Application of Linear Regression Classification to Low-Dimensional Datasets

Abstract

The Traditional Linear Regression Classification (LRC) method fails when the number of data in thetraining set is greater than their dimensions. In this work, we proposed a new implementation of LRC toovercome this problem in the pattern recognition. The new form of LRC works even in the case of havinglow-dimensional excessive number of data. In order to explain the new form of LRC, the relation betweenthe predictor and the correlation matrix of a class is shownfirst. Then for the derivation of LRC, the nullspace of the correlation matrix is generated by using the eigenvectors corresponding to the smallesteigenvalues. These eigenvectors are used to calculate the projection matrix in LRC. Also the equivalenceof LRC and the method called Class-Featuring Information Compression (CLAFIC) is shown theoretically.TI Digit database and Multiple Feature dataset are used to illustrate the use of proposed improvement onLRC and CLAFIC