Constrained Hierarchical Clustering via Graph Coarsening and Optimal Cuts

TL;DR

This paper introduces a novel hierarchical clustering method that incorporates structural constraints using graph coarsening and optimal cuts, effectively handling complex constraints while maintaining computational efficiency.

Contribution

It proposes a two-step approach combining regularized least-squares and graph coarsening to enforce constraints in hierarchical clustering, improving over existing methods.

Findings

Performs well compared to state-of-the-art algorithms.

Computationally efficient and scalable.

Effectively incorporates horizontal and vertical constraints.

Abstract

Motivated by extracting and summarizing relevant information in short sentence settings, such as satisfaction questionnaires, hotel reviews, and X/Twitter, we study the problem of clustering words in a hierarchical fashion. In particular, we focus on the problem of clustering with horizontal and vertical structural constraints. Horizontal constraints are typically cannot-link and must-link among words, while vertical constraints are precedence constraints among cluster levels. We overcome state-of-the-art bottlenecks by formulating the problem in two steps: first, as a soft-constrained regularized least-squares which guides the result of a sequential graph coarsening algorithm towards the horizontal feasible set. Then, flat clusters are extracted from the resulting hierarchical tree by computing optimal cut heights based on the available constraints. We show that the resulting approach compares very well with respect to existing algorithms and is computationally light.