Global Modular Principal Component Analysis

Abstract

Modular Principal Component Analysis (ModPCA) divides a pattern into sub-patterns and extracts local Principal Components (PCs) from the sub-patterns. It is aimed to discriminate patterns better, as compared to PCA, by exploiting local variations that are confined to sub-patterns or sub-images. In contrast to ModPCA, PCA based classification does well by extracting trends global to the patterns and exhibits superior dimensionality reduction as compared to ModPCA. It is observed that, ModPCA which performs partitioning, does not catch variations spread across sub-patterns. As a result, when compared to PCA, it shows lower dimensionality reduction and consequently does not yield better classification when such global variations are widespread in the data. Now, it is crucial to exploit both local and global variations for better classification and dimensionality reduction. To overcome these issues of global PCA and local ModPCA methods, we bring-in a novel hybrid method which extracts PCs with global and local properties. Empirical results on standard UCI and face data confirm the higher dimensionality reduction of the proposed method over ModPCA, and improved overall classification against PCA and ModPCA methods. The proposed method is also proved to be robust in terms of classification over ModPCA with a variety of partitions.