[mlpack] 318/324: Center the reconstructed approximation and the kernel matrix.

[Barak A. Pearlmutter]

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bap pushed a commit to branch svn-trunk
in repository mlpack.

commit ed50e1c9bb27db2878baa2250e886b3dc55f988a
Author: marcus <marcus at 9d5b8971-822b-0410-80eb-d18c1038ef23>
Date:   Fri Aug 15 16:52:11 2014 +0000

    Center the reconstructed approximation and the kernel matrix.
    
    git-svn-id: http://svn.cc.gatech.edu/fastlab/mlpack/trunk@17031 9d5b8971-822b-0410-80eb-d18c1038ef23
---
 .../kernel_pca/kernel_rules/nystroem_method.hpp    | 26 ++++++++++++++--------
 1 file changed, 17 insertions(+), 9 deletions(-)

diff --git a/src/mlpack/methods/kernel_pca/kernel_rules/nystroem_method.hpp b/src/mlpack/methods/kernel_pca/kernel_rules/nystroem_method.hpp
index 34bcf62..044db4e 100644
--- a/src/mlpack/methods/kernel_pca/kernel_rules/nystroem_method.hpp
+++ b/src/mlpack/methods/kernel_pca/kernel_rules/nystroem_method.hpp
@@ -45,21 +45,29 @@ class NystroemKernelRule
       nm.Apply(G);
       transformedData = G.t() * G;
 
+      // Center the reconstructed approximation.
+      math::Center(transformedData, transformedData);
+
       // For PCA the data has to be centered, even if the data is centered. But
       // it is not guaranteed that the data, when mapped to the kernel space, is
-      // also centered. Since we actually never work in the feature space we 
+      // also centered. Since we actually never work in the feature space we
       // cannot center the data. So, we perform a "psuedo-centering" using the
       // kernel matrix.
-      arma::rowvec rowMean = arma::sum(transformedData, 0) / 
-          transformedData.n_cols;
-      transformedData.each_col() -= arma::sum(transformedData, 1) /
-          transformedData.n_cols;
-      transformedData.each_row() -= rowMean;
-      transformedData += arma::sum(rowMean) / transformedData.n_cols;
+      arma::colvec colMean = arma::sum(G, 1) / G.n_rows;
+      G.each_row() -= arma::sum(G, 0) / G.n_rows;
+      G.each_col() -= colMean;
+      G += arma::sum(colMean) / G.n_rows;
 
       // Eigendecompose the centered kernel matrix.
-      arma::svd(eigvec, eigval, v, transformedData);
-      eigval %= eigval / (data.n_cols - 1);
+      arma::eig_sym(eigval, eigvec, transformedData);
+
+      // Swap the eigenvalues since they are ordered backwards (we need largest
+      // to smallest).
+      for (size_t i = 0; i < floor(eigval.n_elem / 2.0); ++i)
+        eigval.swap_rows(i, (eigval.n_elem - 1) - i);
+
+      // Flip the coefficients to produce the same effect.
+      eigvec = arma::fliplr(eigvec);
 
       transformedData = eigvec.t() * G.t();
     }

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