An Ising Framework for Constrained Clustering on Special Purpose Hardware.

The recent emergence of novel hardware platforms, such as quantum computers and Digital/CMOS annealers, capable of solving combinatorial optimization problems has spurred interest in formulating key problems as Ising models, a mathematical abstraction shared by a number of these platforms. In this work, we focus on constrained clustering, a semi-supervised learning task that involves using limited amounts of labelled data, formulated as constraints, to improve clustering accuracy. We present an Ising modeling framework that is flexible enough to support various types of constraints and we instantiate the framework with two common types of constraints: pairwise instance-level and partition-level. We study the proposed framework, both theoretically and empirically, and demonstrate how constrained clustering problems can be solved on a specialized CMOS annealer. Empirical evaluation across eight benchmark sets shows that our framework outperforms the state-of-the-art heuristic algorithms and that, unlike those algorithms, it can solve problems that involve combinations of constraint types. We also show that our framework provides high quality solutions orders of magnitudes more quickly than a recent constraint programming approach, making it suitable for mainstream data mining tasks.