Kernel relative principal component analysis for pattern recognition

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Since the accuracy of pattern recognition is not enough, this research is done for making pattern recognition more accurate by applying the kernel method, which can realize complicated discrimination boundary with a non-linear mapping, to the relative principal component analysis, which is proposed by our research group and can extract principal components under the effect of another signal which has to be suppressed.The results of this research are as follows.1) The theorem of the kernel principal component analysis (KRPCA) was established and its closed form that can provide the solution of KRPCA with a kernel function and samples were obtained.2) A simple closed form of KRPCA for a non-singular kernel Gram matrix was provided. Then, KRPCA can be realized by computer more simply.3) By computer simulation with standard recognition problems, the advantages of KRPCA were shown.4) The kernel sample space method and the one with suppression feature that are the KRPCAs in a special case were proposed. Its closed forms were provided. Although they are restricted version of KRPCA, they achieved similar performance to KRPCA. Since their solution are very simple, the theory of additive learning for them was provided.5) The existing kernel method uses a kind of nonlinear function. By extending it, we proposed the theory of asymmetric kernel method that uses two kinds of nonlinear functions. It will be a basis for future progress of kernel method. A classifier by using it was constructed and its advantages were shown.6) For other researches, we provided a new theory of subband filter bank, showed its advantage in image coding, and researches a computer architecture for recognition and signal processing.