Greedy Algorithm for a Training Set Reduction in the Kernel Methods

Abstract

We propose a technique for a training set approximation and its usage in kernel methods. The approach aims to represent data in a low dimensional space with possibly minimal representation error which is similar to the Principal Component Analysis (PCA). In contrast to the PCA, the basis vectors of the low dimensional space used for data representation are properly selected vectors from the training set and not as their linear combinations. The basis vectors can be selected by a simple algorithm which has low computational requirements and allows on-line processing of huge data sets. The proposed method was used to approximate training sets of the Support Vector Machines and Kernel Fisher Linear Discriminant which are known method for learning classifiers. The experiments show that the proposed approximation can significantly reduce the complexity of the found classifiers (the number of the support vectors) while retaining their accuracy.

The authors were supported by the European Union projects ICA 1-CT-2000- 70002, IST-2001-32184 ActIpret, by the Czech Ministry of Education under project MSM 212300013, by the Grant Agency of the Czech Republic project 102/03/0440. The authors would like to thank to the anonymous reviewers for their useful comments.