An efficient multiple kernel learning in reproducing kernel Hilbert spaces (RKHS)

Author:

Xu Lixiang12,Luo Bin1,Tang Yuanyan3,Ma Xiaohua2

Affiliation:

1. School of Computer Science and Technology, Anhui University, Hefei 230601, Anhui, P. R. China

2. Department of Mathmatics and Physics, Hefei University, Hefei 230601, Anhui, P. R. China

3. Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Macau, China

Abstract

The reproducing kernel Hilbert space construction is a bijection or transform theory which associates a positive definite kernel with a Hilbert space of functions. Recently, reproducing kernel Hilbert space (RKHS) has come wildly alive in the pattern recognition and machine learning community. In this paper, we propose a novel method named multiple kernel learning with reproducing property (MKLRP) to achieve some classification tasks. The MKLRP consists of two major steps. First, we find the basic solution of a generalized differential operator by delta function, and prove this basic solution is a new specific reproducing kernel called H2-reproducing kernel (HRK) in RKHS. Second, in RKHS, we prove that the HRK satisfies the condition of Mercer kernel. Furthermore, a novel specific multiple kernel learning (MKL) called MKLRP, which is based on reproducing kernel is proposed. We perform an extensive experimental evaluation on synthetic and real-world data, which shows the effectiveness of the proposed approach.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

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