Matrix decompositions such as the singular value
decomposition (SVD) are simple, well-known tools for data mining that have been used in a wide variety of data mining applications such as
text retrieval, web page ranking, and face recognition. But matrix decompositions are restricted to two-way, tabular data. In many cases, it is more natural to arrange data into an N-way hyperrectangle, which is referred to as a higher-order tensor for N > 2. I will describe tensor decompositions such as CANDECOMP/PARAFAC and Tucker. These decompositions have been in use for several decades in psychometrics and chemometrics and have recently become popular in
signal processing, numerical analysis, neuroscience, computer vision, and data mining. I will discuss several examples of tensor decompositions being used for hyperlink analysis for web search, computer vision, bibliometric analysis, cross-language document clustering, and dynamic network traffic analysis.
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