A Bayesian analysis of self-organizing maps
Neural Computation
A type of duality between self-organizing maps and minimal wiring
Neural Computation
On the distribution and convergence of feature space in self-organizing maps
Neural Computation
Self-organizing maps
A unifying objective function for topographic mappings
Neural Computation
Sammon's mapping using neural networks: a comparison
Pattern Recognition Letters - special issue on pattern recognition in practice V
GTM: the generative topographic mapping
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Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A polygonal line algorithm for constructing principal curves
Proceedings of the 1998 conference on Advances in neural information processing systems II
A Unified Model for Probabilistic Principal Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularized Principal Manifolds
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Data visualisation and manifold mapping using the ViSOM
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Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Mining massive document collections by the WEBSOM method
Information Sciences: an International Journal - Special issue: Soft computing data mining
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Multi-view face identification and pose estimation using B-spline interpolation
Information Sciences—Informatics and Computer Science: An International Journal
Adaptive topological tree structure for document organisation and visualisation
Neural Networks - 2004 Special issue: New developments in self-organizing systems
Two topographic maps for data visualisation
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A hyperplane based indexing technique for high-dimensional data
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A Triangulation Method for the Sequential Mapping of Points from N-Space to Two-Space
IEEE Transactions on Computers
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Subspace based feature selection for pattern recognition
Information Sciences: an International Journal
Decoding Population Neuronal Responses by Topological Clustering
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
Information Sciences: an International Journal
Principal Manifolds for Data Visualization and Dimension Reduction
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Face recognition: a convolutional neural-network approach
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Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets
IEEE Transactions on Neural Networks
Limitations of nonlinear PCA as performed with generic neural networks
IEEE Transactions on Neural Networks
Self-organizing mixture networks for probability density estimation
IEEE Transactions on Neural Networks
ViSOM - a novel method for multivariate data projection and structure visualization
IEEE Transactions on Neural Networks
Derivation of a class of training algorithms
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
PRSOM: a new visualization method by hybridizing multidimensional scaling and self-organizing map
IEEE Transactions on Neural Networks
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
On the relevance of linear discriminative features
Information Sciences: an International Journal
Nonlinear dimensionality reduction using a temporal coherence principle
Information Sciences: an International Journal
Circle detection using electro-magnetism optimization
Information Sciences: an International Journal
Feature extraction using a fast null space based linear discriminant analysis algorithm
Information Sciences: an International Journal
Image-based facial sketch-to-photo synthesis via online coupled dictionary learning
Information Sciences: an International Journal
Visual query processing for efficient image retrieval using a SOM-based filter-refinement scheme
Information Sciences: an International Journal
On nonlinear dimensionality reduction for face recognition
Image and Vision Computing
A local distribution net for data clustering
PRICAI'12 Proceedings of the 12th Pacific Rim international conference on Trends in Artificial Intelligence
Using the idea of the sparse representation to perform coarse-to-fine face recognition
Information Sciences: an International Journal
Two-factor face authentication using matrix permutation transformation and a user password
Information Sciences: an International Journal
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Dimensionality reduction has long been associated with retinotopic mapping for understanding cortical maps. Multisensory information is processed, fused and mapped to an essentially 2-D cortex in an information preserving manner. Data processing and projection techniques inspired by this biological mechanism are playing an increasingly important role in pattern recognition, computational intelligence, data mining, information retrieval and image recognition. Dimensionality reduction involves reduction of features or volume of data and has become an essential step of information processing in many fields. The topic of manifold learning has recently attracted a great deal of attention, and a number of advanced techniques for extracting nonlinear manifolds and reducing data dimensions have been proposed from statistics, geometry theory and adaptive neural networks. This paper provides an overview of this challenging and emerging topic and discusses various recent methods such as self-organizing map (SOM), kernel PCA, principal manifold, isomap, local linear embedding, and Laplacian eigenmap. Many of them can be considered in a learning manifold framework. The paper further elaborates on the biologically inspired SOM model and its metric preserving variant ViSOM under the framework of adaptive manifold; and their applications in dimensionality reduction with face recognition are investigated. The experiments demonstrate that adaptive ViSOM-based methods produce markedly improved performance over the others due to their metric scaling and preserving properties along the nonlinear manifold.