Interpretable Clustering via Multi-Polytope Machines

TL;DR

This paper introduces a novel interpretable clustering method that constructs polytopes around clusters to provide explanations, using a MINLP formulation and a two-phase optimization approach, outperforming existing methods.

Contribution

It presents a new interpretable clustering framework that constructs polytopes with customizable constraints, formulated as a MINLP, and optimized via a two-phase approach.

Findings

Outperforms state-of-the-art clustering algorithms on synthetic and real datasets.

Provides interpretable cluster explanations through polytope construction.

Supports constraints like axis-parallel hyperplanes and sparse coefficients.

Abstract

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few state-of-the-art algorithms provide any rationale or description behind the clusters found. We propose a novel approach for interpretable clustering that both clusters data points and constructs polytopes around the discovered clusters to explain them. Our framework allows for additional constraints on the polytopes - including ensuring that the hyperplanes constructing the polytope are axis-parallel or sparse with integer coefficients. We formulate the problem of constructing clusters via polytopes as a Mixed-Integer Non-Linear Program (MINLP). To solve our formulation we propose a two phase approach where we first initialize clusters and polytopes using alternating minimization, and then use coordinate descent to boost clustering performance. We benchmark our approach on a suite of synthetic and real world clustering problems, where our algorithm outperforms state of the art interpretable and non-interpretable clustering algorithms.