A Novel Implementation Algorithm for Calculation of Common Vectors

Common vector approach (CVA), discriminative common vector approach (DCVA) and linear regression classification (LRC) are subspace methods used in pattern recognition. Up to now, there were two well-known algorithms to calculate the common vectors: ( i ) by using the Gram-Schmidt orthogonalization process, ( ii ) by using the within-class covariance matrices. The purpose of this paper is to introduce a new implementation algorithm for the derivation of the common vectors using the linear regression idea. The derivation of the discriminative common vectors through LRC is also included in this paper. Two numerical examples are given to clarify the proposed derivations. An experimental work is given in AR face database to compare the recognition performances of CVA, DCVA, and LRC. Additionally, the three implementation algorithms of common vector are compared in terms of processing time efficiency.