The Classic Cross-Correlation and the Real-Valued Jaccard and Coincidence Indices

TL;DR

This paper compares traditional similarity measures like inner product and correlation with newer indices such as real-valued Jaccard and coincidence, analyzing their geometric properties and sign considerations.

Contribution

It introduces a detailed comparison and geometric analysis of classic and recent similarity indices, including sign handling and scalar field surface geometry.

Findings

Comparison of classic and recent similarity indices

Analysis of sign considerations in similarity measures

Geometric interpretation of scalar field surfaces

Abstract

In this work we describe and compare the classic inner product and Pearson correlation coefficient as well as the recently introduced real-valued Jaccard and coincidence indices. Special attention is given to diverse schemes for taking into account the signs of the operands, as well as on the study of the geometry of the scalar field surface related to the generalized multiset binary operations underling the considered similarity indices. The possibility to split the classic inner product, cross-correlation, and Pearson correlation coefficient is also described.