Orthogonal Multiset Canonical Correlation Analysis based on Fractional-Order and Its Application in Multiple Feature Extraction and Recognition

Abstract

Multiset canonical correlation analysis (MCCA) can simultaneously reduce the dimensionality of multi-set data. Thus, MCCA is a very important method for multiple feature extraction. However, in small sample size problem, covariance matrix cannot be estimated accurately so that the projections in MCCA are usually not optimal in such case for recognition purpose. In order to address this problem, we propose a novel method called orthogonal MCCA based on fractional-order (FbOMCCA). Compared with MCCA, there are two improvements in FbOMCCA: firstly, orthogonality constraint, as a popular criterion used in feature extraction, is introduced. It makes multiset canonical projective vectors less affected by poor estimation of covariance matrix. Secondly, inspired with the idea of fractional order, we incorporate fractional-order within-set and between-set scatter matrices to further reduce the deviations of sample covariance matrices. Furthermore, a novel algorithm based on eigen decomposition is proposed to gradually obtain multiset canonical projective vectors. Experimental results on UCI multiple feature dataset, and CENPARMI handwritten Arabic numerals database show that FMOCCA has better recognition rates and robustness than existing MCCA-related methods.