A Generalized Framework for Predictive Clustering and Optimization
This work addresses the need for more flexible supervised clustering methods in data science, though it is incremental as it builds on existing clusterwise regression concepts.
The authors tackled the problem of limited design space in supervised clustering by introducing a generalized optimization framework that supports various cluster definitions and objectives, and they developed both global optimization and scalable greedy algorithms, demonstrating interpretable cluster structures on four real-world datasets.
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.