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, 100 equality constraints
------------------------------------------------------------
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
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+00 0.000
1 : 4.57E+00 5.25E-01 0.000 0.4840 0.9000 0.9000 2.18 1 1 1.1E+00
2 : 4.02E+00 3.30E-01 0.000 0.6289 0.9000 0.9000 2.94 1 1 4.2E-01
3 : 2.94E+00 1.01E-01 0.000 0.3061 0.9000 0.9000 2.18 1 1 8.9E-02
4 : 2.45E+00 4.48E-02 0.000 0.4427 0.9000 0.9000 0.99 1 1 4.8E-02
5 : 2.20E+00 2.20E-02 0.000 0.4906 0.9000 0.9000 0.78 1 1 2.9E-02
6 : 2.05E+00 1.19E-02 0.000 0.5417 0.9000 0.9000 0.76 1 1 1.8E-02
7 : 1.94E+00 5.82E-03 0.000 0.4894 0.9000 0.9000 0.85 1 1 1.0E-02
8 : 1.88E+00 2.56E-03 0.000 0.4391 0.9000 0.9000 0.91 1 1 4.7E-03
9 : 1.85E+00 1.09E-03 0.000 0.4273 0.9000 0.9000 0.97 1 1 2.1E-03
10 : 1.85E+00 9.38E-06 0.000 0.0086 0.9000 0.0000 0.94 1 1 7.2E-04
11 : 1.83E+00 1.99E-06 0.000 0.2124 0.9146 0.9000 0.99 1 1 1.5E-04
12 : 1.83E+00 4.10E-08 0.000 0.0206 0.9900 0.9783 0.98 1 1 3.8E-06
13 : 1.83E+00 1.25E-08 0.000 0.3052 0.7618 0.9000 1.00 1 1 1.2E-06
14 : 1.83E+00 5.25E-09 0.000 0.4199 0.9000 0.9000 1.00 1 1 4.8E-07
15 : 1.83E+00 1.07E-09 0.000 0.2033 0.9000 0.9000 1.00 1 1 9.8E-08
16 : 1.83E+00 9.47E-12 0.000 0.0089 0.9990 0.9990 1.00 3 4 8.1E-10
iter seconds digits c*x b*y
16 0.1 Inf 1.8257002529e+00 1.8257002532e+00
|Ax-b| = 1.5e-09, [Ay-c]_+ = 5.1E-10, |x|= 1.3e+01, |y|= 4.2e-01
Detailed timing (sec)
Pre IPM Post
1.000E-02 1.000E-01 0.000E+00
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=2, |skip| = 0, ||L.L|| = 1.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +1.8257