycoABjsYTbzbA+wAoA0wBo1SJCGgPCFi\nIRdwM9DSu/0Dz2Da0IuEnKV5Ql2rJE69D/wXMEXV21G3KivV4AhW8I1ZquJynfxSsbi4mJUrV/LO\nO+9w+PBhzjvvPPr160eXLl1qEaxEox3AIcxdjVIOoNKBkxoARSQAt6I7TRIiyhMilkoAxgP/Ag7y\nLXAQMzGJSEhZmidUyJE49AnwHmBSxDg0DoO1anAE69/BLD6TPw18PjU1lcLCQv92YWGhv8mjT3p6\nOq1ataJhw4Y0bNiQn//856xevVon6DGkFNC9vuiQiE5OJISUJ0Qslgj8Dvi/uNS5SsLF0jyhG14S\nZzYDbwLmvvtNmCb8YqkQ9GnNyspi06ZNbN26laKiIubOnUt2dnbAPoMHD+bDDz+kpKSEw4cPs3z5\ncrp16xbGLyYSj75yOgCJRcoTIpYru8lS7GAUEsMszRO66SVxpghoDByiD5B2kr0lyoXgCJaUlERO\nTg5XXHEFJSUljB07lszMTHJzcwEYN24cXbt2ZcCAAZx99tkkJCRwyy236ARdJKTeAT4AQO0XJKSU\nJ0Qs5uuu0hEPm3icZsBduHnQyaAk1liaJ1wejyesbclNfzF3OD9CpJbygFWcD1zudChxzA0Ec/hx\nuVx47qvD6x4O7nMl9Fwul2NZ4mvgBf9WC8wkpxI5JcBcYCNgZqq6CY1UJIYb5QkxdD0R70qBacB3\nQEv+zA+VNYqQOOQmfvOEulZJHNoP6EIhJoSgKaRImcZOBxCHXsJXxGmNZqqSMFCeEIkBCcBY77qZ\nwarUwWgkxliaJ9S1SuLKxbh5D/P318fpYCR4OoJJiCQCJWSfdD8Jte/9a9no7pKEgfKESIxIApoB\n+/kWeIAMYBRuJjsalcQAS/OEzpkkjqzgPczd3nHAKQ5HIyLRoxlg2oRIZLnwtcFRSxwREamaC5gA\nNPJubwXmar5JiVuW1p9EauN/wBvAMVyYhpmaqSpG6AgmYrkETHuo404HIrFKeUIkhtTDFHMexYyx\ntp61QA9HYxLrWZonLA1bpKY2A6/6t25EM1XFFB3BRCzXBDiKCjkSNsoTIjGmEdAZ2AD4Rr4UCYKl\necLSsEVqYjswy791NdDRsVgkLKJksDERqatfUr7YLhJyyhMiMagd8AOwx+lAJBZYmidUyJEY9rJ/\nbQDQzblAJFx0BJMQMX3sd6NxciItA42OI2GlPCESg/pj2uLs4XPgPJRJJAiW5gkNdiwxrAQwB/ZO\nzgYi4ZJUh0WkEgcBeMXhKEQk5JQnRGLUQKAp3wOTOV2DHkvdWZonVMiRGNaPqPlLk/BIrMMiUonj\n5f4rkXQEOOZ0EBLLlCdEYlQSZuDjhsDXvAwq5kjdWJonVMiRGPYLINnpICScLK2gi4jPQaDI6SAk\nlilPiMSw+sCdQALrMHPUitSapXkiSsIQEakDHcFELLfW6QAk1ilPiMS4RkBzYC8rgZVcgJuPHI5J\nrGJpnlCLHBGxl6VNISV6qDOV0zY7HYDEOuUJkThwI2XDHX/EcidDEftYmicsrT+JiKAjmATlGPBa\nwCNdnAkkbn0A7PCuJ9LCO0C9SEgpT4jEgRbAUHxZ/VOgr5PhiF0szROWhi0igo5gUmfFwBPAUcBM\nOf4boI2DEcWbz4B3AHMP9TZKaORoPBKzlCdE4kRDpwMQW1maJywNW6QmZqPZUGKcjmBSR8/im3K8\nPXALZU2yJfx2Agv8WzcBbR2LRWKe8oRI3NEQ+lIrluYJjZEjMawQKHU6CBGJQrv9a9ehIk6kNab8\nndNn+RVu3I5FIyIisSAN6AEk8xPg5lzlFolpltafRESImsHGxGYq4kTeKcBdwA/A08AioIGjEUkM\nU54QiRMNgOHAfuAxTBdedbeSGrA0T6hFjsQwc4Hmofzdd4kpSXVYRAJsBw2y64AGQCowyrv9H/Y5\nGI3EMOUJkTjTDLgdcx3woSYil5OzNE+okCMxbIB/7WVcuLnVwVgkLCw98Eo0eQWNpeWktkAy4PGO\nWSQSYsoTInGoJTAOgLcBN9mORiNRztI8EXQhp7CwkIsvvpju3bvTo0cPHn/88VDEJRICZwO/8q57\ngGfUMifWJNZhqUR+fj5du3alS5cuPPzww1V+3CeffEJSUhLz5s0L4ZeIbdGfIzSOlrP2YeYQEwkT\n5YmoF/15Qux0KvAz7/p81joZikQ3S/NE0IWc5ORk/vnPf7J27VqWLVvG1KlTWbduXbBvKxIifQE3\ncCFQyixng5FQC0EFvaSkhAkTJpCfn8+XX37JSy+9VOkxrKSkhPvuu48BAwbg8XjC9IViTzTmiO+o\n2JnK0s7RMWGj0wFIrFOeiHrRmCckVnTzr72Kua0rcgJL80TQhZxTTz2VXr16AdCkSRMyMzP55ptv\ngn1bkRA7C9B935gTggPvihUr6Ny5MxkZGSQnJzNixAjy8vJO2O+JJ55g+PDhtG7dOkxfJjZFW474\nEZgW8MhlQH1HYhGA9U4HILFOeSLqRVuekFiS4V/zoEKOVMHSPBHSMXK2bt3KqlWr6Nu3byjfVkSk\nciFoCrlz507S09P922lpaezcufOEffLy8hg/fjwALpdmOqoLp3PEfuBJynemuhC4wJFYxOew0wFI\nrFOesIrTeUJE4pCleSJkQ/UcPHiQ4cOH89hjj9GkSZMKzxaUW8+gfHVUROLDVu8SUjU4ghWsNEtV\nanIQveeee/jb3/6Gy+XC4/GoyXwdVJ8jIpMllgDHgSbAQW4EOoXhU0SkrraiPBHPTpYndD0hdZOM\nr03+MuB8R2ORYG1FecInJIWc4uJihg0bxg033MCQIUMq2aN/KD5GRCyWQeApV0Eo3rQGR7D+PzOL\nz+RnAp9PTU2lsLDQv11YWEhaWlrAPp999hkjRowAYM+ePSxatIjk5GSyszULQk2cPEdEJksc9/6b\nBRSoiBMlXJjGwRp0WpQn4llN8oSuJ6RuxgJPAbAYWEw2buY7GpHUXQbKE7UIu3oej4exY8fSrVs3\n7rnnnmDfTiQMfgJmAuobG3NCUIrOyspi06ZNbN26lfbt2zN37lxeeumlgH2++uor//qYMWMYNGiQ\nTs5rSDlCqpeEaaNcqlKOhIfyRNRTnpDwOhX4HbAHmA7M50vKD4Mscc/SPBH0GDkfffQRs2bN4r33\n3qN379707t2b/Pz8YN9WJITqAYcAOAKscDQWCakQ9GlNSkoiJyeHK664gm7dunHNNdeQmZlJbm4u\nubm5kfkeMUw5QqrXGWgMwH+oOJuYSAgoT0Q95QkJvyaYdhzXAvAy8FU1e0ucsTRPuDxh7sRr+ou5\nw/kRIjWwE3i63PZQ3MxzKhjBHBWCOfy4XC48X9ThdWcF97kSei6XKyJZ4mXgS0zj/ALlpShRiimx\nPwf8ALTjL3wb2pkYxFpulCfE0PWEhM4XwGuYrr1jcfPMSfaXaOYmfvOEzpUkTqQCI8ttz2O7U6FI\n6IRgukCJPwcBMxG5OC8B0yJnPNAU+JYZqBushJDyhIgEOAsYgMk0z/K9w9FIFLA0T6iQI3GkI9DD\nv7XeuUAkVCw98IqzPgdgrcNRSKAk4A7AzEYxmTNxM8nJgCRWKE+IyAkyvf96eJJE3NztaDTiMEvz\nhAo5EmcuwAx6JjEhBH1aJf6Y2as0tG70aQBc6l3fAJpVREJBeUJETtAcOM+7XgJM5YCD0YjDLM0T\nKuRInGnnXSQmWFpBF2cEnqQp/UWnCzBdrABWsdjJUCQ2KE+ISKWuAHp514+TAxx2MBpxkKV5Qmey\nImIvSw+8EnlLgEL/VgJlJ28SXVzATd5/4WPAzSW4cTsYk1hNeUJEqjQYOBOAY8AjNMbNHx2NSBxg\naZ6IkjBEROpARzCpgY+ADwMemUBZqw+JPimYwY+f9G6/CzRyLhyxm/KEiFTJBYwApmMmQTgATOU4\nOnTEFUv/Z6tFjsQh89daiGZGsZ0nsfaLxJcfgbf9W2cCvwNaOBWO1Fgb4GZ8LXNgAXWYHVREeUJE\nTsIFjAZ+C7QGfuINR+ORSLM1T6iQI3GoP5BAITCZ3g7HIsEoSar9IvHlMOYUzbS/uRZo4mQ4Uitp\nmG5WqQC8Bri53smAxELKEyJyci7MZXFfAPY7GotEmq15IkrCEImkRMru8q7iLcxwZ2KfaDmQiki4\npGNa5qwDXgZmsx3o4GhMYhPlCRERqY6tecLSsEWC0QAzRsZjAPwXM0+K7tPb53hiXRoVatppEbu4\ngG5ANjCf5zGN312Y0XR+Q9TMBCpRSHlCRGrOXA3sAI4ADR2NRSLF1jyhQo7EqRQgGSjGBRx3OBqp\nm5KkuhzCikIeh4hEwjnAp3j4