Multimedia similarity search has been playing a critical role in many novel applications. Typically, multimedia objects are described by high-dimensional feature vectors (or points) which are organized in databases for retrieval. Although many high-dimensional indexing methods have been proposed to facilitate the search process, efficient retrieval over large, sparse and extremely high-dimensional databases remains challenging due to the continuous increases in data size and feature dimensionality. In this paper, we propose the first framework for Data Co-Reduction (DCR) on both data size and feature dimensionality. By utilizing recently developed co-clustering methods, DCR simultaneously reduces both size and dimensionality of the original data into a compact subspace, where lower bounds of the actual distances in the original space can be efficiently established to achieve fast and lossless similarity search in the filter-and-refine approach. Particularly, DCR considers the duality between size and dimensionality, and achieves the optimal co-reduction which generates the least number of candidates for actual distance computations. We conduct an extensive experimental study on large and real-life multimedia datasets. with dimensionality ranging from 432 to 1936. Our results demonstrate that DCR outperforms existing methods significantly for lossless retrieval, especially in the presence of extremely high dimensionality.
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