Online kernel nonnegative matrix factorization

Nonnegative matrix factorization (NMF) has become a prominent signal processing and data analysis technique. To address streaming data, online methods for NMF have been introduced recently, mainly restricted to the linear model. In this paper, we propose a framework for online nonlinear NMF, where the factorization is conducted in a kernel-induced feature space. By exploring recent advances in the stochastic gradient descent and the mini-batch strategies, the proposed algorithms have a controlled computational complexity. We derive several general update rules, in additive and multiplicative strategies, and detail the case of the Gaussian kernel. The performance of the proposed framework is validated on unmixing synthetic and real hyperspectral images, comparing to state-of-the-art techniques.