Figure 8.10: Approximate linear discrimination via linear programming
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;
cvx_begin
variables a(n) b(1) u(N) v(M)
minimize (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 linear programming');
Calling SeDuMi: 203 variables (3 free), 100 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 = 100, order n = 207, dim = 207, blocks = 1
nnz(A) = 200 + 600, nnz(ADA) = 100, nnz(L) = 100
Handling 6 + 0 dense columns.
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 5.18E+001 0.000
1 : 1.53E+001 2.32E+001 0.000 0.4484 0.9000 0.9000 2.92 1 1 1.4E+000
2 : 1.38E+001 6.94E+000 0.000 0.2989 0.9000 0.9000 1.34 1 1 5.7E-001
3 : 1.12E+001 2.10E+000 0.000 0.3032 0.9000 0.9000 0.87 1 1 3.0E-001
4 : 1.03E+001 1.05E+000 0.000 0.4984 0.9000 0.9000 0.79 1 1 2.1E-001
5 : 9.94E+000 6.88E-001 0.000 0.6561 0.9000 0.9000 0.68 1 1 1.8E-001
6 : 9.50E+000 2.38E-001 0.000 0.3459 0.9000 0.9000 0.37 1 1 1.8E-001
7 : 8.22E+000 1.34E-001 0.000 0.5623 0.9000 0.9000 0.13 1 1 1.3E-001
8 : 7.83E+000 8.96E-002 0.000 0.6698 0.9000 0.9000 0.62 1 1 1.2E-001
9 : 7.65E+000 7.10E-002 0.000 0.7920 0.9000 0.9000 0.27 1 1 1.2E-001
10 : 6.79E+000 3.11E-002 0.000 0.4378 0.9000 0.9000 0.79 1 1 6.2E-002
11 : 6.47E+000 1.43E-002 0.000 0.4609 0.9000 0.9000 0.85 1 1 3.3E-002
12 : 6.36E+000 7.87E-003 0.000 0.5494 0.9000 0.9000 0.83 1 1 2.2E-002
13 : 6.21E+000 2.33E-003 0.000 0.2957 0.9000 0.9000 0.93 1 1 6.6E-003
14 : 6.15E+000 1.05E-004 0.000 0.0452 0.9900 0.9900 0.96 1 1
iter seconds digits c*x b*y
14 0.1 14.8 6.1485694323e+000 6.1485694323e+000
|Ax-b| = 9.8e-014, [Ay-c]_+ = 2.1E-015, |x|= 9.0e+001, |y|= 2.4e+000
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): +6.14857