Wasserstein k-means++ for Cloud Regime Histogram Clustering

Much work has sought to discern the different types of cloud regimes, typically via Euclidean k-means clustering of histograms. However, these methods ignore the underlying similarity structure of cloud types. Wasserstein k-means clustering is a promising candidate for utilizing this structure during clustering, but existing algorithms do not scale well and lack the quality guarantees of the Euclidean case. We resolve this by generalizing k-means++ guarantees to the Wasserstein setting and providing a scalable minibatch algorithm for Wasserstein k-means. Our methods empirically perform well and lead to new, different cloud regime prototypes.