  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.
