Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Automating the Construction of Internet Portals with Machine Learning
Information Retrieval
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
The CMU Pose, Illumination, and Expression Database
IEEE Transactions on Pattern Analysis and Machine Intelligence
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Local Fisher discriminant analysis for supervised dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
A Modified Non-negative Matrix Factorization Algorithm for Face Recognition
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 03
Non-negative Matrix Factorization on Manifold
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
IEEE Transactions on Neural Networks
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
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Nonnegative matrix factorization (NMF) is an unsupervised learning method for low-rank approximation of nonnegative data, where the target matrix is approximated by a product of two nonnegative factor matrices. Two important ingredients are missing in the standard NMF methods: (1) discriminant analysis with label information; (2) geometric structure (manifold) in the data. Most of the existing variants of NMF incorporate one of these ingredients into the factorization. In this paper, we present a variation of NMF which is equipped with both these ingredients, such that the data manifold is respected and label information is incorporated into the NMF. To this end, we regularize NMF by intra-class and inter-class k-nearest neighbor (k-NN) graphs, leading to NMF-kNN, where we minimize the approximation error while contracting intra-class neighborhoods and expanding inter-class neighborhoods in the decomposition. We develop simple multiplicative updates for NMF-kNN and present monotonic convergence results. Experiments on several benchmark face and document datasets confirm the useful behavior of our proposed method in the task of feature extraction.