Discriminant projective non-negative matrix factorization
Abstract
Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W(T) X as their coefficients, i.e., X≈WW(T) X. Since PNMF learns the natural parts-based representation Wof X, it has been widely used in many fields such as pattern recognition and computer vision. However, PNMF does not perform well in classification tasks because it completely ignores the label information of the dataset. This paper proposes a Discriminant PNMF method (DPNMF) to overcome this deficiency. In particular, DPNMF exploits Fisher's criterion to PNMF for utilizing the label information. Similar to PNMF, DPNMF learns a single non-negative basis matrix and needs less computational burden than NMF. In contrast to PNMF, DPNMF maximizes the distance between centers of any two classes of examples meanwhile minimizes the distance between any two examples of the same class in the lower-dimensional subspace and thus has more discriminant power. We develop a multiplicative update rule to solve DPNMF and prove its convergence. Experimental results on four popular face image datasets confirm its effectiveness comparing with the representative NMF and PNMF algorithms.
Read the paper
Related studies
- In silico toxicology protocols
- QM7-X, a comprehensive dataset of quantum-mechanical properties spanning the chemical space of small organic molecules
- Quantum Informed Machine-Learning Potentials for Molecular Dynamics Simulations of CO2's Chemisorption and Diffusion in Mg-MOF-74
- In-silico strategies in nano-drug design: Bridging nanomaterials and pharmacological applications
- mRNA codon optimization with quantum computers
- The computational power of the human brain
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.