Dimensionality reduction and information extraction for pattern recognition

降维本研究认为降维方法作为模式识别的预处理。主成分分析（PCA）是一种常用的降维方法，但它没有利用训练样本的类别信息，因而不能满足我们的要求。另一方面，另一种流行的方法LDA（线性判别分析）使用类别信息。然而，它有一个限制，根据类的数量减少的维数。这种限制可能会导致过度还原。为了克服这些问题，我们考虑了降维方法的基础上减少数据的类之间的差异作为一个标准的goodness ofreduction.First，我们已经检查了一种方法，我们测量的基础上Kullback-Leibler信息的分布的差异。该方法使用类信息，并且它对nu没有任何限制。 ...更多信息 降维数。通过对基本任务的实验，我们观察到，对于线性不可分离任务，该方法与PCA和LDA等方法相比，降低了错误分类率.该方法的两个问题是（1）使用多维正态分布拟合，（2）优化时需要迭代计算.对于（2），我们提出了一种方法，其中对整个数据应用仅白化一个类的线性变换，然后执行PCA。该方法不需要迭代计算，但具有与原方法相似的性质。另一方面，对于（1），我们改进了我们的方法，不同类之间的虚拟势。最后一种方法实现了较低的错误分类率。信息表示对于多标记学习任务，我们考虑了两种信息表示方法，神经网络方法和条件分布方法，并研究了它们的行为。少

Dimensionality ReductionThe present study considers dimensionality reduction methods as a preprocessing of pattern recognition. Though PCA(principal component analysis) is a most popular conventional method of dimensionality reduction, it has a drawback for our purpose because it does not use class informations which are attatched to training samples. On the other hand, another popular method LDA(linear discriminant analysis) uses class information. However, it has a restriction on the number of reduced dimension according to the number of classes. This restriction can cause excessive reduction. In order to overcome these problems, we have considered dimensionality reduction methods based on the difference between classes in the reduced data as a criterion for goodness ofreductions.First, we have examined a method in which we measure the difference of distributions based on Kullback-Leibler information. This method uses class informations, and it does not have any restriction on the nu … More mber of reduced dimension. Through experiments with fimdamental tasks, we have observed that this method decreases the rate of wrong classifications compared with PCA and LDA for linear non-separatable tasks, and so on.Two problems of this methods are (1)it uses fitting of multidimensional normal distributions, and (2)it needs iterative calculations in optimization. As for (2), we have proposed a method in which a linear transformation, that whitens only one class, is applied to the whole data and then PCA is performed. It does not need iterative calculations any more, whereas it has similar property to the previous method. On the other hand, as for (1), we improved our method with a virtual potential between different classes. The last methods realizes lower rate of wrong classifications than the previous methods for dimensionality reduction to particularity low dimensions.Information RepresentationFor multi-labeled learning tasks, we have considered two ways of information representation, neural network method and and conditional distribution method, and their behaviors are invesitigated. Less