SAGA: Sparse And Geometry-Aware non-negative matrix factorization through non-linear local embedding

Nicolas Courty (1) , Xing Gong (2) , Jimmy Vandel (3) , Thomas Burger (3)

1 OBELIX - Environment observation with complex imagery
2 NLPR - National Laboratory of Pattern Recognition [Beijing]
3 BIG - Institut de Biosciences et de Biotechnologies de Grenoble (ex-IRTSV)

This paper presents a new non-negative matrix factorization technique which (1) allows the decomposition of the original data on multiple latent factors accounting for the geometrical structure of the manifold embedding the data; (2) provides an optimal representation with a controllable level of sparsity; (3) has an overall linear complexity allowing handling in tractable time large and high dimensional datasets. It operates by coding the data with respect to local neighbors with non-linear weights. This locality is obtained as a consequence of the simultaneous sparsity and convexity constraints. Our method is demonstrated over several experiments, including a feature extraction and classification task, where it achieves better performances than the state-of-the-art factorization methods, with a shorter computational time.

Domaines: Machine Learning [stat.ML]

Nicolas Courty, Xing Gong, Jimmy Vandel, Thomas Burger. SAGA: Sparse And Geometry-Aware non-negative matrix factorization through non-linear local embedding. Machine Learning, 2014, pp.1--23. ⟨hal-01018683⟩