Convex Relaxations of Bregman Divergence Clustering
This work addresses clustering problems for data scientists by providing more flexible and efficient methods, though it appears incremental as it builds on existing convex relaxation frameworks.
The authors tackled the limitations of existing convex relaxations for clustering, which were restricted to specific models and sensitive to imbalanced clusters, by proposing a new class of convex relaxations for Bregman divergence clustering that improves clustering quality and scalability, resulting in tighter clusterings that enhance accuracy over state-of-the-art methods.
Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these shortcomings, we propose a new class of convex relaxations that can be flexibly applied to more general forms of Bregman divergence clustering. By basing these new formulations on normalized equivalence relations we retain additional control on relaxation quality, which allows improvement in clustering quality. We furthermore develop optimization methods that improve scalability by exploiting recent implicit matrix norm methods. In practice, we find that the new formulations are able to efficiently produce tighter clusterings that improve the accuracy of state of the art methods.