Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 205025, 7 pages
Research Article

Correlation Kernels for Support Vector Machines Classification with Applications in Cancer Data

Advanced Modelling and Applied Computing Laboratory, Department of Mathematics, Run Run Shaw Building, The University of Hong Kong, Pokfulam Road, Hong Kong

Received 26 March 2012; Revised 13 June 2012; Accepted 13 June 2012

Academic Editor: Luca Toldo

Copyright © 2012 Hao Jiang and Wai-Ki Ching. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


High dimensional bioinformatics data sets provide an excellent and challenging research problem in machine learning area. In particular, DNA microarrays generated gene expression data are of high dimension with significant level of noise. Supervised kernel learning with an SVM classifier was successfully applied in biomedical diagnosis such as discriminating different kinds of tumor tissues. Correlation Kernel has been recently applied to classification problems with Support Vector Machines (SVMs). In this paper, we develop a novel and parsimonious positive semidefinite kernel. The proposed kernel is shown experimentally to have better performance when compared to the usual correlation kernel. In addition, we propose a new kernel based on the correlation matrix incorporating techniques dealing with indefinite kernel. The resulting kernel is shown to be positive semidefinite and it exhibits superior performance to the two kernels mentioned above. We then apply the proposed method to some cancer data in discriminating different tumor tissues, providing information for diagnosis of diseases. Numerical experiments indicate that our method outperforms the existing methods such as the decision tree method and KNN method.