# A Generalized Framework for Predictive Clustering and Optimization

arXiv: https://arxiv.org/abs/2305.04364 · HTML: https://mlsanity.com/paper/2305.04364/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 61 references that are in the map.
- First posted on arXiv 7 May 2023.

## Builds on (most cited first, 2 of 2)

- [Solving L1-regularized SVMs and related linear programs: Revisiting the effectiveness of Column and Constraint Generation](https://mlsanity.com/paper/1901.01585/) (2019)
- [Generalized Majorization-Minimization](https://mlsanity.com/paper/1506.07613/) (2015)

## Built on by (most cited first, 1 of 1)

- [Near-optimal Linear Predictive Clustering in Non-separable Spaces via MIP and QPBO Reductions](https://mlsanity.com/paper/2511.10809/) (2025)

## Abstract (arXiv)

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.