Correlation Angles and Inner Products: Application to a Problem from Physics

TL;DR

This paper explores the use of covariance as an inner product to define correlation measures in vector spaces, applying these concepts to climate science to analyze correlations through geometric measures like diameter and area.

Contribution

It introduces a novel geometric framework for correlation analysis using covariance as an inner product, with specific applications to climate science data.

Findings

Covariance as an inner product enables new correlation measures.

Geometric measures like diameter and area relate to correlation in climate data.

Application demonstrates the utility of the approach in real-world climate studies.

Abstract

Covariance is used as an inner product on a formal vector space built on n random variables to define measures of correlation Md across a set of vectors in a d-dimensional space. For d = 1, one has the diameter; for d = 2, one has an area. These concepts are directly applied to correlation studies in climate science.