Efficiently Approximating Spread Dimension with High Confidence

TL;DR

This paper introduces a pseudo spread dimension as a computationally efficient approximation of spread dimension, along with a formula to estimate the associated standard error, enhancing the practical application of intrinsic dimension estimation.

Contribution

The paper presents the pseudo spread dimension and derives a standard error formula, improving the efficiency and confidence in spread dimension approximation.

Findings

Pseudo spread dimension provides a fast approximation method.

Derived a standard error formula for the approximation.

Enhances practical use of spread dimension in biodiversity analysis.

Abstract

The concepts of spread and spread dimension of a metric space were introduced by Willerton in the context of quantifying biodiversity of ecosystems. In previous work, we developed the theoretical basis for applications of spread dimension as an intrinsic dimension estimator. In this paper we introduce the pseudo spread dimension which is an efficient approximation of spread dimension, and we derive a formula for the standard error associated with this approximation.