A fundamental study on the evaluation of a feature extraction method for pattern recognition

Feature extraction can be considered as a problem of finding a transformation that maps an n-dimensional pattern space down to a d-dimensional feature space without significantly increasing the degree of overlap between different class distributions. In a feature space, a classifier is generally designed. In order for the classifier to be reliable in predicting the future performance of a classifier, the feature space provided by a feature extraction method must have two properties. The first property is a statistical one that the pattern distribution in the feature space is a normal distribution. The second property is a topological one that the above transformation is a continuous function. In this paper, we investigate the evaluation of a feature extraction method in terms of both of the statistical and topological properties using the real data set.