Online Nonnegative and Sparse Canonical Polyadic Decomposition of Fluorescence Tensors

Abstract

The NonNegative Canonical Polyadic Decomposition (NN-CPD) is used in many fields such as in chemistry, biology and medicine. The data coming from these fields can be dynamic which lead to use real-time or “online” decomposition. Even though there are a variety of online tensor decomposition algorithms, the main assumption of all these algorithms is that the rank of the decomposition is known and/or does not vary over time. However this should not be the case in experimental conditions. In this work, we propose three algorithms to compute the online NN-CPD based on sparse dictionary learning for tracking chemical components in water by using a set of Emission and Excitation Matrices (EEMs) of fluorescence. The methods developed in this work is not limited to this application field and it addresses the major challenges posed by the variation of the CPD rank in real-time. First, the algorithms take into account the unknown factors and the variation of tensor rank. Second, previous extracted information are used to decompose upcoming new tensors. In addition to the development of these algorithms, one of the contributions of this paper is the real-time acquisition of fluorescence data in a semi-controlled environment. These algorithms were applied on these real datasets and compared to state of the art algorithms.