  In this paper, we propose a provably correct algorithm for convolutive
nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is
a convolutive variant of nonnegative matrix factorization (NMF), which
functions as an NMF with additional sequential structure. This model is useful
in a number of applications, such as audio source separation and neural
sequence identification. While a number of heuristic algorithms have been
proposed to solve CNMF, to the best of our knowledge no provably correct
algorithms have been developed. We present an algorithm that takes advantage of
the NMF model underlying CNMF and exploits existing algorithms for separable
NMF to provably find a solution under certain conditions. Our approach
guarantees the solution in low noise settings, and runs in polynomial time. We
illustrate its effectiveness on synthetic datasets, and on a singing bird audio
sequence.
