Strong Coresets for Hard and Soft Bregman Clustering with Applications to Exponential Family Mixtures
This provides a unified solution for efficient clustering on large datasets, applicable across multiple distortion measures and mixture models, though it is incremental in extending coreset theory to a broader class.
The paper tackles the problem of scaling clustering models to massive datasets by proposing a single algorithm to construct strong coresets for a large class of hard and soft clustering problems based on Bregman divergences, which includes popular distortion measures and relates to exponential family mixtures, and demonstrates its practicality in empirical evaluation.
Coresets are efficient representations of data sets such that models trained on the coreset are provably competitive with models trained on the original data set. As such, they have been successfully used to scale up clustering models such as K-Means and Gaussian mixture models to massive data sets. However, until now, the algorithms and the corresponding theory were usually specific to each clustering problem. We propose a single, practical algorithm to construct strong coresets for a large class of hard and soft clustering problems based on Bregman divergences. This class includes hard clustering with popular distortion measures such as the Squared Euclidean distance, the Mahalanobis distance, KL-divergence and Itakura-Saito distance. The corresponding soft clustering problems are directly related to popular mixture models due to a dual relationship between Bregman divergences and Exponential family distributions. Our theoretical results further imply a randomized polynomial-time approximation scheme for hard clustering. We demonstrate the practicality of the proposed algorithm in an empirical evaluation.