Figure 8.8: Simplest linear discrimination
n = 2;
randn('state',3);
N = 10; M = 6;
Y = [1.5+1*randn(1,M); 2*randn(1,M)];
X = [-1.5+1*randn(1,N); 2*randn(1,N)];
T = [-1 1; 1 1];
Y = T*Y; X = T*X;
fprintf('Finding a separating hyperplane...');
cvx_begin
variables a(n) b(1)
X'*a - b >= 1;
Y'*a - b <= -1;
cvx_end
fprintf(1,'Done! \n');
linewidth = 0.5;
t_min = min([X(1,:),Y(1,:)]);
t_max = max([X(1,:),Y(1,:)]);
t = linspace(t_min-1,t_max+1,100);
p = -a(1)*t/a(2) + b/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(t,p, '-r');
axis equal
title('Simple classification using an affine function');
Finding a separating hyperplane...
Calling SeDuMi: 19 variables (3 free), 16 equality constraints
------------------------------------------------------------------------
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 3 free variables
eqs m = 16, order n = 23, dim = 23, blocks = 1
nnz(A) = 112 + 0, nnz(ADA) = 256, nnz(L) = 136
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 1.07E+000 0.000
1 : 5.00E+000 3.75E-001 0.000 0.3524 0.9000 0.9000 -2.43 1 1 3.4E+000
2 : 3.87E+000 8.61E-002 0.000 0.2294 0.9000 0.9000 -0.26 1 1 1.3E+000
3 : 2.22E-001 2.78E-003 0.000 0.0323 0.9900 0.9900 0.62 1 1 5.0E-002
4 : 7.52E-006 1.04E-007 0.000 0.0000 1.0000 1.0000 0.99 1 1
iter seconds digits c*x b*y
4 0.0 7.9 0.0000000000e+000 -3.2461697005e-019
|Ax-b| = 4.1e-014, [Ay-c]_+ = 3.0E-019, |x|= 4.7e+001, |y|= 3.9e-019
Detailed timing (sec)
Pre IPM Post
0.000E+000 0.000E+000 0.000E+000
Max-norms: ||b||=1, ||c|| = 0,
Cholesky |add|=0, |skip| = 0, ||L.L|| = 2.50456.
------------------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0
Done!