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We present a novel anytime version of partitional clustering algorithm, such as k-Means and EM, for time series. The algorithm works by leveraging off the multi-resolution property of wavelets. The dilemma of choosing the initial centers is mitigated by initializing the centers at each approximation level, using the final centers returned by the coarser representations. In addition to casting the clustering algorithms as anytime algorithms, this approach has two other very desirable properties. By working at lower dimensionalities we can efficiently avoid local minima. Therefore, the quality of the clustering is usually better than the batch algorithm. In addition, even if the algorithm is run to completion, our approach is much faster than its batch counterpart. We explain, and empirically demonstrate these surprising and desirable properties with comprehensive experiments on several publicly available real data sets …