Major bugfix for nonlinear GenSVM

Nonlinear GenSVM depends on the eigendecomposition of the
kernel matrix. Mathematically, the Sigma vector in the code
should contain the square root of the eigenvalues. Taking
the square root was however neglected, which resulted in
poor performance of nonlinear GenSVM. This is now fixed,
which means that the performance of nonlinear GenSVM will
be much better.

3 files changed, 38 insertions, 40 deletions

diff --git a/tests/aux/test_eigendecomp.m b/tests/aux/test_eigendecomp.m
index 921f44b..f3ff4ab 100644
--- a/tests/aux/test_eigendecomp.m
+++ b/tests/aux/test_eigendecomp.m
@@ -23,7 +23,7 @@ ratios = eigenvalues ./ eigenvalues(end, end);
 cutoff = 1e-2;
 
 realP = fliplr(P(:, ratios > cutoff));
-realSigma = flipud(eigenvalues(ratios > cutoff));
+realSigma = sqrt(flipud(eigenvalues(ratios > cutoff)));
 
 r = sum(ratios > cutoff);
 
diff --git a/tests/aux/test_kernel_pre.m b/tests/aux/test_kernel_pre.m
index a1c8337..69f6f1e 100644
--- a/tests/aux/test_kernel_pre.m
+++ b/tests/aux/test_kernel_pre.m
@@ -1,32 +1,32 @@
 function test_kernel_pre()
-  
+
   kerneltype = 'rbf';
   rand('state', 123456);
   n = 10;
   m = 5;
   cutoff = 5e-3;
-  
+
   X = rand(n, m);
   Z = [ones(n, 1), X];
-  
+
   set_matrix(Z, "data->Z", "data->m+1");
-  
+
   K = zeros(n, n);
   if strcmp(kerneltype, 'poly')
-    # Polynomial kernel
-    # (gamma * <x_1, x_2> + c)^d
+    % Polynomial kernel
+    % (gamma * <x_1, x_2> + c)^d
     gamma = 1.5;
     c = 3.0;
     d = 1.78;
-    
+
     for ii=1:n
       for jj=1:n
         K(ii, jj) = (gamma * (X(ii, :) * X(jj, :)') + c)^d;
       end
     end
   elseif strcmp(kerneltype, 'rbf')
-    # RBF kernel
-    # exp(-gamma * norm(x1 - x2)^2)
+    % RBF kernel
+    % exp(-gamma * norm(x1 - x2)^2)
     gamma = 0.348
     for ii=1:n
       for jj=1:n
@@ -34,8 +34,8 @@ function test_kernel_pre()
       end
     end
   elseif strcmp(kerneltype, 'sigmoid')
-    # Sigmoid kernel
-    # tanh(gamma * <x_1, x_2> + c)
+    % Sigmoid kernel
+    % tanh(gamma * <x_1, x_2> + c)
     gamma = 1.23;
     c = 1.6;
     for ii=1:n
@@ -44,29 +44,27 @@ function test_kernel_pre()
       end
     end
   end
-  
-  K(1, 2)
 
-  [P, Sigma] = eig(K);
+  [P, values] = eig(K);
 
-  eigenvalues = diag(Sigma);
+  eigenvalues = diag(values);
   ratios = eigenvalues ./ eigenvalues(end, end);
- 
+
   realP = fliplr(P(:, ratios > cutoff));
-  realSigma = flipud(eigenvalues(ratios > cutoff));
-  
+  realSigma = sqrt(flipud(eigenvalues(ratios > cutoff)));
+
   assert_matrix(realSigma, "data->Sigma", "1");
-  
+
   r = sum(ratios > cutoff);
   fprintf("mu_assert(data->r == %i);\n", r);
-  
+
   M = realP * diag(realSigma);
-  
+
   newZ = [ones(n, 1) M];
   assert_matrix_abs(newZ, "data->Z", "data->r+1");
-  
+
   assert_matrix(Z, "data->RAW", "data->m+1");
-  
+
 end
 
 function set_matrix(A, name, cols)
@@ -98,4 +96,4 @@ function assert_matrix_abs(A, name, cols)
     end
   end
   fprintf("\n");
-end
\ No newline at end of file
+end
diff --git a/tests/aux/test_train_kernel.m b/tests/aux/test_train_kernel.m
index 7bf14b8..b561bd4 100644
--- a/tests/aux/test_train_kernel.m
+++ b/tests/aux/test_train_kernel.m
@@ -1,21 +1,21 @@
 function [V] = test_train_kernel()
-  
+
   clear;
   more off;
   rand('state', 654321);
-  
+
   n = 10;
   m = 5;
   classes = 4;
   cutoff = 5e-3;
-  
+
   X = rand(n, m);
   Z = [ones(n, 1), X];
   set_matrix(Z, "data->Z", "data->m+1");
-  
+
   y = [2 1 3 2 3 2 4 1 3 4];
   set_matrix(y, "data->y", "1");
-  
+
   p = 1.2143;
   kappa = 0.90298;
   lambda = 0.00219038;
@@ -36,24 +36,24 @@ function [V] = test_train_kernel()
 
   eigenvalues = diag(Sigma);
   ratios = eigenvalues ./ eigenvalues(end, end);
- 
+
   realP = fliplr(P(:, ratios > cutoff));
-  realSigma = flipud(eigenvalues(ratios > cutoff));
-  
+  realSigma = sqrt(flipud(eigenvalues(ratios > cutoff)));
+
   assert_matrix(realSigma, "data->Sigma", "1");
-  
+
   r = sum(ratios > cutoff);
   fprintf("mu_assert(data->r == %i);\n", r);
-  
+
   M = realP * diag(realSigma);
   size(M)
-  
+
   assert_matrix(Z, "data->RAW", "data->m+1");
-  
-  seedV = zeros(size(M, 2) + 1, classes - 1);  
+
+  seedV = zeros(size(M, 2) + 1, classes - 1);
   [W, t] = msvmmaj(M, y, rho, p, kappa, lambda, epsilon, 'show', 0, seedV);
   V = [t'; W];
-  
+
   fprintf('\n');
   assert_matrix_abs(V, "model->V", "model->K-1");
 
@@ -89,4 +89,4 @@ function assert_matrix_abs(A, name, cols)
     end
   end
   fprintf("\n");
-end
\ No newline at end of file
+end