Pattern Classification on Local Metric Structure

A metric is an important concept in pattern classification problems. Many metrics have been applied to pattern classification problems, e.g., the Mahalanobis distance or shift-invariant distance. However, a metric is not uniform in whole domain, in other words, structure of patterns are different in each local domain. Several approaches that utilize such local structure have been proposed. In this paper, we systematize them and propose a framework to describe patterns by a d-dimensional vector and local metric matrix at the point. Then, we introduce two distance measurements to this framework. Experimental results demonstrate advantages of the proposed methods.