Similarity metrics, metrics, and conditionally negative definite functions

TL;DR

This paper explores similarity metrics that are not necessarily positive definite and introduces a general theorem to generate a broad family of positive definite similarity metrics.

Contribution

It presents a new theorem that constructs a large family of positive definite similarity metrics from non-positive definite ones.

Findings

Identifies conditions under which similarity metrics are positive definite.

Provides a method to transform non-positive definite metrics into positive definite ones.

Expands the toolkit for designing similarity measures in machine learning.

Abstract

Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.