Fast online low-rank tensor subspace tracking by CP decomposition using recursive least squares from incomplete observations

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Abstract: We consider the problem of online subspace tracking of a partially observed high-dimensional data stream corrupted by noise, where we assume that the data lie in a low-dimensional linear subspace. This problem is cast as an online low-rank tensor completion problem. We propose a novel online tensor subspace tracking algorithm based on the CANDECOMP/PARAFAC (CP) decomposition, dubbed OnLine Low-rank Subspace tracking by TEnsor CP Decomposition (OLSTEC). The proposed algorithm especially addresses the case in which the subspace of interest is dynamically time-varying. To this end, we build up our proposed algorithm exploiting the recursive least squares (RLS), which is the second-order gradient algorithm. Numerical evaluations on synthetic datasets and real-world datasets such as communication network traffic, environmental data, and surveillance videos, show that the proposed OLSTEC algorithm outperforms state-of-the-art online algorithms in terms of the convergence rate per iteration.

Has companion code repository: https://github.com/hiroyuki-kasai/OLSTEC

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