4. Multiresolution Clustering of Time Series and Application to Images

Clustering is vital in the process of condensing and outlining information, since it can provide a synopsis of the stored data. However, the high dimensionality of multimedia data today presents an insurmountable challenge for clustering algorithms. Based on the well-known fact that time series and image histograms can both be represented accurately in a lower resolution using orthonormal decompositions, we present an anytime version of the k-means algorithm. The algorithm works by leveraging off the multiresolution property of wavelets. The dilemma of choosing the initial centers for k-means is mitigated by assigning the final centers at each approximation level as the initial centers for the subsequent, finer approximation. In addition to casting k-means as an anytime algorithm, our approach has two other very desirable properties. We observe that even by working at coarser approximations, the achieved quality is better than the batch algorithm, and that even if the algorithm is run to completion, the running time is significantly reduced. We show how this algorithm can be suitably extended to chromatic and textural features extracted from images. Finally, we demonstrate the applicability of this approach on the online image search engine scenario.