hu+9j+wC/i+n8he+U19xqZTyhIjU3JlAIsWU8DCNgbtxM8XpoCTM\nbM0TOu8REZGYZ+6bbHI4CgnedZzY/uY7XkCD14uISLBcmC69AIfwzWAlEo3UIkdErFWSqA4VUjNH\nAHgTuMfZQCRITYB7wT+H1fvAEbYBD2JOwROBYcAZjsQn0UZ5QkRqZySQi2nz+RO5wHjU+iGW2Zon\n9DspcWwwGlnBbiUk1nqR+FRa7r9iu8ZAP+9yF9AISKQE0032GDAbcDPGsQgleihPiEjtJAC3YoZh\ngN3AA6Sq1WcMszVPqEWOxLEeQB5Q4nQgUkfHo+RAKiJOaQjcAbwH9MGcgG8B8oHpfAu0cy44iQLK\nEyJSe4nA7ZiJUQ4CO5kF3EDZvLcSO2zNEyrkiIi1SnQIExEaA1eV224FrAJ28TSmzNPSibAkKihP\niEjdJAN3Ym4OzGcLR3kVM1OixBZb84S6VomItWxtCiki4eQCrgFMZ7onSOQnR+MRJylPiEjd1Qe6\nYQo6SawF3PRxNiQJOVvzhAo5ImItWw+8Elll/dpPcTAKiawWwIXe9RKeRJ1o45XyhIgErzGmmJMI\nfMK7DkcjoWVrnrCzHZGICETNgVSiV1vMULiHgQy2Mwo3LsCN29G4JBIuBf4LlFCEmbmsibMBiQOU\nJ0QkNJpjxs15gqXAUq4AztP5RAywNU+oRY7EsRyg2OkgJAjHSaz1Upn8/Hy6du1Kly5dePjhh094\n/sUXX6Rnz56cffbZXHDBBaxZsybcX01CJBmYANQDtgLzHY1GIk/DUsY75QkRCZ2WQHvv+luY8djE\ndrbmCbXIkTimURNsF4rByUpKSpgwYQJLliwhNTWVPn36kJ2dTWZmpn+fjh07snTpUpo3b05+fj63\n3nory5YtC/qzJTIaYRpE/wtzytXZ2XAkolzeRRPHxivlCREJrSuA573reawDMqvZW6KfrXlCLXJE\nxFqh6NO6YsUKOnfuTEZGBsnJyYwYMYK8vLyAfc477zyaN28OQN++fdmxY0dEvp+ETlPgTO/6bicD\nkQirj0514pvyhIiE1mnAtf6tuYCbUY5FI8GzNU+oRY6IWKsmfVo/LTjEZwWHq3x+586dpKen+7fT\n0tJYvnx5lfs/++yzDBw4sHaBSlTZB8AuzAg6EtuygA+cDkIcpDwhIqF3JjAMeM27PYOdQKpzAUkQ\nbM0TKuSISEzL6t+YrP6N/du5k/cEPO9y1XwMjffee4/nnnuOjz76KGTxSeStBmADKuTEg/7Ax3go\nYRPQ2+FoJDopT4hI7Z0FHAXeBDw8C9wGtHE0JgmXaMwTam8sItYKxeBkqampFBYW+rcLCwtJS0s7\nYb81a9Zwyy23MH/+fFJSUsL6vSS8POX+K/HgGgDyADfXOxuKRJzyhIiETx/g/wAXUwo8SSJu7nY4\nJqktW/OECjkSxwaDpdPNiVFCUq2XirKysti0aRNbt26lqKiIuXPnkp2dHbDP9u3bGTp0KLNmzaJz\nZw2VK2KXTsA53vXZbHcyFIk45QkRCa/GwC+AvkAJ8CQHnQ1IasnWPKGuVRLHemDu0ZY4HYjUUU36\ntJ5MUlISOTk5XHHFFZSUlDB27FgyMzPJzc0FYNy4cTzwwAPs3buX8ePHA5CcnMyKFSuC/myJrBYB\nW58CF6A0GA88mMEpVwIe3gdudDYgiSDlCRGJjF9hulqt5v9hZswEM6PVlY7FJDVha55weTyesLYv\nN/3F3OH8CJEgPISLYu4GTnE6lDjjBoI5/LhcLt73/KzWr/uFa0VQnyuh53K5IpIlSoGngW+92+lA\nofJTHHgFWAtAQ+AezFxWEv3cKE+IoesJsYMHmA5sq/B4Fm4+jXw4ccBN/OYJ3YoUEWuFooIu8SMB\nuBmYCvyImbfKnHTVfIA6sc0ifEWcesAEVMSJN8oTIhI5LqArJxZyPuUd4JeRD0hqwNY8oUKOiFir\nssHGRKqTCIwHHgcOADADGImKObHqM//azZiRDCS+KE+ISGT1BVphhm44BrwOwAeYVqHnOxaXVMXW\nPKHBjkXEWqEYnEziTzKmZUZDAL4mk8m41WQ/RrkAFy7KxiuQ+KI8ISKRlQB0wbTM6YmZlLweAIsB\nN4Mdi0wqZ2ueiI4oRByRAxQ7HYQEwdamkOK8+phizmPAOuBtZ8ORsGkAHEaD2scv5QkRcdapwB+A\nQuB5II8vgW6OxiTl2Zon1CJH4thPTgcgQSohsdaLiE9jYLh3/QugfDcciRW/cDoAcZjyhIg4LwEz\ne+K1ALwMuBnpZEBSjq15Qi1yRMRatvZpleiR7P3XjJfzMXCuY7FIOGRhBjyWeKU8ISLR40xgKDAP\nmMkOIM3ZgAR784QKOSJirWjpoyr2MxNIHkKzWMWaIqBE/1fjmPKEiESXs4HvgQ95FrgS0907CTgD\nLC0p2M3WPGFn1CIiIiGQDjTF1yLnKB2ZzI3AZA1+HAO+I5GnKME0aNdgxyIiEh1OAz7EAywIeLw9\ncAtuJjsRlFhGhRwRsVa09FEVeyVhBj3+F3AE+Ap41dGIJDQ+BJZQArQFRqEWOfFKeUJEok8XzETk\nH1d4/BtgplqRRpiteUKDHUscG4waMNrN1sHJJLr4ZrCq591eC5guOWKnpcASAJoDt6KTnXimPCEi\n0elyTDGnebmlPvAVrzgZVhyyNU+oRY7EsR5AHpqW1l62Dk4m0acxZdORlwAXMoVLAbe6WFnoe/9a\nb1Suj3fKEyISvS73Lj6HgH/xJcW4ORe3ZtOMCFvzhAo5ImItWwcnk+jUDLgdmIrpmNPQ2XBEJASU\nJ0TEHo2BOzG3lT5jCXCpswHFBVvzhJ1Ri4hgb59WiV4tgVuAacDbAKwEznEwIqmbBKDU6SAkCihP\niIhdfLeVcvgQD+sxLUuTgGFACydDi1G25gl1GxcRa9nap1WiWztgNL6BBuczFDc3qYuVRVyoQ5X4\nKE/EjoE6DkvcaAkMAWAPsAvYCTxOEm7+Pwfjik225gm1yJE45nE6AAlStBxIJfacBlwLzAbm+R/9\nCujoUERSc00w9yx3OR2IRAHlidixEIA1wNnOBiISEe0reew48ASHgUYRjiaW2Zon1CJH4tgrQDEe\nYBEq69joOIm1XkRq6gzglwGPvO1MIFJL3TDFHBHlidgzD/iX00GIREBrYDwwwLuc5n28iBzgmFNh\nxSBb84Ra5EgcuwrYBBSzAZjMObhZ6XBMUhu2Dk4m9mgTsKVyrx3SgQZOByFRQnki9tRjHwm4SQFu\nAh5SlyuJWW29C0BfYAmwncMU8lea8Sf26wgXArbmCTujFgmJRsBdwD8xg2KuJB/4eRDvmATUC0Fk\nUjO2NoUUEZHIUJ6IHUOAPKDYu/0tkAOY7iYuTBuFRKC+A9GJhJsLuAxzzTIN+I5/A2MwXWz0m193\ntuYJFXIkzjXFTPP3OOBhGbA8yHfMBnoHG5bUiK0HXhEJtz1OByBRQnkidvQCOgCHMe0j5wO7AcjF\nXMr6xsX6Fab1gkgsSsDMrzmVH/iRR8s9cyWQ5UxQVrM1TwQ9Rk5+fj5du3alS5cuPPzww6GISSTC\nUoDbgGTAhQeCWvIAN9dE9itIUGpyHLvrrrvo0qULPXv2ZNWqVRGO0G6xkye6Ox2A1EgpKuRIqClP\nhFdN80QLIA3TgXIccApgyjnlBzdfxBB1t5KYlogZP6dlwDXIAsDNcCcDi2uRzhNBtcgpKSlhwoQJ\nLFmyhNTUVPr06UN2djaZmZlBBSUSeW2BiVU8NxvYWMnj7YDrMK16fNYDc4C5fIY54QBz0pEcmkCl\nnFAMNlaT49jChQvZvHkzmzZtYvny5YwfP55ly5YF/dnxwPY8ccj77ynAPi50MhSpsW+AEqeDkCih\nPBH96ponkoDbganAT5iOJ76RzP4DmHOyrmGLW8RZyZheBX8lcOjjV/kEaOXd0jXIydmaJ4Iq5KxY\nsYLOnTuTkZEBwIgRI8jLy7PmBF2kZq6m8kFOEzmxUVuaf+0NoOy04hRgAm4eDEuE8SoUg5PV5Dg2\nf/58Ro0aBUDfvn3Zt28fu3btom3btpW9pZRjc57YBcz3/g3vYzDm71mi31dOByBRRHki+gWTJ+oB\n92BGyQEzhcXL3vWzmUM/73obzEWPWy11JOb8zvvvOsysbvAmUHYN0gy4EzcPORCbHWzNE0FFvXPn\nTtLT0/3baWlpLF9e2QgjBeXWM7yLiC1q82fSBBgILPRu+wpA+4BcSglBf0ZLbfUuoVSTPq1bC7ax\nrWB7lc/X5DhW2T47duzQCXoN1DRPFJRbz8D5LPEjZtQF8zf8SzTylU2+dzoAqaOtKE/Eo2DzhIuy\nFgfdgF8DrwNrvAtAc0zbBZHY4/vtPxtT0pyPGfY4CSgC9gNPUQKWjgQTaCvKEz5BFXJcrprenewf\nzMeIWOZnmAPnB5T1Wi0BdvMscDPxeV8/g8CL84IQvGdNDrzp/TuS3r+jf3vp5A8Cnq/pcczjCWyV\nVfPjX3yr6c+pf3jDqLWnMSOtwHnARY7GIrVVdlxQSccuGShPxKNQ54memLOwdzBnYMcxXa+mAmb6\nZt+FbxrQqcZxikS/czBlywxMLiwBngR+4GngVuy/oZyB8oRPUIWc1NRUCgsL/duFhYWkpaVV8wqR\neHGhd/EpBv7FTg4xmU7ADbiZ7ExoMSQUo8zX5DhWcZ8dO3aQmpoa9GfHA1vzxFH/WiHmMkCTPNqj\nP+Y+vIcvATeX4OZdZ0MSxyhPRL9w5Ik+3gXMpWwOsBeADwP2GwzkqbuVxJTyxUnfoMiP8R0HeIDT\ngNG6BqnA1jwRVFEuKyuLTZs2sXXrVoqKipg7dy7Z2dnBvKVIjEoG7gIaAFuA15wNJ0YcJ7HWS0U1\nOY5lZ2czY8YMAJYtW8Ypp5yi5vI1ZH+e2EHlY2RJ9ErBnLj6im/v8qmD0YizlCeiX7jzRCJmUOQm\nlTyXB5hBkUViVRJwsXd9GzBHZzUV2JongrrFmJSURE5ODldccQUlJSWMHTvWigEsRZxRH9ND+5/A\n/1gAXOVsQNYLxeBkVR3HcnPNCCnjxo1j4MCBLFy4kM6dO9O4cWOef/75oD83XtiYJ04s3djeEDke\ntQFuAdYCS1kAfMGJJz3tgUuoW3fXr6l4b7/2ugHnBvkeUj3liegXiTyRDEzA3EY7jDnGf+N/dm9I\nP0sk+nQFFmF6CGzg35g5d12YNqzR3046vGzNEy5PxY5aIWb6fbnD+REiltmPKeZ4gJ/jZqnD8TjD\nzYn9RGvD5XJxp+eRWr/uCdfvg/pcCT2XyxU1WeJ74N+UL+RcSVkDfbHTFmBmNc/3xM3qWr3jduB5\nQtVW61e4WRSSd4o1bpQnxAhHnviCsvbR3TEXtY2Ay9EMVxKLDmCuP0orPO4CxuHmqciHFAJu4jdP\nqNO/SMTVK7e+lP9ihlOV2gtFn1YRn73AU5S/OL8EFXFiQSfMMPPvYsY8Kq7w/GrygQE1fLfvKF/E\nORfYABysZM9kIB04rdxjpcBnFfZfxGrMAK0SesoTUpWzgCOYeUbXlnt8Hb5RRuJ5rlGJPU0xPQMe\np2xa8o7A58A0fgBaOheco2zNEyrkiERcA2AceCvfb3kf0eTGtVdZH1WRunoLc9ruAjz8Es1WFUvS\ngJGYAsqXwA/ex1cAHpZhhkeuySXbIcwp8KXAEgZhOsnuAlZV2NOFOVE+v8Lj/b37f4Ip6pipkt/2\nPtsEGI3JCxI85Qmpzs8wl7dbvdvrMO2mPwdgCqZbvAv4JTpTE/ulYIo5KzA3GTIxWedDcoDG3r1O\nA4YTP7Ps2ponVMgRccSpwBjMfV0z2F4e1+BmrpNBWScUfVpFfI57//058L6KODGqCebSzScLM9l8\nEYdr9T4XsoRLvesuzDH9VzV8rW//QUAXYA5Q1kbnIPA3mgB34+ahWkUlJ1KekJPJ9C5gCrSPYzqh\nmKzgywx53EAes9TdSqzXgsA2qJcCR/DwmT8PrQXWcgaT2BgXxRxb84TaC4o45jTg2nLbc/nKqVBE\nxK+R0wFIBLXGdLu6DhhVbulNYDfY8lKAfiH6/K7ArzHz6vTyfnYqppwz1X8JKSKR4RsUubI8cDTC\nsYhEziDMBAHl24Ju5D8ORSM1Y2f5SSRmnIlpvPgx8A0zgbFo9PiasrVPq4hEkzbepbzTgcGYgZIr\njqnTgMonMq6rnkBb7+ekY7LAv4HdTANuIz7uupUC0zEDSUPoxmpQnpDaqg/cRVl3q+8xI2y9Cpjf\n0A5OhCUSZqnA9cBPwDyglNVQ6VQArTGDRMRKIcHWPBErP38Ri/XwLivwsJBnSABuw82TDscV/Ww9\n8Hbm9JMAACAASURBVIqILTpF6HNOLbeeAIwAnuB74AHSmURhTDdv9wAzKCviAPxAA0LRBkJ5Quqi\nAaa9HN5/GwELAHjOX1hthCnBbuHPoN8ziQnp3iWVskGRT7QbeJA2/IXvY+JGg615QoUckajxM+Aw\nUADkshfTgF+qZuuBV0Skei0xgyR/DBTyIuY+aSwWczzAy5jWD/WBY3QCdoAKORJFsjAzXL1L2aXt\nQXxjW00DhmH+Qhtghk8WsVkKcDvwJGZMz1blnvNgWo1+z3NANuY3vyGhbasaSbbmCRVyRKJKf8yp\nwnIeIwm4Bzf/cDakKGbrKPMS3Uwz4nWUDX8p4oTLgJXAUTYDkzkLGIY7xgZbfQPz1wb1OMY9mHYO\nR4ASCEH+U56QULkIM3pWMea38wV8gyLvgnKtqG/BtGeItb9ViTetgT9gRo6q2O7mNGAtO4AnA24x\nXAN0te5339Y8oUKOSNT5FbAZMz3uExzBVLnlRLaOMi/R7RvAd3ou4hwXZtjVf2IuG78g1obifhtT\nqjLdUu6k7PuFLuspT0golW9xMAF4DE6Y8e5Q5MIRCbP6VTw+CHOtcozA7ldzMIP228XWPBEL3dpE\nYoyHsmEej5EDFDkYTTQrIbHWi0hVVLqR6NMEM+yq73RtOfMxJZ0vgP1OhRUCHwIf4esudgfh6o6i\nPCHhUh9TzGmG+T32tUuYTeB4T8YmzF/ttghFJxJODTDF9yaU/fb78tQMVmB+278EK2ZftDVP2Fl+\nEolpLsy05M8BhRwCptAcuBM3DzoaWbSJlgOp2O9NTON4IwkzALlINGiOGasgFyhmJb5WLGBaskzA\nzWPOhFZHnwJLvOsekglnu1PlCQmnRsC95bZXAvMxZ3BDcdMQ+IDAws7FwC9Q1yuxXRPgd+W2SzBH\n90UsDNivNTAeNw9ELrRasjVPqJAjEpVcmMHFcjGXlz8BuZSiZnTl2dqnVaLLe8An/q0EArt4iESD\nVpiRNzYDazCTdRcDe4EnOYg9g0z+D9/sPz4jCWchR3lCIukczAhPb2MmcK7MeyjDSCxKBPpiehb4\nbjf8gJnj6lk8RO+A/bbmCRVyRKJWAnArkIM5Wd/Ns8DNRO+BMNJs7dMq0eN74H3/VgvM3EDNnQpH\npBptvMv53u1j/397dx4fVXn2f/wzIYAgAoKSKEFxQ4IVjEupWq0tBheU8igqtQpV0bphUX+2PK9n\nafApQl2qCKitrYjVuldBpUhEQy2IVlEqiKUq0bAkLhQQWRPm98c1k3USkpkzc8595vt+vY7MPldM\n5lxnrnPf1w38BtjBNGA8we+n9hHwTINbLsWWuk0f5QnJtJOxUus7Ce7bGPv3JQCtTyqh9J3YBtYz\n50NgLfdjTcABBgKH+BBZc1zNE25GLZI12mFD6pcDr7CWb5jIYcAllDDR39ACwNWhkBIc8aaU3YBN\nXI/GvIk7OgIjgCfZAfyavYGfUcJt/obVjArgsQa3XAgclvb3VZ4QP5wS2xpbja12BXA8U+mArQl0\nItZ1RNOtJFz+A2vYv53PsZNnAO8CMJoSHvEproZczRM6YhUJvPbYgpfjsDT/MfCsrxEFhavNySR4\ncur9V8QdhcBBscvfAPcFsrFkFdYzxNY2yQV+CAzIyHsrT0iQHIIt0AzWTWQxNip0GjZZUiRcOmLf\nX+qPHeka+/ePrMl8QAm5mic0IkfEGfEO8XcDy3kROMffgBr4EJv33Rrd0xmIiCTwLPXbOdc5HejX\nyscXYEuOanJnsPwEeAA717mR3wLXEJyy5Aas21sUm3KyiP+EgBwEi/ihEBgFvBe7XoVNspoEwK+p\nW8HtWOqmqIi4am9s9cX52BpWA7ETDy/xB2zCMNh6veej7NAWKuSIOGVvrJhzL29Tw9ucSgl/9Tso\nPsJmwbZWFbl4sSChq83JRNJnE2dxNysa3boWW0+ise78qfbc2J4f/zmXsZSZGvofMDnAT4n3U/sC\nuJUCfska30tum4H7sH4hcDKLKM54DMoTEkT9YxvY5yNeirVWydti98zjLObxF+1zxXldgZGNbttK\nlNdqTxlVAR9wIL9kXcZzl6t5QoUcEed0w5ZGXgb8lcXUtb70Q9O+B/V1BIbQdH2G1SRuA9g2rjYn\nE0mPN4CX+UsbnrGRuuabrfFu2wKSjIn3U/sDtkLIGh7DWnf7VczZipWWrGR/LPhQxAHlCQm++ktb\nNN4f2/58OzYqWyRMvgf0Bb4GnseyxTr+iLXBz2TucjVPuBm1SNY7ESvk2EDFTlgXnUxr2PcA4ARs\ncGRcIYlXAOqCN4UcNyvoEjw7AHiSuu4FrnkXeBmwg5/vAx08fPXdwKvEpwLMB4bG