Stability of Information in the Heat Flow Clustering

TL;DR

This paper introduces a novel stability-based clustering method inspired by thermodynamics, which identifies meaningful data structures by analyzing the stability of information entropy over a heat flow analogy.

Contribution

It develops a quantitative stability approach for clustering that uses a thermodynamic analogy to detect persistent data structures through entropy analysis.

Findings

Stable entropy over a range of parameters indicates real data structures.

The method effectively distinguishes meaningful clusters from noise.

Thermodynamic analogy provides a new perspective on clustering stability.

Abstract

Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a quantitative ``stability'' method of determining clusters, where stable or persistent clustering signals are used to indicate real structures have been identified in the underlying dataset. This method is based on modulating clustering methods by controlling a parameter -- through a thermodynamic analogy, the modulation parameter is considered ``time'' and the evolving clustering methodologies can be considered a ``heat flow.'' When the information entropy of the heat flow is stable over a wide range of times -- either globally or in the local sense which we define -- we interpret this stability as an indication that essential features of the data have been found, and create clusters on this basis.