A new penalized nonnegative third-order tensor decomposition using a block coordinate proximal gradient approach: Application to 3D fluorescence spectroscopy

作者：Xuan Vu; Chaux Caroline^*; Thirion Moreau Nadege; Maire Sylvain; Carstea Elfrida Mihaela

来源：Journal of Chemometrics, 2017, 31(4): e2859.

DOI：10.1002/cem.2859

• block alternating minimization
• constrained optimization
• nonnegative tensor factorization (NTF)
• proximal approaches
• 3D fluorescence spectroscopy

In this article, we address the problem of tensor factorization subject to certain constraints. We focus on the canonical polyadic decomposition, also known as parallel factor analysis. The interest of this multilinear decomposition coupled with 3D fluorescence spectroscopy is now well established in the fields of environmental data analysis, biochemistry, and chemistry. When real experimental data (possibly corrupted by noise) are processed, the actual rank of the observed tensor is generally unknown. Moreover, when the amount of data is very large, this inverse problem may become numerically ill-posed and consequently hard to solve. The use of proper constraints reflecting some a priori knowledge about the latent (or hidden) tracked variables and/or additional information through the addition of penalty functions can prove very helpful in estimating more relevant components rather than totally arbitrary ones. The counterpart is that the cost functions that have to be considered can be nonconvex and sometimes even nondifferentiable, making their optimization more difficult and leading to a higher computing time and a slower convergence speed. Block alternating proximal approaches offer a rigorous and flexible framework to properly address that problem since they are applicable to a large class of cost functions while remaining quite easy to implement. Here, we suggest a new block coordinate variable metric forward-backward method, which can be seen as a special case of majorize-minimize approaches to derive a new penalized nonnegative third-order canonical polyadic decomposition algorithm. Its interest, efficiency, robustness, and flexibility are illustrated thanks to computer simulations performed on both simulated and real experimental 3D fluorescence spectroscopy data.
The problem of tensor factorization is addressed (CP or PARAFAC), targeting applications in 3D fluorescence spectroscopy. With complicated scenarios, most algorithms are unable to identify the relevant components, leaving the end user to decide which components have a chemical meaning. For decision automation, algorithms can be helped to recover more reliable components thanks to additional information or constraints. Here, we suggest a new block coordinate variable metric forward-backward method to derive a new penalized nonnegative third-order CPD algorithm.

• 出版日期2017-4