Online nonnegative matrix factorization based on kernel machines

Fei Zhu (1) , Paul Honeine (1)

1 LM2S - Laboratoire Modélisation et Sûreté des Systèmes

Nonnegative matrix factorization (NMF) has been increasingly investigated for data analysis and dimension-reduction. To tackle large-scale data, several online techniques for NMF have been introduced recently. So far, the online NMF has been limited to the linear model. This paper develops an online version of the nonlinear kernel-based NMF, where the decomposition is performed in the feature space. Taking the advantage of the stochastic gradient descent and the mini-batch scheme, the proposed method has a fixed, tractable complexity independent of the increasing samples number. We derive the multiplicative update rules of the general form, and describe in detail the case of the Gaussian kernel. The effectiveness of the proposed method is validated on unmixing hyperspectral images, compared with the state-of-the-art online NMF methods.

Mots clés: data analysis; Gaussian processes; gradient methods; geophysical image processing; hyperspectral imaging; matrix decomposition; Signal processing; Europe; Linear programming; Encoding; Kernel; unmixing hyperspectral imaging; online learning; kernel machines; Nonnegative matrix factorization; Computational complexity; Stochastic processes; online nonnegative matrix factorization; kernel machine; dimension-reduction; nonlinear kernel-based NMF; stochastic gradient descent scheme; minibatch scheme; Gaussian kernel; hyperspectral unmixing

Domaines: Apprentissage [cs.LG]; Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Fei Zhu, Paul Honeine. Online nonnegative matrix factorization based on kernel machines. Proc. 23rd European Conference on Signal Processing (EUSIPCO), 2015, Nice, France. pp.2381 - 2385, ⟨10.1109/EUSIPCO.2015.7362811⟩. ⟨hal-01965987⟩