A new topological entropy-based approach for measuring similarities among piecewise linear functions

TL;DR

This paper introduces a topological entropy-based method using persistent entropy for comparing piecewise linear functions, demonstrating its effectiveness in classifying noisy signals from electrical motors with high accuracy.

Contribution

It presents a novel topological entropy approach and an algorithm that leverages persistent homology for signal comparison and classification.

Findings

Achieved 94.52% AUC in classification tasks

Validated stability of persistent entropy for comparison

Demonstrated effectiveness on noisy electrical motor signals

Abstract

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem for persistent entropy. The theorem is used in the implementation of a new algorithm. The algorithm transforms a discrete piecewise linear function into a filtered simplicial complex that is analyzed with persistent homology and persistent entropy. Persistent entropy is used as discriminant feature for solving the supervised classification problem of real long length noisy signals of DC electrical motors. The quality of classification is stated in terms of the area under receiver operating characteristic curve (AUC=94.52%).