Farness preserving Non-negative matrix factorization

Abstract

Dramatic growth in the volume of data made a compact and informative representation of the data highly demanded in computer vision, information retrieval, and pattern recognition. Non-negative Matrix Factorization (NMF) is used widely to provide parts-based representations by factorizing the data matrix into non-negative matrix factors. Since non-negativity constraint is not sufficient to achieve robust results, variants of NMF have been introduced to exploit the geometry of the data space. While these variants considered the local invariance based on the manifold assumption, we propose Farness preserving Non-negative Matrix Factorization (FNMF) to exploits the geometry of the data space by considering non-local invariance which is applicable to any data structure. FNMF adds a new constraint to enforce the far points (i.e., non-neighbors) in original space to stay far in the new space. Experiments on different kinds of data (e.g., Multimedia, Earth Observation) demonstrate that FNMF outperforms the other variants of NMF.