Hyperbolic Continuous Structural Entropy for Hierarchical Clustering

TL;DR

This paper introduces HypCSE, a hyperbolic neural network approach for hierarchical clustering that optimizes a continuous structural entropy on structure-enhanced graphs, improving clustering performance.

Contribution

The paper proposes a novel hyperbolic neural network framework that jointly learns graph structures and minimizes continuous structural entropy for hierarchical clustering.

Findings

HypCSE outperforms existing methods on seven datasets.

The approach effectively captures hierarchical data structures.

Graph structure learning enhances clustering quality.

Abstract

Hierarchical clustering is a fundamental machine-learning technique for grouping data points into dendrograms. However, existing hierarchical clustering methods encounter two primary challenges: 1) Most methods specify dendrograms without a global objective. 2) Graph-based methods often neglect the significance of graph structure, optimizing objectives on complete or static predefined graphs. In this work, we propose Hyperbolic Continuous Structural Entropy neural networks, namely HypCSE, for structure-enhanced continuous hierarchical clustering. Our key idea is to map data points in the hyperbolic space and minimize the relaxed continuous structural entropy (SE) on structure-enhanced graphs. Specifically, we encode graph vertices in hyperbolic space using hyperbolic graph neural networks and minimize approximate SE defined on graph embeddings. To make the SE objective differentiable for optimization, we reformulate it into a function using the lowest common ancestor (LCA) on trees and then relax it into continuous SE (CSE) by the analogy of hyperbolic graph embeddings and partitioning trees. To ensure a graph structure that effectively captures the hierarchy of data points for CSE calculation, we employ a graph structure learning (GSL) strategy that updates the graph structure during training. Extensive experiments on seven datasets demonstrate the superior performance of HypCSE.