Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
EMPATH: face, emotion, and gender recognition using holons
NIPS-3 Proceedings of the 1990 conference on Advances in neural information processing systems 3
A new approach to dimensionality reduction: theory and algorithms
SIAM Journal on Applied Mathematics
Modelling the dynamics of nonlinear partial differential equations using neural networks
Journal of Computational and Applied Mathematics
The Bilipschitz criterion for dimension reduction mapping design
Intelligent Data Analysis
Squigraphs for fine and compact modeling of 3-D shapes
IEEE Transactions on Image Processing
Joint manifolds for data fusion
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Skew-Radial Basis Function Expansions for Empirical Modeling
SIAM Journal on Scientific Computing
Intrinsic dimension estimation via nearest constrained subspace classifier
Pattern Recognition
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This article introduces a new architecture and associated algorithms ideal for implementing the dimensionality reduction of an m-dimensional manifold initially residing in an n-dimensional Euclidean space where n » m. Motivated by Whitney's embedding theorem, the network is capable of training the identity mapping employing the idea of the graph of a function. In theory, a reduction to a dimension d that retains the differential structure of the original data may be achieved for some d ≤ 2m + 1. To implement this network, we propose the idea of a good-projection, which enhances the generalization capabilities of the network, and an adaptive secant basis algorithm to achieve it. The effect of noise on this procedure is also considered. The approach is illustrated with several examples.