  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.
