Self-organizing maps
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A Tutorial on Support Vector Machines for Pattern Recognition
Data Mining and Knowledge Discovery
Extended isomap for pattern classification
Eighteenth national conference on Artificial intelligence
Two-Dimensional PCA: A New Approach to Appearance-Based Face Representation and Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Journal of Cognitive Neuroscience
Linear and nonlinear dimensionality reduction for face recognition
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Face recognition: a convolutional neural-network approach
IEEE Transactions on Neural Networks
Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
ViSOM - a novel method for multivariate data projection and structure visualization
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Generalized Linear Discriminant Analysis: A Unified Framework and Efficient Model Selection
IEEE Transactions on Neural Networks
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Principal component analysis (PCA) has long been a dominating linear technique for dimensionality reduction. Many nonlinear methods and neural networks have been proposed to extend PCA for complex nonlinear data. They include kernel PCA, local linear embedding, isomap, self-organising map (SOM), and visualization induced SOM (ViSOM), a variant of SOM for a faithful and metric-preserving mapping. In this paper, we investigate these nonlinear manifold methods for face recognition, and compare their performances with linear PCA. Results from the experiments on real-world face databases show that although nonlinear methods have greater capability than PCA, the differences in classification rate of most nonlinear methods and PCA are insignificant. However, ViSOM has produced marked improvement over PCA and other nonlinear methods. A nonlinearity measure is used to quantify the degree of nonlinearity of a data set in the reduced subspace. It can be used to indicate the effectiveness of nonlinear or linear dimensionality reduction.