7oliQ6RdWfw6\nzNoDlwHrgcf5iB08S9NzoJmwA+v5sRPIByo514cojPKEuCAXK8Uuw0ZDbqP+iorl1I3fEQmTg2P/\n7gbmAtv5BPgVdizTDrgAODzNUbiaJ1TIEXFSPnbAPhOA2cBsLqKEJzMWQf2+BzaHuwAbKdQafT2J\nId073g0bNnDRRRfx6aef0rdvX5566im6d2/Y4aeiooLRo0fz+eefE4lEuOqqq7jhhhvSGpd4byuQ\nuIeMC1ZiewHzE+oOjbzUHztjvJvF7MViwD7/O4lP+CxJw7tK23TE9q/jgHtYTjXLOYES/p6xCHZh\nfyfxySGVHJWx905EeUJc0QE7HRZ3APFp60/UjsfpDowGbud/CU4nLJFUDcRWMbwbqK6d2l0NPEoE\nuJwS/pC2d3c1T2gPIOKsg4Ef1bv+JJ+k+R23YV94v6B+34OTgDNpfRHHO+nuMj9lyhSKi4tZtWoV\nQ4YMYcqUKU0e0759e+6++25WrFjBkiVLmDFjBitXrvTqRxTZg0+gXgH3YtJTxAHogXViycFGXMS3\nKDADiJfDJAi6ANfHLv+dVzP0rjVYr4+va285ABsT5F+3HuUJcVV/bPHmCHX720rgdgDuxT5pW4mP\nKRVxW7wpcnycyXXY6N8o8BAV2F/7VurPBPCGq3lCI3JEnHYk1uPdliP/I3AFNjbGS1HgKey8f4S6\nHWgR8G7tFIvMS3dzsjlz5rBwoQ1uHjNmDKeddlqTnW9+fj75+fkAdOnShcLCQtatW0dhYWFaY5Ns\nFiVeRoUFtbeeR+L1p7yUB9xEXR+Hp4FNxBsjV2D7JAmG7lihfTF/xabgnpjGd9sN/B74qvaWnsBY\n/F7lTHlCXDYI6EPdl9cXiDdF3gjcVe+RZ5DeT7hIJnQFbsYyyf6xrQZYwB+oyyYHYt93vBqR4mqe\nUCFHxHlHY1+e3iXKX/g9EeAaSrjPs3eYgxVxoH4VvBfvco1n75GM1jQn+6bsbbaWJdePp6qqiry8\nPADy8vKoqmp56k15eTnvvvsugwcPTur9RPasBngQOy9bZxg2MDkTulDXEaczVsiRoPoBsBTYzsvA\ny4yghOc9f5co8AjWncd0xRZB97/vgPKEuK5HbANrijwDW668vva8zARe5v80xVWc14mGp6RPwRp+\nL6r9DrIWuJW+wBhgYsrv6GqeUCFHJBQ6AIOxyU9lwG/5N7CvB69cSqKVajoBI/D7TGtrhjbuddpg\n9jqtbkf45cTfNri/uLiYysrKxk9j0qRJDa5HIhEikeZ/3i1btjBy5EimTp1Kly5q/CpeiwL/xNpf\n2t9rfHTc92nYV8E/2/0OQJrIxabgzoxdf541eDtqM4pN7iuvvWUQVloMxiGm8oSESbwp8nSsiB7P\nA7uAVT7GJZJexdi3mhfr3VaOzRdInat5IhhZVkQ8chpWzHmTqeQC4ynhzqRf7W/AotprEezwoXvs\nsv+7Dy+ak5WWljZ7X15eHpWVleTn57N+/Xp69eqV8HG7du3i/PPP55JLLmHEiBEpxyR+OcnvAJoR\nH++wGoB9sLEO7fH/kzgYasd3FPMcJ/McJTojHDAHY00kPwZsApyXhZwXgA8B+4v8GUFbwUx5QsKm\nPTAeawQL8BFWTH0SOJ+S2rVDO2Drhk7SPllC4VjsRME2bF3EXdhff+pczRNqdiwSOmdhkyyqgWm1\nK4e01dvAK7XXcoCrsbmq7QlCEQdsTmtbt7YYPnw4s2bNAmDWrFkJd6rRaJQrrriCAQMGMH78eE9+\nLsm8boAdJATRM8SLOJ2wFradCcYn8Rjg9NjlV7DV7CSI2pGOv5ZSbOKWvf44glbEAeUJCacIlgPa\nA4VYjzSwjom/i23TY1tdyUfEZTnYX3xXrCmyd2UMV/OECjkioXR47N8d3ItNxlgIrGjhGduA12OP\nm0v9wYsXY0WcvHQEmpIactu8tcWECRMoLS2lX79+vPrqq0yYMAGAdevWMWzYMAAWLVrEo48+ymuv\nvUZRURFFRUXMmzfP859V0iOeBG1SkNfrIHjhBeKf3A5YEaejn+Ek8F1sLFMU+/IgQbQX9hcELc/M\nb734iE37DF2HHVwHj/KEZIOB2ITGvbAcEf+aaT3MplN3JOjNCAYRf+2DHRF935NXczVPRKLRaFqP\nXG0OWEk630JEmohiPRE+S3DfKZTweoNbdgD3QILRO5diQ/LToYRUdj+RSIQDom1fcH195NCU3le8\nF4lEfMsSu4H7gC+xUmV8ee1gTA8qi202luIGgvpV2c73/qr2WolvcUhz/o2N7FqH5YczKSH5QsI7\nWInRfBs4O7XwmqU8IcbPPOGiGqwpcuNRkvlYnpuo/5sSGtmbJzQiRySUIsBPSDyK5nUW17u2CztX\n07CIcyg2EiddRRyRYIhPGuyGjVSYSXwp7SB8ifsHYDFeQ3CLOOKCfYErYxvAPJYl+UrLqV/EAetZ\nICJB0g7LG/s0ur2SulVIRcRtfk+vF5G0ycEWqvwzsBE4CDvgfoD5WHPK9lhS/6b2OZ2xAo6XrTDT\nx4vmZCK52MSQu7BGsA8ANp3pW/4FxVJgAxHsq3fPPTw6WH6H7XskeA7EivwP8xw2BaN/G569G+vB\nUedSoLdHsaWH8oRkq/bY5JNngK3Y6Yl1xNf5+Zi6k3WfYWN1OmQ8RpEgcDVPqJAjEmrtgAsa3XYZ\nMDPBpKue2NdZdwbq1ex2c8crwdMB6IN1D/gCsMNev3wAzCGCfVoP8DGS5KzzOwBpUV+sSLmcJwD4\nCSU83KpnRmk8Vi34ozaVJySbdQR+XO/6+8SLsX/kKOBrrIwTbx/7K025kizkap5QIUck6xyMnS3/\nF7YSTjmWwq/BpSIOQHW1mztekeZ9TPx86cXYODoR7/0HNsGiBpjFOmysThgpT4jUORrri/giDRfA\n2AzcD9g+QZ8ZyS6u5gkVckSy0oGxrSs2DuEUXNwd1FS7F7NIYmuBN4n3xTkfOMLPcNooBzv0r6m9\nZSnBXc49FRuwiQoXAt19jiUV7bAGxS8AUV7AGqDuyRsNru3rfVhpoDwh0tDxwN7YaTywku5m4CsA\nJgOdgKFY2Uck/FzNE25GLSIeKfI7gJTUOFpBF2noc+DB2mvn4N7hcw4wBnio9pY5XMgcngrVMP3N\nwHQi7OYU7uEHBGV1s2TVtc+uaeFRce8Ar9ReOx040fOI0kF5QqSpwtgG9mmehu3hoJocvqYbz1LM\nswzA9f2cyJ65midUyBERZ7m64xWp82/iA9oBfoCdLXXRQVgvhsdi1//iYyze24591dlNFFgCfMff\ngDy1pzXaVlB/parLcWnSn/KESMvaYx0Sp2Ld4XZjmekp4BIf4xLJFFfzhAo5zvoauI+Gi0b/lKZt\nMZcBLwE7E7xGoseLuKN6l5s7Xgmmg7BmxyYTHUO+xooD9jX6RODUDLxrOh2BTdR8HZt49LW/4Xjo\nE2BX7bWdwPTaS66u9NITiABRvsBWMky0gtXHwNOxy5cAjzpUxAHlCZHW6Aj8DOucCNb0fwHwKGDt\nkN363Iu0hat5QoUcJ20F7qX+QWUEiPDbJo/c3cwrRIB2/JbhwEA0bFLctLtGuzDxzinAeqxfQCd+\nz3hgclr3jfcT30sfA5yRxnfKpPiEHVfLG4ntX3upDzaV7FOgK7cxDpjkZA7tAYzCyjTVCVewqiD+\nRQ5gBI9yTCYD9ITyhEjrdKSumNsf6Ex8JN5DDAROBu53cl8n0jJX84SbUWe9V4gXcSL1bk00NDqS\n4La4auDP2I5bxEmODoWUYIpgLWwfwc5K2oiLXdjAc6/tJD6i8kjgh2l4B/FSXSHnG+Ai7O9kMzAF\ncHey1ZHAT4BKbB2bWazC2hhvwqbJ1R1buNHcuAnlCZGkHIdlqVewNvzvA5Ydu2AZMz6qT8RxjuYJ\nFXIc8XNKqMaKL/GB+AcDI1J4zXJgNvA4cBklHIxG5ohjHN3xSnBFgEuB3wPrgB5M4jpsjR/v9o/V\ndOU2NmP78VHoUNgNZwLz2ADcX/sbi8YaBX+Em4UcgILYtgt4mT8B1Pv5zOnYX6uDlCdEkvZdrJiz\niPjeYFbtfYdgTe713UGc52ieUCEn8D4BPuP2RrcegO08c1J45fi5tdnATOLD4SuB/BReVSSDqvX1\nV7yXA1yBdSH7CpsAtR9gh7Gp/s3VAPezGdvTjvHgFSVTvoNlzmeoP7XZpij9yJeIvHUi9hf/Ng3H\n+J6MfZ1zlPKESEqKsWLO0ka3f8OeG6WLOMHRPKFCTuBsxVoLgnVrWFx7T/xP7ADsS0YqRZy4Imwt\njpeJLzv4ADAOGy4pIpKd2gHXYN3IvoxtNk6n/qiLQ4G9