## Attachment 'sheet14.m'

Download```
1 function sheet14
2
3 % generate some data
4 sheet14_data
5
6 % plot data
7 plot(X(Y == 1, 1), X(Y == 1, 2), 'r+', ...
8 X(Y == -1, 1), X(Y == -1, 2), 'bo');
9
10 % learn an SVM
11 width = 0.01;
12 C = 1e5;
13
14 K = rbfkern(width, X);
15 svm = trainSVM(K, Y, C);
16 Yh = predictSVM(K, svm);
17
18 % predict the solution
19 N = 50;
20 [MX, MY] = meshgrid(linspace(0, 1, N), linspace(0, 1, N));
21 XP = [reshape(MX, N*N, 1), reshape(MY, N*N, 1)];
22 KP = rbfkern(width, XP, X);
23 YP = predictSVM(KP, svm);
24 F = reshape(YP, N, N);
25 hold on
26 contour(MX, MY, F, [-1, 0, 1]);
27 % comment out next line for octave
28 surf(MX, MY, F, 'FaceAlpha', 0.2); shading interp; caxis([-2 2])
29 hold off
30 grid
31 colormap([linspace(1, 0, 100)', linspace(1, 0, 100)', ones(100, 1), ;
32 0 0 0;
33 ones(100, 1), linspace(0, 1, 100)', linspace(0, 1, 100)'])
34
35 title(sprintf('Error rate: %.2f%%', mean(sign(Yh) ~= Y) * 100));
36
37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
38 %
39 % Your solution below
40
41 % 3a. train a support vector machine using the built-in generic quadratic
42 % optimizer (quadprog for matlab, qp for octave). Return a structure with
43 % the following entries:
44 %
45 % svm.alpha - learned alphas
46 % svm.b - learned b
47 % svm.y - training Ys
48 function svm = trainSVM(K, Y, C)
49 N = length(Y);
50 % ...
51
52 % 3b. Predict the labels given the kernel matrix built from the
53 % test/training data points, and the svm structure returned by trainSVM.
54 function Yh = predictSVM(K, svm)
55 % ...
56
57 % 3c. Compute the rbf kernel. If Y is missing, assume X = Y. Do not use
58 % for loops to compute the pairwise distances!
59 function K = rbfkern(w, X, Y)
60 % ...
```

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