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Group $K$-Means

We study how to learn multiple dictionaries from a dataset, and approximate any data point by the sum of the codewords each chosen from the corresponding dictionary. Although theoretically low approximation errors can be achieved by the global solution, an effective solution has not been well studied in practice. To solve the problem, we propose a simple yet effective algorithm \textit{Group $K$-Means}. Specifically, we take each dictionary, or any two selected dictionaries, as a group of $K$-means cluster centers, and then deal with the approximation issue by minimizing the approximation errors. Besides, we propose a hierarchical initialization for such a non-convex problem. Experimental results well validate the effectiveness of the approach.