  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.
