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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01018683
Contributor : Nicolas Courty <>
Submitted on : Friday, July 4, 2014 - 4:40:02 PM
Last modification on : Thursday, April 2, 2020 - 1:54:58 AM
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  • HAL Id : hal-01018683, version 1

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

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