Best subspace tensor approximations
For researchers in data compression, imaging, and genomics, this provides a novel method for tensor approximation, though the paper lacks concrete performance numbers or comparisons.
The paper addresses the problem of approximating tensors with sparse representations, proposing a method based on best subspace approximations as an alternative to tensor SVD generalizations. The approach offers a new way to compute low-rank tensor decompositions.
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.