Math @ Duke

Publications [#243796] of Mauro Maggioni
Papers Published
 Mahoney, MW; Maggioni, M; Drineas, P, TensorCUR decompositions for tensorbased data,
in Proc 12th Annual SIGKDD,
Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, vol. 2006
(2006),
pp. 327336
(last updated on 2017/12/11)
Abstract: Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensorbased extension of the matrix CUR decomposition. The tensorCUR 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 tensorCUR 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 of the 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 tensorCUR 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 tensorCUR decomposition is used to reconstruct missing entries in a userproductproduct 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 productproduct comparisons from a new user. Copyright 2006 ACM.


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