SubXPCA and a generalized feature partitioning approach to principal component analysis

In this paper we propose a general feature partitioning framework to PCA computation and raise issues of cross-sub-pattern correlation, feature ordering dependence, selection of sub-pattern size, overlap of sub-patterns and selection of principal components. These issues are critical to the design and performance of feature partitioning approaches to PCA computation. We show several open issues and present a novel algorithm, SubXPCA which proposes a solution to the cross-sub-pattern correlation issue in the feature partitioning framework. SubXPCA is shown to be a general technique since we derive PCA and SubPCA as special cases of SubXPCA. We show SubXPCA has theoretically better time complexity as compared to PCA. Comprehensive experimentation on UCI repository data and face data sets (ORL, CMU, Yale) confirms the superiority of SubXPCA with better classification accuracy. SubXPCA not only has better time performance but is also superior in its summarization of variance as compared to SubPCA. SubXPCA is shown to be robust in its performance with respect to feature ordering and overlapped sub-patterns.