Zero-error dissimilarity based classifiers

TL;DR

This paper explores conditions under which classifiers based solely on non-Euclidean dissimilarity measures can achieve zero error, focusing on the properties of the distance measure and decision boundary continuity.

Contribution

It derives conditions for zero-error dissimilarity classifiers and discusses when the decision boundary is a continuous function of training distances.

Findings

Conditions for zero-error classification using dissimilarity measures

Continuity of decision boundary under certain conditions

Practical applicability of these conditions

Abstract

We consider general non-Euclidean distance measures between real world objects that need to be classified. It is assumed that objects are represented by distances to other objects only. Conditions for zero-error dissimilarity based classifiers are derived. Additional conditions are given under which the zero-error decision boundary is a continues function of the distances to a finite set of training samples. These conditions affect the objects as well as the distance measure used. It is argued that they can be met in practice.