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.

翻译：聚类是一种强大且广泛使用的数据科学工具。尽管聚类通常被视为无监督学习技术，但也存在监督变体，例如Spath的簇内加权回归，其试图找到可在监督目标上产生低回归误差的数据簇。我们相信簇内加权回归仅是监督聚类模型中一个尚未被广泛探索的设计空间的单一顶点。本文定义了一种面向预测性聚类的通用优化框架，该框架允许不同的聚类定义（任意点分配、最近中心、边界框）以及回归与分类目标。随后，我们提出一种利用混合整数线性规划（MILP）在该通用框架下进行全局优化的联合策略。为缓解大规模数据集的可扩展性问题，我们还提供了受Majorization-Minimization（MM）框架启发的高度可扩展贪心算法。最后，通过四个真实数据集的实验，我们证明了所提模型能够揭示数据中可解释的离散聚类结构。