Representation of a Fisher Criterion Function in a Kernel Feature Space

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In this brief, we consider kernel methods for classification (Shawe-Taylor and Cristianini, 2004) from a separability point of view and provide a representation of the Fisher criterion function in a kernel feature space. We then show that the value of the Fisher function can be simply computed by using averages of diagonal and off-diagonal blocks of a kernel matrix. This result further serves to reveal that the ideal kernel matrix is a global solution to the problem of maximizing the Fisher criterion function. Its relation to an empirical kernel target alignment is then reported. To demonstrate the usefulness of these theories, we provide an application study for classification of prostate cancer based on microarray data sets. The results show that the parameter of a kernel function can be readily optimized.
Publisher
IEEE-Inst Electrical Electronics Engineers Inc
Issue Date
2010-02
Language
English
Article Type
Article
Citation

IEEE TRANSACTIONS ON NEURAL NETWORKS, v.21, pp.333 - 339

ISSN
1045-9227
URI
http://hdl.handle.net/10203/103756
Appears in Collection
BiS-Journal Papers(저널논문)EE-Journal Papers(저널논문)
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