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The K-means algorithm is arguably the most popular data clustering method,commonly applied to processed datasets in some "feature spaces", as is inspectral clustering. Highly sensitive to initializations, however, K-meansencounters a scalability bottleneck with respect to the number of clusters K asthis number grows in big data applications. In this work, we promote a closelyrelated model called K-indicators model and construct an efficient,semi-convex-relaxation algorithm that requires no randomized initializations.We present extensive empirical results to show advantages of the new algorithmwhen K is large. In particular, using the new algorithm to start the K-meansalgorithm, without any replication, can significantly outperform the standardK-means with a large number of currently state-of-the-art random replications.

Big-Data Clustering: K-Means or K-Indicators?