Dimensionality reduction for classification, comparison of techniques and dimension choice

Abstract

We investigate the effects of dimensionality reduction using different techniques and different dimensions on six two-class data sets with numerical attributes as pre-processing for two classification algorithms. Besides reducing the dimensionality with the use of principal components and linear discriminants, we also introduce four new techniques. After this dimensionality reduction two algorithms are applied. The first algorithm takes advantage of the reduced dimensionality itself while the second one directly exploits the dimensional ranking. We observe that neither a single superior dimensionality reduction technique nor a straightforward way to select the optimal dimension can be identified. On the other hand we show that a good choice of technique and dimension can have a major impact on the classification power, generating classifiers that can rival industry standards. We conclude that dimensionality reduction should not only be used for visualisation or as pre-processing on very high dimensional data, but also as a general pre-processing technique on numerical data to raise the classification power. The difficult choice of both the dimensionality reduction technique and the reduced dimension however, should be directly based on the effects on the classification power. © 2008 Springer-Verlag Berlin Heidelberg.