Neural computation and self-organizing maps: an introduction
Neural computation and self-organizing maps: an introduction
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
Neural Computation
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
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Regularized Principal Manifolds
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Data visualisation and manifold mapping using the ViSOM
Neural Networks - New developments in self-organizing maps
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
A kernel view of the dimensionality reduction of manifolds
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Adaptive topological tree structure for document organisation and visualisation
Neural Networks - 2004 Special issue: New developments in self-organizing systems
Online data visualization using the neural gas network
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Two topographic maps for data visualisation
Data Mining and Knowledge Discovery
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
Decoding Population Neuronal Responses by Topological Clustering
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
Principal Manifolds for Data Visualization and Dimension Reduction
Principal Manifolds for Data Visualization and Dimension Reduction
Time-series prediction using self-organising mixture autoregressive network
IDEAL'07 Proceedings of the 8th international conference on Intelligent data engineering and automated learning
Face recognition: a convolutional neural-network approach
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
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
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Dimension reduction has long been associated with retinotopic mapping for understanding cortical maps. Multisensory information is processed, fused, fed and mapped to a 2-D cortex in a near-optimal information preserving manner. Data projection and visualization, inspired by this mechanism, are playing an increasingly important role in many computational applications such as cluster analysis, classification, data mining, knowledge management and retrieval, decision support, marketing, image processing and analysis. Such tasks involving either visual and spatial analysis or reduction of features or volume of the data are essential in many fields from biology, neuroscience, decision support, to management science. The topic has recently attracted a great deal of attention. There have been considerable advances in methodology and techniques for extracting nonlinear manifold as to reduce data dimensionality and a number of novel methods have been proposed from statistics, geometry theory and adaptive neural networks. Typical approaches include multidimensional scaling, nonlinear PCA and principal curve/surface. This paper provides an overview on this challenging and emerging topic. It discusses various recent methods such as self-organizing maps, kernel PCA, principal manifold, isomap, local linear embedding, Laplacian eigenmap and spectral clustering, and many of them can be seen as a combined, adaptive learning framework. Their usefulness and potentials will be presented and illustrated in various applications.