Quasi-triangle inequality for absolute correlation distance

TL;DR

This paper demonstrates that the absolute correlation distance adheres to a K-relaxed triangle inequality with the optimal K value of 2, providing a mathematical property relevant for similarity measures.

Contribution

It establishes that the absolute correlation distance satisfies a K-relaxed triangle inequality with the best possible K=2, a novel theoretical insight.

Findings

Absolute correlation distance satisfies a K-relaxed triangle inequality

The optimal K value for this inequality is 2

Provides a mathematical foundation for using correlation distance in similarity measures

Abstract

We show that absolute correlation distance satisfies a K-relaxed triangle inequality, with the best K = 2.