A Solver of Fukunaga Koontz Transformation without Matrix Decomposition

Abstract

Fukunaga Koontz Transformation provides a powerful tool for extracting discriminant subspaces in pattern classification. The discriminant subspaces are generally extracted by a matrix decomposition procedure involving scatter matrices where a nontrivial singularity problem is inevitable when sample number is limited. In this work, instead of matrix decomposition, a novel subspace extraction procedure based on solving a set of least- norm equations is proposed. This subspace extraction procedure does not rely on a large sample number and its computational complexity is only related to the number of samples. Experiments based on benchmark MNIST and PIE face recognition datasets show a promising potential of using the proposed method for certain image based recognition application where the image size is large while the sample number is limited.