Subspace Methods with Globally/Locally Weighted Correlation Matrix

The discriminant function of a subspace method is provided by using correlation matrices that reflect the averaged feature of a category. As a result, it will not work well on unknown input patterns that are far from the average. To address this problem, we propose two kinds of weighted correlation matrices for subspace methods. The globally weighted correlation matrix (GWCM) attaches importance to training patterns that are far from the average. Then, it can reflect the distribution of patterns around the category boundary more precisely. The computational cost of a subspace method using GWCMs is almost the same as that using ordinary correlation matrices. The locally weighted correlation matrix (LWCM) attaches importance to training patterns that are near to an input pattern to be classified. Then, it can reflect the distribution of training patterns around the input pattern in more detail. The computational cost of a subspace method with LWCM at the recognition stage does not depend on the number of training patterns, while those of the conventional adaptive local and the nonlinear subspace methods do. We show the advantages of the proposed methods by experiments made on the MNIST database of handwritten digits.