Universal and Automatic Elbow Detection for Learning the Effective Number of Components in Model Selection Problems

TL;DR

This paper introduces UAED, a universal, automatic method for detecting the optimal number of components in various model selection tasks without needing likelihood functions, applicable across multiple domains.

Contribution

The paper presents a novel, likelihood-free, automatic elbow detection method that is versatile and easy to apply in diverse model selection scenarios.

Findings

Outperforms benchmark techniques in synthetic and real data experiments

Applicable to regression, classification, clustering, and dimension reduction

Does not require likelihood function knowledge

Abstract

We design a Universal Automatic Elbow Detector (UAED) for deciding the effective number of components in model selection problems. The relationship with the information criteria widely employed in the literature is also discussed. The proposed UAED does not require the knowledge of a likelihood function and can be easily applied in diverse applications, such as regression and classification, feature and/or order selection, clustering, and dimension reduction. Several experiments involving synthetic and real data show the advantages of the proposed scheme with benchmark techniques in the literature.