Title: Orthogonalized ALS: A Theoretically Principled Tensor Decomposition Algorithm for Practical Use,
Abstract: The popular Alternating Least Squares (ALS) algorithm for tensor
decomposition is efficient and easy to implement, but often converges to poor
local optima---particularly when the weights of the factors are non-uniform. We
propose a modification of the ALS approach that is as efficient as standard
ALS, but provably recovers the true factors with random initialization under
standard incoherence assumptions on the factors of the tensor. We demonstrate
the significant practical superiority of our approach over traditional ALS for
a variety of tasks on synthetic data---including tensor factorization on exact,
noisy and over-complete tensors, as well as tensor completion---and for
computing word embeddings from a third-order word tri-occurrence tensor.