Two variants of trace ratio problem with additional constraints and applications

Abstract

Conventional dimensionality reduction methods such as Principal Component Analysis (PCA) and Fisher Linear Discriminant Analysis (FLDA) target to reduce the dimensionality of given feature vectors effectively. These methods have been widely used in several classification problems because of the simple implementation, but these methods cannot be used for the purpose of achieving better classification performance. In this thesis, we propose two new dimensionality reduction methods distinct from the conventional dimensionality reduction methods based on learning. We aim to design two methods which can reduce the dimensionality of given feature vectors effectively and also improve the discriminative power of them. We first formulate each of two new problems by adding new constraints, respectively into trace ratio (TR) problem, which is one of the several criterions of FLDA and solve them by our own proposed ways. We call the first method as Discriminative Component Selection (DCS) method and the second method as Discriminative Feature Combination (DFC) method. DCS is applied to texture classification problem on Outex\_TC\_0010 and Outex\_TC\_0012 databases. The results will show that DCS has the best results among several state-of-the-arts methods with comparable dimension. Moreover, DCS has more advantages than conventional dimensionality reduction methods. DFC is applied to generalize Spatial Pyramid Matching (SPM) and tested on 15-Scene database, which is widely used database of scene classification problem. The results will show that DFC-SPM has better classification performance with much less dimension than that of SPM.