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Background: Microarray techniques provide promising tools for cancer diagnosis using gene expression profiles. However, molecular diagnosis based on high-throughput platforms presents great challenges due to the overwhelming number of variables versus the small sample size and the complex nature of multi-type tumors. Support vector machines (SVMs) have shown superior performance in cancer classification due to their ability to handle high dimensional low sample size data. The multi-class SVM algorithm of Crammer and Singer provides a natural framework for multi-class learning. Despite its effective performance, the procedure utilizes all variables without selection. In this paper, we propose to improve the procedure by imposing shrinkage penalties in learning to enforce solution sparsity.
Results: The original multi-class SVM of Crammer and Singer is effective for multi-class classification but does not conduct variable selection. We improved the method by introducing soft-thresholding type penalties to incorporate variable selection into multi-class classification for high dimensional data. The new methods were applied to simulated data and two cancer gene expression data sets. The results demonstrate that the new methods can select a small number of genes for building accurate multi-class classification rules. Furthermore, the important genes selected by the methods overlap significantly, suggesting general agreement among different variable selection schemes.
Conclusions: High accuracy and sparsity make the new methods attractive for cancer diagnostics with gene expression data and defining targets of therapeutic intervention.
Availability: The source MATLAB code are available from http://math.arizona.edu/~hzhang/software.html.
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This is the first time for us to submit a manuscript to Cancer Informatics. We thank the peer reviewers for their insightful comments, which have improved our manuscript markedly. We were pleased to find that the staff were extremely helpful and kept us informed of the progress of the submission step-by-step. Our experience with Cancer Informatics has been tremendous. Thank you very much!