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

TL;DR

This paper introduces OLSTEC, an online tensor subspace tracking algorithm using CP decomposition and recursive least squares, effectively handling high-dimensional, partially observed, time-varying data streams.

Contribution

The paper presents a novel online tensor subspace tracking method based on CP decomposition and RLS, capable of tracking dynamic subspaces from incomplete data.

Findings

OLSTEC outperforms existing algorithms in convergence speed.

Effective on synthetic and real-world datasets.

Handles time-varying subspaces with high accuracy.

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.