Online Nonnegative Canonical Polyadic Decomposition: Algorithms and Application

Abstract

The Nonnegative Canonical Polyadic Decomposition (NN-CPD) is now widely used in signal processing to decompose multi-way arrays thanks to nonnegative factor matrices. In many applications, a three way array is built from collections of 2D-signals and new signals are regularly recorded. In this case one may want to update the factor matrices after each new measurement without computing the NN-CPD of the whole array. We then speak of Online NN-CPD. In this context the main difficulty is that the number of relevant factors is unknown and can vary with time. In this paper we propose two algorithms to compute the Online NN-CPD based on sparse dictionary learning. We also introduce an application example of Online NN-CPD in environmental sciences and evaluate the performances of the proposed approach in this context on real data.