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On the Role of Sampling in Underdetermined Tensor Decomposition with Kronecker and Khatri-Rao Structured Factors

This paper introduces the problem of learning Khatri- Rao structured dictionaries for tensor data, which is inspired from the CANDECOMP/PARAFAC decomposition of tensors. Unlike Kronecker-structured dictionaries which have recently been shown to be locally identifiable under a separable sparsity assumption on coefficient vectors, we show that Khatri-Rao dic tionaries are globally identifiable for arbitrary sparsity patterns. We provide the expected sample complexity to learn Khatri-Rao structured dictionaries and conduct numerical experiments which agree with the theoretical results.