Author:

Keywords:

SISTA, BIOTENSORS - 339804;info:eu-repo/grantAgreement/EC/FP7/339804, Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Nonnegative matrix factorization (NMF), nonnegative polynomials, polynomial approximation, CONSTRAINED LEAST-SQUARES, ALGORITHMS, SEPARATION, SPARSE, TENSOR, DECOMPOSITION, C16/15/059#53326574, 0801 Artificial Intelligence and Image Processing, 0906 Electrical and Electronic Engineering, 1005 Communications Technologies, Networking & Telecommunications, 4006 Communications engineering, 4009 Electronics, sensors and digital hardware, 4603 Computer vision and multimedia computation

Abstract:

© 2017 IEEE. Nonnegative matrix factorizationisakey toolinmany data analysis applications such as feature extraction, compression, and noise filtering. Many existing algorithms impose additional constraintstotake into account prior knowledgeandtoimprove the physical interpretation. This letter proposes a novel algorithm for nonnegative matrix factorization, in which the factors are modeled by nonnegative polynomials. Using a parametric representation of finite-interval nonnegative polynomials, we obtain an optimization problem without external nonnegativity constraints, which can be solved using conventional quasi-Newton or nonlinear least-squares methods. The polynomial model guarantees smooth solutions and may realize a noise reduction. A dedicated orthogonal compression enables a significant reduction of the matrix dimensions, without sacrificing accuracy. The overall approach scales well to large matrices. The approach is illustrated with applications in hyperspectral imaging and chemical shift brain imaging.