Utilization of Singularity Exponent in Nearest Neighbor Based Classifier

Abstract

Classifiers serve as tools for classifying data into classes. They directly or indirectly take a distribution of data points around a given query point into account. To express the distribution of points from the viewpoint of distances from a given point, a probability distribution mapping function is introduced here. The approximation of this function in a form of a suitable power of the distance is presented. How to state this power - the distribution mapping exponent -- is described. This exponent is used for probability density estimation in high-dimensional spaces and for classification. A close relation of the exponent to a singularity exponent is discussed. It is also shown that this classifier exhibits significantly better behavior (classification accuracy) than other kinds of classifiers for some tasks.