A weak component approach of subspace analysis

In the linear discriminative analysis, especially in the high dimension case, it is insufficient to project the data onto a one-dimensional subspace for the two-category classification problem. Therefor a weak component approach (WCA) was proposed to project patterns to a low dimensional subspace with rich number of classification features. The role of the weak component in pattern classification was discussed. And the abundance of discriminative information contained in weak components was explored. Firstly, a definition of the weak component was given. Secondly, an improved regularization method was proposed. The regularization is a biased estimate of the variance in the corresponding dimension of the training data and the population data. Then a construction method of the feature subspace based on weak component was given, which extracts the eigenvector of the scatter matrixes according to their discriminative information. Finally, the proposed approach was validated in the experiments by comparing it with LDA. A better classification accuracy of the presented method was achieved. As WCA extracts the dims on which the data distributes closer, it is applicable to the high-dimensional data which distributes elliptically.