signal manifold by extended kernel method and its application

为了提高信号处理和模式识别的性能，需要对信号和模式进行适当的度量，并在此基础上发展处理和识别方法.本文根据这一概念，改进了马氏度量理论，提出了一种基于核函数的马氏度量计算方法，并且提供了可以在不估计后验概率的情况下获得与最大后验方法等效的结果的准则和计算方法。我们还提出了一种方法来直接估计两个概率密度函数之间的L2距离，并显示其性质的收敛性和偏差。提出了一种在Stiefel流形上计算样本平均值的算法，以及用少量基函数提取特征的自适应核主成分分析方法。实验结果表明，所开发的方法的优点。

In order to improve the performance of signal processing and pattern recognition, it is necessary to obtain a proper metric for signals and patterns and develop processing and recognition methods based on the metric.According to the concept, we improve the theory of Mahalanobis metric, develop a calculation method of Mahalanobis metric using kernel functions, and provide criteria and calculation methods that can obtain a equivalent result with the maximum posteriori method without estimating a posteriori probability. We also propose a method to directly estimate the L2 distance between two probability density functions and show its properties with respect to convergence and bias. We develop an algorithm to calculate the sample average on Stiefel manifold, and the adaptive kernel principle component analysis that can extract features with a small number of basis functions. The advantages of developed methods are shown by experimental results.