Online low-rank subspace tracking by tensor decomposition under incomplete data: OLSTEC

摘要

This paper considers the problem of online tensor 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 specifically addresses the case in which data of interest are fed into the algorithm over time infinitely, and their subspace are dynamically time-varying. To this end, we build up our proposed algorithm exploiting the recursive least squares (RLS), which is a second-order gradient algorithm.