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• W15671940 abstract "It is more and more common to encounter applications where the collected data is most naturally stored or represented in a multi-dimensional array, known as a tensor. The goal is often to approximate this tensor as a sum of some type of combination of basic elements, where the notation of what is a basic element is specific to the type of factorization employed. If the number of terms in the combination is few, the tensor factorization gives (implicitly) a sparse (approximate) representation of the data. The terms (e.g. vectors, matrices, tensors) in the combination themselves may also be sparse. This chapter highlights recent developments in the area of non-negative tensor factorization which admit such sparse representations. Specifically, we consider the approximate factorization of third and fourth order tensors into non-negative sums of types of outer-products of objects with one dimension less using the so-called t-product. A demonstration on an application in facial recognition shows the potential promise of the overall approach. We discuss a number of algorithmic options for solving the resulting optimization problems, and modification of such algorithms for increasing the sparsity." @default.
• W15671940 created "2016-06-24" @default.
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• W15671940 date "2013-09-13" @default.
• W15671940 modified "2023-09-27" @default.
• W15671940 title "Nonnegative Tensor Decomposition" @default.
• W15671940 cites W1919986261 @default.
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• W15671940 doi "https://doi.org/10.1007/978-3-642-38398-4_5" @default.
• W15671940 hasPublicationYear "2013" @default.
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