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Modern applications such as Internet traffic, telecommunication records, and large-scale social networks generate massive amounts of data with multiple aspects and high dimensionalities. Tensors (i.e., multi-way arrays) provide a natural representation for such data. Consequently, tensor decompositions such as Tucker become important tools for summarization and analysis. One major challenge is how to deal with high-dimensional, sparse data. In other words, how does one compute decompositions of tensors where most of the entries of the tensor are zero. Specialized techniques are needed for computing the Tucker decompositions for sparse tensors because standard algorithms do not account for the sparsity of the data.
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