document: Tensor-CUR decompositions for tensor-based data Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices , we develop a tensor-based extension of the matrix CUR decomposition . The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different than the others . In this case , the tensor-CUR decomposition approximately expresses the original data tensor in terms of a basis consisting of underlying subtensors that are actual data elements and thus that have natural interpretation in terms ofthe processes generating the data . In order to demonstrate the general applicability of this tensor decomposition , we apply it to problems in two diverse domains of data analysis : hyperspectral medical image analysis and consumer recommendation system analysis . In the hyperspectral data application , the tensor-CUR decomposition is used to compress the data , and we show that classification quality is not substantially reduced even after substantial data compression . In the recommendation system application , the tensor-CUR decomposition is used to reconstruct missing entries in a user-product-product preference tensor , and we show that high quality recommendations can be made on the basis of a small number of basis users and a small number of product-product comparisons from a new user .
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