Ezz7E+wQt7FDsMkqX9EDuBJv9uNBE89V\nlQD8CbjYt1i8dyT2e18Vu94TWzjAzbN5TZ0J9Ab+jh2DHId9jRORbHYuVr5eHrseBT7HTgaLiD9U\nyAmUbcDdNDzTZwfFl2MNFtPhxNg7/zV2PYdpjAd+o6GSEnTVfgcgYZZLwyVZYS3wbO39g4BvJXje\nkyT+0+yG9R3ZBysSheWrf2MDsJMDVspaxQmUMIwwDb8Pw+ib5uRip3iK/A7EO8oTIimLAOfHNrAV\nCacC7wEnUcLQ2O3h2c9LVnE0T6iQEyh/o3ERB2y5z3QVceJ+gH1ReRtbQ+VewA7DE51tFgkIR3e8\n4o6OwPXAPVh74vqWxbbW2gR0ir1eOtonB0Vn7Ge8F5tI9vfYbSK+UJ4Q8dw+wLXYogCLsdx2iq8R\niaTA0TyhQk5g7MJWvbCdYUes+j0UOCxDEZyDTbNaTvzv+RHsvLFIQDm64xW3dMYmnD4K7EjhdTph\nhflsWCmwG3aQPwM7ObAQgDewMaAiGaQ8IZIWPbCJpQ8AC7CTwfAElu3aAacS78ApEmiO5gkVcnyz\ngnN5mq9qr9nZ2t7AWPxrfnk+Ns3qY2BvqhhPCe3RUEkJqKYD2ETSIj4dSlqvJ9YH6HfEG2K+zH/y\nMpOVTySTlCdE0iYPa//wEPY9Bj6sva89bzMeuEP7fAk6R/NEGPssOuAt4GlewIYjLsZ2fvthTYz9\n7Jsdwc4YF2ATq2ZAbGlVkQCqSWITkYw5APhJvev/8ikOyWLKEyJp1Qf77tDYLmy0jta2ksBzNE9o\nRE5G7AL+iE1cigJfAFY06Rf7d2/gLIJRWYs3V74fi/S3gA2OD0J0IvU4OhRSJJscjK1b9Sds4W5b\n1etQHyOSrKI8IZJ2h2HFnLdj178AviL+8asm3J3hxHmO5omUvpnfcsstFBYWMmjQIM477zw2bdrk\nVVwh8xbwGbZQ3xe1t16KrX0xClvWL0hVtRxs3mt3LOo+3Mp/U4Kq6hIo1UlsbbBhwwaKi4vp168f\nQ4cOZePGjc0+tqamhqKiIs4999wkfpBwUo6QuH7AebXXHuFKSjRlVzJDeSLQlCfC43DsO80orOF9\nb6xdw75M4n+0z5cgczRPpFTIGTp0KCtWrGDZsmX069ePyZMnp/JyIbWLeJvH+i4k+Ocjc7FmlXsD\nFcCvAHgcFXMkMNK8450yZQrFxcWsWrWKIUOGMGXKlGYfO3XqVAYMGEAk4ufkyGBRjpD6BmIjTwEe\nxE4SxBd2F0kb5YlAU54IpwjWLmI/4N9Yr7TdvkYk0gJH80RKhZzi4mJycuwlBg8ezJo1a1J5OYd9\nAdyOlTpuA1bHbq/BuszsJA84M7ZdDgzwIcpkdMCq6nWrrKzCfs5fAZOBT32JSwRI+453zpw5jBkz\nBoAxY8bw/PPPJ3zcmjVrmDt3LmPHjiUaVaEzTjlCGhsMfD92+T4A7sQO8yVYqrFy2yt+B5I65YlA\nU54IrxzgamwVwyrgYUAngyWQHM0Tns3meeihh/jRj37UzL1l9S73jW1hsQk7HLX/2e2A9swCbCxO\nDbA/Nk3J1Q4znbCld+8h/ncb7/BUTXdmMh6taiWtUR7bPNSaHen7ZbC8LKmXr6qqIi8vD4C8vDyq\nqqoSPu7GG2/kjjvuYPPmzUm9TzZoOUeEO0tIQ9/DxuG8CcBu2jGVG4E7lUcC5DlgLbCWH/A3Xs3Y\n76Yc5YnspTwRPrnAddh3iM+ACBM5EviQX+Lv8i7irnKUJ8weCznFxcVUVlY2uf22226rnbs1adIk\nOnTowMUXX9zMq3y73uXmPrRRbCZlYxGslJApu0i8Bll7mjbq2g1MJ17EicRu2VHvEd1xu4gT1wXb\nEddfxSqKlbG+9CsocUxfGh52laX+kq3Z8RaeZlvcExMb3N3cPm7SpEkNrkcikYTDHF988UV69epF\nUVERZWVlrQgoXLzJEXBaugKUQDoLa/+/DMsp9wJ2DJDJfC+JRYG6URGvAvB34IQMvHdflCfCR3ki\nu8VH90/FviPZAuWzgRH+BSUO64vyhNljIae0tLTF+x9++GHmzp3LggULWnjU7fUudwZubnT/buwD\nvTzBcxM9PoI3pZEoDWdsVgGPknjO/veB7za67R3iRZ8BwEkJnpVPsJoYp2Jf4CZgQ+z6+9gZ1fsB\n2AjsE7tnG9ZZR5V2Cb6W9nF5eXlUVlaSn5/P+vXr6dWrV5PHLF68mDlz5jB37ly2b9/O5s2bGT16\nNI888kg6ww4Mb3KEZKMRWLZYBewEYBowHjvsF39EsVU2N5FL/WPbl7Ajnb39CctnyhOpUZ6QztQV\nc2y/8l7s1qH+BSXiIT/yRCSawkTdefPmcfPNN7Nw4UL222+/xG+QhoZu8eW6RwG/T2q4bw0wl/14\nx5PRJEdgS6tmY9niJew8XWOHAx9p2KS0qCSlPgGRSASeSOL5oyKtft+f//zn9OzZk1/84hdMmTKF\njRs3ttigbOHChdx555288MILbY8rhFqTI8B+lyWZC0sCJArMxIbcg61s9Wf9NfjoaWAFe2EltXVA\n/BDyQqyUk9mp1MoTYac8kV3+jc1liI/uHwIs0G9WUpK9eSKlYS3jxo1jy5YtFBcXU1RUxLXXXpvw\ncRGPtyiwBfg9YKN4Vse2psOZzNZ6j/kE651eV8RJNg6wgV3ZWsQBGIatRAIN/x98BNgce5E0qkli\na4MJEyZQWlpKv379ePXVV5kwYQIA69atY9iwYQmfo9VI6rQ2R0j2igA/AfJi19/0LxRhIbCC9lhf\nvL2w1TUvjN37FI4ub6A8EWjKE9llX6zlRPwTYGOwErXWEMkgR/NESiNyWiMSifBfHr/mG8TnbDd0\nBHWrYcRtBuaQeLJUV+AaUpv61LhrTraKdxX6BuujE7/+beBs1AxZEvGggj4rieePaX0FXTJDZ1rl\n31ifnFxgl/4afPAadmLsK84Fjmt071LsWApsFZp8MpXXlSfEKE+EyxrgD9jJ+fOBo9F3BUlW9uaJ\njLRv8brYcSrWLGtRo9v/FdtaIz5XUzPxvRH/HXfH/r/eixUr38L+X4ukRRuX/xORYHJ9QQD3fUq8\nA16i38WxWHPq+cBvsTxvp2wcOJ2lPCESOAXApdjUzWfR9zHxmaN5wtljp2JgMNAxia0nKuKkUzfs\njF38j2spEF/ZS8RT1UlsIhI4OViWsI/odl9jyT5RbEyU5el2zTzqJOCU2KOmA/BrbNxzwClPiARS\n/ambjwNWUI4C/wQWk3gVYZE0cDRPOL2g0lmxTYJnf2As8CB2mDeCiRyDhk2KxwKyIxWR1HTBpkf/\nC+jMFI7AerDdppyRZlHgMWATYL+HwhYePQTrZvE2ANXk8htuBO4I8u9JeUIksAYAw4lP3ZzJ0diq\nuAD7Mp/rgf8L8v5FwsHRPOF0IUeC7UBgDPAw8DzWOFHEU47ueEWkoQi2cMBDQAWwDCgH7EOuQ5X0\n+TPx5Qn2wkYr72my1DlYMWcF9tux0Tk7sDHPAaQ8IRJox2L7lFLqijhg4wR/B8BuHJ5EIi5wNE/o\nUyFp1RdbJh7gCSB+aC7iCUeHQopIUxHgMqBH7LqNEXnNr3CyxMeATae6ntafcBmJTYuA+Hoz0wjs\nNAjlCZHAOxk4A+gd2+L7oioAZqIWDZJWjuYJFXIk7foDI2qvPcxplHCNhkmKF3YlsYlIYOXQeGpP\nojUnxTvFgPUO7NKGZ0WwRqW9a2/ZwjlMCub0aeUJESecCFwZ224C9q69p4KbmOhTVJIVHM0TKuRI\nRhwDnBm7XAbcD8BXPkUjoVGTxCYiIjFtKd80FAEuB/aLXX8TmwAROMoTIs7pgI0SjE/YXOBjLJIF\nHM0TKuRIxnwHOK3BLTOID54XSYqjQyFFpLUC2nclFKLYqRXomuQrtMNWqewGfIH1xKubAhGN3eoz\n5QkRJ3UCxmFd0pYBMM/PcCTMHM0TKuRIRp2GLRtvdtOOu/l/QRyKLSIivuoEwPd8jiKsohzORGAt\ne1O3BHAycoHrsGkQnwF7M5EelLAPE4EZ/Eg5XkSS1AXbv7QDYAmnURLMKZwiPlAhRzLuLGBg7HIN\n9Ve8EGkjRyvoIrJnRwLxco546QVgJh9hDUXHYdMYUtEB+7K1F/ANsAH4Onbf4wB8muI7pEB5QsRp\n+wI/xaZzlgGvALDav4AkfBzNE1rTU3zxH9hh3SbgAGA1u9AQemmzgOxIRUTc8S7xbjY/pfUrVe1J\nZ+Bn1JVs1gMLa++dGfu3PfBfHr1jKylPiDivF3AF8AfgbwDMAs6j7tSwSAoczRMq5IgvItjBdNtD\n4gAAHAVJREFU4yasd87qFBouShYLSNd4ERHXRLDii5c6YStVEvu3IzC/wSN2kRObFhEBhmLTrdM6\nVUJ5QiQUCrDV8h6pveXPXMyf+ZOmWkmqHM0TKuSI7xz97EgQBKRrvIh4T7khHXYTH40TbfmBnjgJ\n2Eb8DDoN3nc38BfiB6IfAPs3enaqE75ilCdEQuNQ4CLgydj1PwE2DvBgnyKSUHA0T6iQI74ZCJQC\nzwE3UkI30nxWTsLH0aGQItK8AcAiYAVwIiX0xfrlKD+kKkrdFCfogWelkhYNAb5N0911JfZl7AUA\nnmryvG54tK6l8oRIqBQCPwRm194yk6uBB5QjJFmO5gk1OxbfnAycgBVBpwFb/A1HXORoczIRaV5v\n7IwrwBtYs1wfW+WGyGdABWArTF2NTW/KhH2whqX1t0JgVAvP8WwJBOUJkdApAs6od/3r5h4o0hqO\n5gkVcsRXw4BvYZ+H3wBwn5/hiGt2JbGJSODFz7jGPQzAVj9CCZGPAetbcz2ZGY2zJ/2BEdjSwpFG\nW1ev3kR5QiSUTgROjV1+AvBoDJ9kI0fzhKZWie+GA8uJz9r/wtdYxDGOzmkVkT0rwqbfbiXeV+Vr\nvG/Pm00qAfgewVrU/ZjYlkiJF2+gPCESWj/AcsTbQC53cyM24lBTcaVNHM0TKuSIiLsCMrRRRMQV\nmZpOFRjKEyKhdg7WVH0F1qphvL/hiIsczROaWiW+a/hHGAW+8icQcU+a57Ru2LCB4uJi+vXrx9Ch\nQ9m4cWPCx23cuJGRI0dSWFjIgAEDWLJkSZI/kIgkYsUHnXtK3m7iI3Ky7v+i8oRI6I0EDgG2A78D\nYJWf4YhrHM0TKuSI73Kpm+MKkMM0btKQSGmNNM9pnTJlCsXFxaxatYohQ4YwZcqUhI/72c9+xtln\nn83KlSv5xz/+QWFhYZI/kIgkcjQAPX2OwkVR4A0KuBXYTDdsylpWUZ4QCb0ItogKwAYA5vsWizjI\n0TyhQo4Ewg+wFazAzht+6GMsInFz5sxhzJgxAIwZM4bnn3++yWM2bdrE66+/zuWXXw5Abm4u3bp1\ny2icImF38p4fIk1EsTW/XmYN1jfiOrJwRE6aKU+IiEhL0pUnVMiRwIivYAXwKmADJEVaUJPE1gZV\nVVXk5eUBkJeXR1VVVZPHrF69mv3335/LLruMY489liuvvJKtW7W6joj4bTbx6QUdsSJOEFaqyjjl\nCZGs0LCJ+5fAZn8CEfc4mid0YkYC5XysYdnHQEemkBe7/WCgL/BHTbmS+lozR/XLMviqrNm7i4uL\nqaysbHL7pEmTGlyPRCJEIk3bhFZXV7N06VKmT5/OCSecwPjx45kyZQq33nprK4ITEUmHl4H3ADvQ\nu54sXu9LeUIkK/QGjsdWsALI5TfcCNyh7w6yJ47mCRVyJFAiwCXA74G1wGex2z8DXgegDDgt84FJ\nMLVmx9v9NNviVk1scHdpaWmzT83Ly6OyspL8/HzWr19Pr169mjymoKCAgoICTjjBJgeOHDmy2bmv\nIiLp9ybwBgDtsJE4+/gZjt+UJ0SyRv0VrKqBZ/0NR1zhaJ7Q1CoJnAhwBTAcOBM4nfp/qGXAr+pt\nryd4hW+wnvW/AbakNVbxWZqbkw0fPpxZs2YBMGvWLEaMGNHkMfn5+fTp04dVq2wKwyuvvMJRRx2V\n1I8jIg11j/37IgCvYX1fpGX/BCyX/hTY19dYAkB5QiSrjAQOjV22CSxt/FBL9nE0T0Si0Whaj4oi\nkYgGtEnK1gEP0vAQPoLN9288OK2Gus9XB2Anv6DxzFkJghJS2f1EIhH4fhLPfy3S6vfdsGEDF154\nIZ999hl9+/blqaeeonv37qxbt44rr7ySl156CYBly5YxduxYdu7cyWGHHcbMmTPVyLINlCekOTuA\nqUB8lnh/4EN+SdM9v5h/AH+uPSFS4HM0qSoB5QkBlCekbaLUje7fF5te+n/6Cwqp7P0+oUKOOGM1\n8EgbHl/3h90ZOy/ZBRtoLsHgwY73lCSe/3rrd7ySGcoT0pKtwD3AztpbjsXGbEpD/8RWqYLR1J2R\ndlkJHhRylCdCQXlC2mo3cB/W9jgPqOJ/0WSUMMre7xPqkSPOOAQYD3zdisdGgflABVD3NeBiGh7a\n5qCzuo5rzZxWEXFaZ2AcNjLHPvJLsVGWxf4FFTifEi/iXEg4ijieUZ4QyUo5wNXANOJTrB4GRmH5\nQ8f/Uo+jeUKFHHFKt9jWGpdhnXKsf3gUeKzB/e2BbwOLuAHo4VWIkkma9iySFfYBrgWmY2dZYRE/\nZBGzs/4cfSXwEvHTFj8EBvgZThApT4hkrVys4ftU4Bs+A27nSOCfmqIr9TmaJzS+TEIrB7gS2D92\nPVJvA/vMLgLsq8E/sclbFaiZpkNqkthExEk9sEmy8X34JwkftQXblzfePk9/gBn3FfAA8SLOGUCR\nn+EElfKESFbrgBVzOsauWzv42X6FI0HkaJ7QiBwJtXbYWdxEI+ZeAt4D7Pzu47W398cGXpZk/Zle\nBzg6FFJEkpMHXA48BLwPDKOE3vXuX0j8IL2hrth+vbFlQCHwsHP7+83kMC02OglOAU70M5wgU54Q\nyXqdsYbHdVN03+Mk3mMoOt4XnM0TKuRI6EWwaVSN/RDYDnzY6PaNaY9IPOPojldEktcH+DHwKFaQ\nb43N2FTbRN4EbG3EA1MNLUO+Ae6tLeIcDwzxMZrAU54QEWyK7nXYOPwaYDFa01ZiHM0TKuRI1ooA\nFwFPUTdEfyfWcWB+k0dvxM7ddgROoG2rX32CnQvIb3R7FFgJfFHvtn2wwfGatysi0pzDgQuAF6G2\noJGMHbWXfgeciu3bD8XKRUH1J+JHnYXAOb7GIiLijn2xKbr3Y0fhVsiPouNucZEKOZLV4sWcuA1Y\npX4xcDwl5GMH+n+l7oA/j3n8FLi1VUMx3wOe5zvAfo3u+Rgr4zTWnzlcBEzUUM89c7Q5mYik7qjY\nloqy2Gb+CsABvMZVWH4I5pD77wJPEkHrdrWK8oSI1NMLuAL4A9ZV7XwmcjRB3d9LRjiaJ1TIEakn\n3kzzAeDtZh5ThS1guOcK/krgeQCWtCGG1QSmh1bw6X+UiKTgNGAb8bOyZj3wR+BSPwJqlUKsfedO\nvwNxg/KEiDRSgO3jHwGexfaoksUczRMq5Ig0Em+mOZ+mQ/a/wA6dPwPgGWxwf2NvAx9Qf02VA2nd\noM312MifV9sWcvZydE6riATHWdik2Y9j1z/H9t7PNnjUC8Ag4KBMhtaMr4CdREnc/00aUZ4QkQQO\nBS7EWizYkiefAgf7GJH4xtE8oUKOSAJ9sGGXjW3FOt7vAHqwggNZ0eD+TcQXgq1zHjCwle9bf2rX\nYZTQCSsA9QGOAKZq2GdDju54RSRYfhDbwFoJ3wMsB/pQQjesNL+bd7gSeNDX/fBm2jGNGmyC1T4+\nRuIM5QkRacYAYDgwB4CZnIH1YJuh4+3s4mieUCFHpA3qL1+4Iba15CxaX8SBhlO7Pq53+/tADmBr\nr3RtwyuGnKNzWkUkuPYGxmH7+QoaFucfBGzMTq8MR/UNdirhd9RgK1WdnuEInKU8ISItOBZbxXY+\n8HJssyP8Hv4FJZnlaJ5QIUekjfbBDvKX0PJqKQeRXCPOPOBqYGns+udY3xx7r3uBG7GvGuLqnFYR\nCbauWNH+Tawb2ibgw9p77wduwNY/yYQd2FjNbYDlFa1U1QbKEyKyBydhe9jXa2+ZDoxHJ0+zhKN5\nQoUckSR0A85I4+vnYaN54p7ChvZDNZ24g/HAZA37dHYopIgE377AmfWuvwy8AUCUvZnKLWRilZNd\nwDTiRZxDgZFpfsfQUZ4QkVYYgu1pbbGT3eTyG24E7tDxdvg5midUyBFxwAXYKiqfYElmGmAH+Fne\n6tLRHa+IuOcMbP/7XuzfrWl/xxps9M8WAHpjq6y0pnG+1KM8ISKtdA62f1+B7TqmA7bMida1CjVH\n84QKOSIOiGAH8A8C67C5vDbgP8s5OqdVRNz0Q+wg/5+k+wB/N7bHt05s+2GrKaqIkwTlCRFpg5HY\n6rRfY/veCnagQk7IOZoncvwOQERaJ4KtpLUfVjjO4zb+N9uHe9YksYmIJCkCjMIWqN0KdOU2/jst\n++FqoBKwqbxXA+3S8C5ZQXlCRNogAuwVu/w9QOsDZgFH84QKOSIOaYcd0HcFqoBZQFaPzIkmsYmI\npCACjAHysXUEHwBsZE4V8EXs1lREgWcAWynxOjR8OiXKEyKSJEcHakhbOZondGwg4phcbDWVe4BP\ngSOZyCjsy0X6G2+KiEgOcCUwA/gS6Mht7Kh3/3BsSdtk9snHMJH3gI7Yvl4D+kVEMmsgsAArqd9E\nCV3RMbYEj0bkiDioA3aA3xHr1TADeMXXiEREsks74Bps0P2ORvfNIb7SYFu9zHvUFew7pxCfiIgk\n5xTgOGwGzTTgG3/DEUko5ULOXXfdRU5ODhs2bPAiHhFppc7YgX4udkb4bwDM9zGi8NmwYQPFxcX0\n69ePoUOHsnHjxoSPmzx5MkcddRRHH300F198MTt2NP5al92UJySs2mP74e7YqMj6zYifa/ZZnwHv\nN9pew/bfb9AOm06lrgxuUJ7whvKEBM25wABsetWdgI2F1+dW2i5deSKlQk5FRQWlpaUcfPDBqbyM\niCRpH+Ba6n+QFzOEEg3/9MiUKVMoLi5m1apVDBkyhClTpjR5THl5OQ8++CBLly7l/fffp6amhiee\neMKHaINJeULCriMwHvhlbDs/dvsu4D8o4ceNtk48BDzbaFsILCYC/BTYN9M/hCRNeSJ1yhMSVBcA\nhxBvibKRLkzmv3SMLW2UrjyRUiHnpptu4vbbb0/lJUQkRT2wA//4meAFwNv+hZNhu5LYWm/OnDmM\nGTMGgDFjxvD88883eUzXrl1p3749W7dupbq6mq1bt9K7d++kf6KwUZ6QbHM0cE7s8nPAY422bc08\nL74yYa90B5h1lCeCTnlCgioCjAYOjF3fAtwPBGbZIvGIm3ki6ULO7NmzKSgoYODAgcm+hIh4JA+4\nnLpizosArPUrnAyqTmJrvaqqKvLy8gDIy8ujqqqqyWN69OjBzTffzEEHHcSBBx5I9+7dOf3005P+\nicJEeUKy1fHAmdiUq9ZsPYBLgQI/gg095YkgU56QoIsX2feLXbfJfw8Cu32KSLznZp5ocdWq4uJi\nKisrm9w+adIkJk+ezPz5df04otHm1+Eqq3e5b2wTEW/1AS4B/hi7fjEP0o8gddkvj21eak1F/HXi\nHYQSaWk/V18kEiESiTR53Mcff8w999xDeXk53bp144ILLuCxxx7jxz/+cStic5/yhEhi34lt0nrl\neJ8llCf8pzwhrmsHXI01Pt4EQCU/5FaKCNJxdrYoR98nTIuFnNLS0oS3L1++nNWrVzNo0CAA1qxZ\nw3HHHcdbb71Fr15NBwWf1tKbiIhnDsPm8z4N/AkbpRMcfWl42FXmwWu2piJ+YmyLazgvtbn9HFjV\nvLKykvz8fNavX59w//b2229z0kkn0bNnTwDOO+88Fi9enDUH6MoTIuKVvnifJZQn/Kc8IWGQizWi\nvwfYCqwEjvE1omzVF32fMElNrfrWt75FVVUVq1evZvXq1RQUFLB06dKEQYlIZh0FDI9dfgiAptXh\n8EjvnNbhw4cza9YsAGbNmsWIESOaPKZ///4sWbKEbdu2EY1GeeWVVxgwYEDSP1FYKE+ISDAoTwSV\n8oS4pgO2UmFHYBUwx99wxDNu5omUlx8HEg4PEhH/HAsUxy5HeIBxoV3JKr073gkTJlBaWkq/fv14\n9dVXmTBhAgDr1q1j2LBhAAwaNIjRo0dz/PHH187xv+qqq1L/0UJGeUJE/KE84QrlCXFBZ6yYkwu8\nC5wU2mPsbOJmnohEW5qM6oFIJKI/bRGflAKLYpf3ArZzE9DVv4AaKGlxLvye2AHf6iSeeUhK7yve\nU54QkURKaLlnyp4oT4SH8oQEzb+xnjm7ge8Dr/FzrMwjmZW93yc8GZEjIsFUDBwXu7wdgHuxmb1h\nkd4KuoiIuE55QkS8ty/WADkCvAbA7cDffYxIkudmnlAhRyTkzgEKa69V04nbgR2+xSMiIiIi4rpe\n2MIidZMCX2Kkxo5JhqiQIxJyEeBC4NDY9W0AzMAGg7quOolNRESyh/KEiKRPH+CSetefAeBTX2KR\nZLmZJ1TIEckCEeBSoF3tLZuBTX6F4yE3h0KKiEimKE+ISHodBpzQ4JZ3/AlEkuRmnsj1OwARyYwI\nVsipAeAnQHcfo/FKMCriIiISVMoTIpJ+nfwOQFLgZp5QIUckK+1F/Rm97gpGRVxERIJKeUJEMqcA\nWMMZfochbeJmnlAhRySLDML66bfnAW7EFkkscbopm5sVdBERyRTlCRFJv0HA68Aa4Bzu4PjY7W4f\nZ2cLN/OEeuSIZJGzsRWsdgHTCMPaVW7OaRURkUxRnhCR9OtJ3QpWLwLL/Q1H2sTNPKFCjkgWia9g\n1RdbvWoaAG/iaiXa1S7zIiKSKcoTIpIZ9Vewegb4yMdYpC3czBMq5IhkmQgwGjgQ2ALAX+jBr/gf\nJ4d+ullBFxGRTFGeEJHMOQy4IHb5UaA3JVzh5DF2NnEzT6hHjkgWygGuAO4DvgI2AL8HIIpbTZCD\nUREXEZGgUp4Qkcw6CtgOvACsBf4AQBWQ519Q0gI384RG5IhkqXbANUDX2PX1ADyMFXNc4WYFXURE\nMkV5QkQy7zjg9Aa3PICdOpXgcTNPqJAjksVygeuw1avMp/Rnom/xtJ2bO14REckU5QkR8cd3gZNr\nr0XJ4V5u1jSrAHIzT2hqlUiW6whcD9wD7AQ2+RtOG7k5FFJERDJFeUJE/FOMLTCyFNgNzIDYJY2n\nCA4384T+gkSEzsC42GWbYrXNt1hERERERMLiXKAwdrkGCMqIDnGbCjkiAsA+1B+iV+NfIG3i5lBI\nERHJFOUJEfFXBLgQOATbw3RhMv+lKVYB4mae0NQqEXGYm0MhRUQkU5QnRMR/EWA08Dts9Pv9gJ04\nbedfUBLjZp7QiBwRqbVv7aVncGP1Kjcr6CIikinKEyISDBFgLLAf8fWrHsT65Yi/3MwTKuSISK2x\nQCcAyslhIkcFfthndRKbiIhkD+UJEQmOdsDVQFcAKsnhVg6jBDdOoIaVm3kiNIWccr8DSINyvwPw\nWLnfAaRBud8BeKwjMBzogJ0fWAHAHB8j2pP0VtCffvppjjrqKNq1a8fSpUubfdy8efPo378/Rxxx\nBL/+9a+T+UEkA8r9DiANyv0OwGPlfgeQBuV+B+Cxcr8DaDPlCWm9cr8DSINyvwPwWLnfAXggF7gO\nW2xkN/AxAE/5GJHXyv0OoI3czBMq5ARYud8BeKzc7wDSoNzvANKgCluOvK6B1lK+SwklgRydk94K\n+tFHH81zzz3Hqaee2uxjampquP7665k3bx4ffPABjz/+OCtXrkzmh5E0K/c7gDQo9zsAj5X7HUAa\nlPsdgMfK/Q6gzZQnpPXK/Q4gDcr9DsBj5X4H4JGO2PF2h9pbVnJsYI+326rc7wDayM08oWbHItJE\nV+BaYDp2puBvxKdcBU1656j2799/j4956623OPzww+nbty8Ao0aNYvbs2RQWFrb8RBERyQDlCREJ\nps7AOOBu7Hh7KUE93g47N/NEaEbkiIi3egBXUbeTWADANr/CaYb/c1rXrl1Lnz59aq8XFBSwdu1a\nz99HRESSoTwhIsG1D3ACdWtXLQbga7/CyVJu5omMjMgpycSbAGUZep9MKvM7AI+V+R1AGpT5HUAa\nlCW4zXrqB21ef0mbn9GlS5cG14uLi6msrGzyuNtuu41zzz13j68XiUTaHIM0VZKh9ynL0PtkUpnf\nAXiszO8A0qDM7wA8VuZ3AG1S0uZnKE8EU0mG3qcsQ++TSWV+B+CxMr8DSCNreXyXz1F4oczvANqg\npM3PCEKeSHshJxpVB24R8Z5X+5bS0tKUnt+7d28qKipqr1dUVFBQUJBqWFlFeUJE0kF5IjyUJ0Qk\nHVzOE5paJSLSCs3t6I8//nj+9a9/UV5ezs6dO3nyyScZPnx4hqMTERG/KU+IiEhLvMwTKuSIiDTj\nueeeo0+fPixZsoRhw4Zx1llnAbBu3TqGDRsGQG5uLtOnT+eMM85gwIABXHTRRWpgKSKSJZQnRESk\nJenKE5FoCMcq3nXXXdxyyy18+eWX9OjRw+9wUnLLLbfw4osv0qFDBw477DBmzpxJt27d/A6rzebN\nm8f48eOpqalh7Nix/OIXv/A7pJRUVFQwevRoPv/8cyKRCFdddRU33HCD32GlrKamhuOPP56CggJe\neOEFv8MRSRvlieBRnnCD8oRki7DkibDkCAhXnghrjgDliUwJ3YiciooKSktLOfjgg/0OxRNDhw5l\nxYoVLFu2jH79+jF58mS/Q2qzmpoarr/+eubNm8cHH3zA448/zsqVK/0OKyXt27fn7rvvZsWKFSxZ\nsoQZM2Y4/zMBTJ06lQEDBqgxo4Sa8kTwKE+4Q3lCskGY8kQYcgSEL0+ENUeA8kSmhK6Qc9NNN3H7\n7bf7HYZniouLycmxX9PgwYNZs2aNzxG13VtvvcXhhx9O3759ad++PaNGjWL27Nl+h5WS/Px8jjnm\nGMC6lhcWFrJu3Tqfo0rNmjVrmDt3LmPHjlVTQQk15YngUZ5wg/KEZIsw5Ykw5AgIX54IY44A5YlM\nClUhZ/bs2RQUFDBw4EC/Q0mLhx56iLPPPtvvMNps7dq19OnTp/Z6QUEBa9eu9TEib5WXl/Puu+8y\nePBgv0NJyY033sgdd9xRm+xFwkh5IpiUJ9ygPCHZIMx5wtUcAeHOE2HJEaA8kUlpX37ca82t0T5p\n0iQmT57M/Pnza29zpQrYmnXnJ02aRIcOHbj44oszHV7KwjysbsuWLYwcOZKpU6fSpUsXv8NJ2osv\nvkivXr0oKiqirKzM73BEUqI8oTwRJMoTIsETtjwR9hwB4c0TYckRoDyRac4Vcppbo3358uWsXr2a\nQYMGATas67jjjuOtt96iV69emQyxzfa07vzDDz/M3LlzWbBgQYYi8lbv3r2pqKiovV5RUUFBQYGP\nEXlj165dnH/++VxyySWMGDHC73BSsnjxYubMmcPcuXPZvn07mzdvZvTo0TzyyCN+hybSZsoT7lGe\nCD7lCQmTsOWJsOcICGeeCFOOAOWJTAvlqlUAhxxyCO+8847TXebBurPffPPNLFy4kP3228/vcJJS\nXV3NkUceyYIFCzjwwAP59re/zeOPP+700pvRaJQxY8bQs2dP7r77br/D8dTChQu588471WVeQk95\nIjiUJ9yiPCHZIgx5Igw5AsKXJ8KcI0B5IhNCO3ktLMPvxo0bx5YtWyguLqaoqIhrr73W75DaLDc3\nl+nTp3PGGWcwYMAALrroImd3unGLFi3i0Ucf5bXXXqOoqIiioiLmzZvnd1ieCcvnR6QlYfk7V54I\nJuUJEfeF4e88DDkCwpcnwp4jIByfnyAL7YgcEREREREREZGwCe2IHBERERERERGRsFEhR0RERERE\nRETEESrkiIiIiIiIiIg4QoUcERERERERERFHqJAjIiIiIiIiIuIIFXJERERERERERBzx/wFmPuSw\nluG8VQAAAABJRU5ErkJggg==\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 overfitting 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 time, 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 12.63% :MKL\n",
"Test error is 26.63% :Subkernel1"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Test error is 15.90% :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",
"#get two circles with radius 2 and 4\n",
"c, feats_tr=get_data(2,4)\n",
"c1, feats_tr1=get_data(2,3)\n",
"_=gray()\n",
"figure(figsize=(10,5))\n",
"subplot(121)\n",
"title(\"Circles with different separation\")\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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54YsvvkDHjh2xZs0aKBQKDB8+HNbW1hg3bhw6duwodfQyp6yM+5s3b6JPnz5Q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\nHfT/AAAEpXfiwGc+AAAAAElFTkSuQmCC\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",
" #Four kernels with different widths \n",
" kernel0=GaussianKernel(feats_tr, feats_tr, 1) \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",
"title('classification with constant separation')\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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6+rLzXjsg3t7eCAsLwxdffKFuUzQGbRW7l6Ibq0oePXqEPXv2ICYmRt2msKiI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\nIKgF/w8KXbsaNzC3wAAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As we can see the MKL classifier classifies them as expected. Now let's 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",
" #vary separation between circles\n",
" c, feats=get_data(4,i) \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 kernel weightings obtained 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": "markdown",
"metadata": {},
"source": [
"Let's plot five of the examples to get a feel of the dataset."
]
},
{
"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). To test, examples not included in training data are used."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"labels = MulticlassLabels(Ytrain)\n",
"feats = RealFeatures(Xtrain) \n",
"Xrem=Xall[:,subset[6000:]]\n",
"Yrem=Yall[subset[6000:]]\n",
"\n",
"#test features not used in training\n",
"feats_rem=RealFeatures(Xrem) \n",
"labels_rem=MulticlassLabels(Yrem)\n",
"\n",
"kernel = CombinedKernel()\n",
"feats_train = CombinedFeatures()\n",
"feats_test = CombinedFeatures()\n",
"\n",
"#append gaussian kernel\n",
"subkernel = GaussianKernel(10,80) \n",
"feats_train.append_feature_obj(feats)\n",
"feats_test.append_feature_obj(feats_rem)\n",
"kernel.append_kernel(subkernel)\n",
"\n",
"#append PolyKernel\n",
"feats = RealFeatures(Xtrain)\n",
"subkernel = PolyKernel(10,2) \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",
"#initialize with test features\n",
"kernel.init(feats_train, feats_test) \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 misclassified examples are surely pretty tough to predict. As seen from the accuracy MKL seems to work a shade better in this case. One could try this out with more and different types 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]F. R. Bach, G. R. G. Lanckriet, and M. I. Jordan. Multiple kernel learning, conic duality, and\n",
"the SMO algorithm. In C. E. Brodley, editor, Twenty-first international conference on Machine\n",
"learning. ACM, 2004\n",
"\n",
"[3] Kernel Methods for Object Recognition , Christoph H. Lampert"
]
}
],
"metadata": {}
}
]
}
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