Two Pseudo‑Common Vectors for Pattern Recognition

Abstract

In this paper, the mathematical model used in fnding the common vectors of classes in pattern recognition problems is reconsidered to obtain possible alternative solutions for the common vectors. Since the number of unknowns is always one larger than the number of equations in the mathematical model, the best solution to the problem seems to be the pseudoinverse solutions. We obtained two forms of common vectors, called “pseudo-common vectors,” using the proposed idea. Computational simplifcations are accomplished as shown in the paper since we know that taking pseudo-inverses is an exhaustive procedure especially in the high-dimensional vector spaces. The two forms of pseudo-common vectors obtained in the paper are used in the classifcation of the data given in TI-Digit, AR-Face, and MNIST databases separately in order to see their efectiveness.