  Decomposing tensors into orthogonal factors is a well-known task in
statistics, machine learning, and signal processing. We study orthogonal outer
product decompositions where the factors in the summands in the decomposition
are required to be orthogonal across summands, by relating this orthogonal
decomposition to the singular value decompositions of the flattenings. We show
that it is a non-trivial assumption for a tensor to have such an orthogonal
decomposition, and we show that it is unique (up to natural symmetries) in case
it exists, in which case we also demonstrate how it can be efficiently and
reliably obtained by a sequence of singular value decompositions. We
demonstrate how the factoring algorithm can be applied for parameter
identification in latent variable and mixture models.
