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arXiv · 0805.4220

Best subspace tensor approximations

S. Friedland·V. Mehrmann
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Abstract

In many applications such as data compression, imaging or genomic data analysis, it is important to approximate a given tensor by a tensor that is sparsely representable. For matrices, i.e. 2-tensors, such a representation can be obtained via the singular value decomposition which allows to compute the best rank $k$ approximations. For $t$-tensors with $t>2$ many generalizations of the singular value decomposition have been proposed to obtain low tensor rank decompositions. In this paper we will present a different approach which is based on best subspace approximations, which present an alternative generalization of the singular value decomposition to tensors.

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S. Friedland, V. Mehrmann. 2008-05-27. Best subspace tensor approximations. https://arxiv.org/abs/0805.4220

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