A Generalized Framework for Predictive Clustering and Optimization
- URL: http://arxiv.org/abs/2305.04364v1
- Date: Sun, 7 May 2023 19:56:51 GMT
- Title: A Generalized Framework for Predictive Clustering and Optimization
- Authors: Aravinth Chembu, Scott Sanner
- Abstract summary: Clustering is a powerful and extensively used data science tool.
In this article, we define a generalized optimization framework for predictive clustering.
We also present a joint optimization strategy that exploits mixed-integer linear programming (MILP) for global optimization.
- Score: 18.06697544912383
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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