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.

Cite

Text

Courty et al. "SAGA: Sparse and Geometry-Aware Non-Negative Matrix Factorization Through Non-Linear Local Embedding." Machine Learning, 2014. doi:10.1007/S10994-014-5463-Y

Markdown

[Courty et al. "SAGA: Sparse and Geometry-Aware Non-Negative Matrix Factorization Through Non-Linear Local Embedding." Machine Learning, 2014.](https://mlanthology.org/mlj/2014/courty2014mlj-saga/) doi:10.1007/S10994-014-5463-Y

BibTeX

@article{courty2014mlj-saga,
  title     = {{SAGA: Sparse and Geometry-Aware Non-Negative Matrix Factorization Through Non-Linear Local Embedding}},
  author    = {Courty, Nicolas and Gong, Xing and Vandel, Jimmy and Burger, Thomas},
  journal   = {Machine Learning},
  year      = {2014},
  pages     = {205-226},
  doi       = {10.1007/S10994-014-5463-Y},
  volume    = {97},
  url       = {https://mlanthology.org/mlj/2014/courty2014mlj-saga/}
}