Simplicial Complex Entropy

TL;DR

This paper introduces a new entropy measure for simplicial complexes that quantifies the expected encoding cost of vertex sequences, facilitating analysis in computational topology.

Contribution

It presents an efficiently computable entropy function for simplicial complexes, enabling analysis of large-scale topological data sequences.

Findings

Entropy can be computed efficiently for large complexes

The entropy measure aids in analyzing sequences in computational topology

Application to complexes with hundreds of simplices demonstrates practicality

Abstract

We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show that the proposed entropy function can be computed efficiently. By computing the entropy of several complices consisting of hundreds of simplices, we show that the proposed entropy function can be used in the analysis of the large sequences of simplicial complices that often appear in computational topology applications.