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: 204 variables (1 free), 100 equality constraints
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SeDuMi 1.1 by AdvOL, 2005 and Jos F. Sturm, 1998, 2001-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Split 1 free variables
eqs m = 100, order n = 205, dim = 206, blocks = 2
nnz(A) = 200 + 400, nnz(ADA) = 100, nnz(L) = 100
Handling 5 + 1 dense columns.
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.09E+000 0.000
1 : 4.57E+000 5.25E-001 0.000 0.4840 0.9000 0.9000 2.18 1 1 1.1E+000
2 : 4.02E+000 3.30E-001 0.000 0.6289 0.9000 0.9000 2.94 1 1 4.2E-001
3 : 2.94E+000 1.01E-001 0.000 0.3061 0.9000 0.9000 2.18 1 1 8.9E-002
4 : 2.45E+000 4.48E-002 0.000 0.4427 0.9000 0.9000 0.99 1 1 4.8E-002
5 : 2.20E+000 2.20E-002 0.000 0.4906 0.9000 0.9000 0.78 1 1 2.9E-002
6 : 2.05E+000 1.19E-002 0.000 0.5417 0.9000 0.9000 0.76 1 1 1.8E-002
7 : 1.94E+000 5.82E-003 0.000 0.4894 0.9000 0.9000 0.85 1 1 1.0E-002
8 : 1.88E+000 2.56E-003 0.000 0.4391 0.9000 0.9000 0.91 1 1 4.7E-003
9 : 1.85E+000 1.09E-003 0.000 0.4273 0.9000 0.9000 0.97 1 1 2.1E-003
10 : 1.85E+000 9.38E-006 0.000 0.0086 0.9000 0.0000 0.94 1 1 7.2E-004
11 : 1.83E+000 1.99E-006 0.000 0.2124 0.9146 0.9000 0.99 1 1 1.5E-004
12 : 1.83E+000 4.10E-008 0.000 0.0206 0.9900 0.9783 0.98 1 1 3.8E-006
13 : 1.83E+000 1.25E-008 0.000 0.3051 0.7618 0.9000 1.00 1 1 1.2E-006
14 : 1.83E+000 5.25E-009 0.000 0.4200 0.9000 0.9000 1.00 1 1 4.8E-007
15 : 1.83E+000 1.07E-009 0.000 0.2033 0.9000 0.9000 1.00 1 1 9.8E-008
16 : 1.83E+000 3.77E-012 0.000 0.0035 0.9990 0.9990 1.00 1 2 3.5E-010
iter seconds digits c*x b*y
16 0.1 Inf 1.8257002345e+000 1.8257002346e+000
|Ax-b| = 5.5e-010, [Ay-c]_+ = 2.3E-010, |x|= 1.3e+001, |y|= 4.2e-001
Detailed timing (sec)
Pre IPM Post
0.000E+000 1.102E-001 0.000E+000
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.8257