Space Complexity Analysis in Hybrid Principal Component Analysis

Abstract

Conventional linear PCA approaches do not adequately handle the issues such as intrinsic spatial structural information of pattern, the complexity of calculating covariance matrix, variations restricted to some parts of a pattern, and small sample size problem, etc. To handle the above challenges, several PCAs in feature partitioning framework have been developed to improve the recognition accuracy. Recently developed approaches such as extended cross-correlation sub-pattern principal component analysis (ESubXPCA) operate on the sub-pattern and whole pattern at a time and captures the local and global variation of patterns by maintaining cross-correlations across sub-pattern and whole pattern sets. Along with recognition accuracy and time, space complexity is also an important parameter to study the relative effectiveness of a PCA approach. In this paper, we have formulated the space complexities of various PCAs in feature partitioning framework and compare them with some similar methods both theoretically and experimentally. The experiment conducted on ORL and YALE face datasets with multiple image resolutions. The experimental results show the technique ESubXPCA exhibits minimum feature dimensionality; SpPCA exhibits minimum space requirements for the covariance matrix and to design the complete recognition system.