A Generalized Framework for Predictive Clustering and Optimization

TL;DR

This paper introduces a flexible, generalized framework for predictive clustering that supports various cluster definitions and objectives, using MILP and scalable algorithms, demonstrated on real datasets.

Contribution

It proposes a novel unified optimization framework for supervised clustering with multiple cluster types and objectives, along with scalable algorithms for large datasets.

Findings

Framework can uncover interpretable cluster structures

Mixed-integer linear programming achieves global optimality

Scalable greedy algorithms perform well on large datasets

Abstract

Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to find clusters of data that yield low regression error on a supervised target. We believe that clusterwise regression is just a single vertex of a largely unexplored design space of supervised clustering models. In this article, we define a generalized optimization framework for predictive clustering that admits different cluster definitions (arbitrary point assignment, closest center, and bounding box) and both regression and classification objectives. We then present a joint optimization strategy that exploits mixed-integer linear programming (MILP) for global optimization in this generalized framework. To alleviate scalability concerns for large datasets, we also provide highly scalable greedy algorithms inspired by the Majorization-Minimization (MM) framework. Finally, we demonstrate the ability of our models to uncover different interpretable discrete cluster structures in data by experimenting with four real-world datasets.