Figure 8.11: Approximate linear discrimination via support vector classifier
n = 2;
randn('state',2);
N = 50; M = 50;
Y = [1.5+0.9*randn(1,0.6*N), 1.5+0.7*randn(1,0.4*N);
2*(randn(1,0.6*N)+1), 2*(randn(1,0.4*N)-1)];
X = [-1.5+0.9*randn(1,0.6*M), -1.5+0.7*randn(1,0.4*M);
2*(randn(1,0.6*M)-1), 2*(randn(1,0.4*M)+1)];
T = [-1 1; 1 1];
Y = T*Y; X = T*X;
g = 0.1;
cvx_begin
variables a(n) b(1) u(N) v(M)
minimize (norm(a) + g*(ones(1,N)*u + ones(1,M)*v))
X'*a - b >= 1 - u;
Y'*a - b <= -(1 - v);
u >= 0;
v >= 0;
cvx_end
linewidth = 0.5;
t_min = min([X(1,:),Y(1,:)]);
t_max = max([X(1,:),Y(1,:)]);
tt = linspace(t_min-1,t_max+1,100);
p = -a(1)*tt/a(2) + b/a(2);
p1 = -a(1)*tt/a(2) + (b+1)/a(2);
p2 = -a(1)*tt/a(2) + (b-1)/a(2);
graph = plot(X(1,:),X(2,:), 'o', Y(1,:), Y(2,:), 'o');
set(graph(1),'LineWidth',linewidth);
set(graph(2),'LineWidth',linewidth);
set(graph(2),'MarkerFaceColor',[0 0.5 0]);
hold on;
plot(tt,p, '-r', tt,p1, '--r', tt,p2, '--r');
axis equal
title('Approximate linear discrimination via support vector classifier');
Calling sedumi: 203 variables, 104 equality constraints
For improved efficiency, sedumi is solving the dual problem.
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SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 104, order n = 203, dim = 204, blocks = 2
nnz(A) = 503 + 0, nnz(ADA) = 714, nnz(L) = 409
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.77E+02 0.000
1 : -5.39E+00 8.55E+01 0.000 0.4840 0.9000 0.9000 2.18 1 1 9.8E+01
2 : -4.32E+00 5.38E+01 0.000 0.6290 0.9000 0.9000 2.94 1 1 3.7E+01
3 : -2.99E+00 1.64E+01 0.000 0.3059 0.9000 0.9000 2.18 1 1 7.4E+00
4 : -2.47E+00 7.28E+00 0.000 0.4428 0.9000 0.9000 0.99 1 1 3.5E+00
5 : -2.21E+00 3.58E+00 0.000 0.4912 0.9000 0.9000 0.78 1 1 1.9E+00
6 : -2.05E+00 1.94E+00 0.000 0.5414 0.9000 0.9000 0.76 1 1 1.1E+00
7 : -1.94E+00 9.49E-01 0.000 0.4899 0.9000 0.9000 0.85 1 1 5.7E-01
8 : -1.88E+00 4.15E-01 0.000 0.4380 0.9000 0.9000 0.91 1 1 2.6E-01
9 : -1.85E+00 1.78E-01 0.000 0.4277 0.9000 0.9000 0.97 1 1 1.1E-01
10 : -1.84E+00 2.38E-02 0.000 0.1339 0.9280 0.9000 0.94 1 1 2.3E-02
11 : -1.83E+00 1.04E-03 0.000 0.0439 0.9900 0.9326 1.00 1 1 1.3E-03
12 : -1.83E+00 1.83E-04 0.000 0.1757 0.9122 0.9000 1.00 1 1 1.4E-04
13 : -1.83E+00 3.98E-05 0.000 0.2170 0.9114 0.9000 1.00 1 1 2.2E-05
14 : -1.83E+00 5.92E-06 0.000 0.1486 0.9000 0.9097 1.00 1 1 4.1E-06
15 : -1.83E+00 1.65E-07 0.061 0.0279 0.9903 0.9900 1.00 1 1 8.1E-08
16 : -1.83E+00 1.25E-08 0.000 0.0755 0.9900 0.9900 1.00 1 1 6.2E-09
iter seconds digits c*x b*y
16 0.1 8.2 -1.8257002098e+00 -1.8257002220e+00
|Ax-b| = 4.3e-09, [Ay-c]_+ = 3.6E-10, |x|= 1.7e+00, |y|= 3.5e+00
Detailed timing (sec)
Pre IPM Post
1.000E-02 7.000E-02 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 5.71996.
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Status: Solved
Optimal value (cvx_optval): +1.8257