Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
A Method for Enforcing Integrability in Shape from Shading Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Fast training of support vector machines using sequential minimal optimization
Advances in kernel methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose
IEEE Transactions on Pattern Analysis and Machine Intelligence
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
On the use of cross-validation to assess performance in multivariate prediction
Statistics and Computing
Coding Facial Expressions with Gabor Wavelets
FG '98 Proceedings of the 3rd. International Conference on Face & Gesture Recognition
Comprehensive Database for Facial Expression Analysis
FG '00 Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition 2000
A generalized kernel approach to dissimilarity-based classification
The Journal of Machine Learning Research
Kernel independent component analysis
The Journal of Machine Learning Research
Kernel k-means: spectral clustering and normalized cuts
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Feature Space Interpretation of SVMs with Indefinite Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
A face authentication system using the trace transform
Pattern Analysis & Applications
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Design Issues for a Colour Photometric Stereo System
Journal of Mathematical Imaging and Vision
Projected Gradient Methods for Nonnegative Matrix Factorization
Neural Computation
Journal of Cognitive Neuroscience
Kernel Discriminant Analysis for Positive Definite and Indefinite Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-negative matrix factorization on Kernels
PRICAI'06 Proceedings of the 9th Pacific Rim international conference on Artificial intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
Face recognition by independent component analysis
IEEE Transactions on Neural Networks
Independent component analysis of Gabor features for face recognition
IEEE Transactions on Neural Networks
The pre-image problem in kernel methods
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
On the Convergence of Multiplicative Update Algorithms for Nonnegative Matrix Factorization
IEEE Transactions on Neural Networks
Nonnegative Matrix Factorization in Polynomial Feature Space
IEEE Transactions on Neural Networks
Computer Vision and Image Understanding
Nonlinear nonnegative matrix factorization based on Mercer kernel construction
Pattern Recognition
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In this, paper general solutions for nonlinear non-negative component analysis for data representation and recognition are proposed. Motivated by a combination of the non-negative matrix factorization (NMF) algorithm and kernel theory, which has lead to a recently proposed NMF algorithm in a polynomial feature space, we propose a general framework where one can build a nonlinear non-negative component analysis method using kernels, the so-called projected gradient kernel non-negative matrix factorization (PGKNMF). In the proposed approach, arbitrary positive definite kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem. Moreover, we propose fixed point algorithms for the special case of Gaussian radial basis function (RBF) kernels. We demonstrate the power of the proposed methods in face and facial expression recognition applications.