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 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 tensor-CUR decomposition is used to compress the data, and we show that classification quality is not substantially redu...

• Type: Conference
• Year: 2006
• Where: KDD
• Authors: Michael W. Mahoney, Mauro Maggioni, Petros Drineas
• Keywords: Data Mining, KDD 2006, Matrix Cur Decomposition, Original Data Tensor, Tensor Decomposition