Kernel relative principal component analysis for pattern recognition

由于模式识别的精度不足，为了提高模式识别的精度，本研究将本课题组提出的在另一个需要抑制的信号的作用下提取主成分的相对主成分分析方法应用于核方法，核方法可以实现非线性映射的复杂识别边界。本研究的结果如下：1)建立了核主成分分析（KRPCA）定理，给出了核主成分分析的封闭形式，并给出了核函数解和样本。2)给出了非奇异核格拉姆矩阵的KRPCA的简单封闭形式。这样，KRPCA可以更简单地在计算机上实现。3)通过标准识别问题的计算机仿真，验证了KRPCA的优势。4)提出了核样本空间法和带抑制特征的krpca作为特殊情况下的krpca。提供了闭式表格。虽然它们是KRPCA的限制版本，但它们取得了与KRPCA相似的性能。由于这类问题的解非常简单，因此提出了一种加性学习的理论。5)现有的核方法使用了一种非线性函数。在此基础上，提出了使用两类非线性函数的非对称核方法理论。这将为核方法的进一步发展奠定基础。利用该方法构造了一个分类器，并说明了其优点。6)在其他方面，我们提出了一种新的子带滤波器组理论，展示了其在图像编码中的优势，并研究了一种用于识别和信号处理的计算机体系结构。

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.