Robust Bregman Clustering
This provides a robust clustering solution for data corrupted by noise, but it is incremental as it extends existing Bregman divergence methods with trimming.
The paper tackles robust clustering of data with clutter noise using a trimmed k-means method based on Bregman divergences, proving convergence to an optimal codebook and achieving a sub-Gaussian convergence rate of 1/√n under mild assumptions.
Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise. The main interest of Bregman divergences is that the standard Lloyd algorithm adapts to these distortion measures, and they are well-suited for clustering data sampled according to mixture models from exponential families. We prove that there exists an optimal codebook, and that an empirically optimal codebook converges a.s. to an optimal codebook in the distortion sense. Moreover, we obtain the sub-Gaussian rate of convergence for k-means 1 $\sqrt$ n under mild tail assumptions. Also, we derive a Lloyd-type algorithm with a trimming parameter that can be selected from data according to some heuristic, and present some experimental results.