Self-organization and associative memory: 3rd edition
Self-organization and associative memory: 3rd edition
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
A unifying objective function for topographic mappings
Neural Computation
Weight-value convergence of the SOM algorithm for discrete input
Neural Computation
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Another look at principal curves and surfaces
Journal of Multivariate Analysis
Statistical tools to assess the reliability of self-organizing maps
Neural Networks - New developments in self-organizing maps
Data visualisation and manifold mapping using the ViSOM
Neural Networks - New developments in self-organizing maps
Online data visualization using the neural gas network
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
A Nonlinear Mapping for Data Structure Analysis
IEEE Transactions on Computers
Topology preservation in self-organizing feature maps: exact definition and measurement
IEEE Transactions on Neural Networks
Limitations of nonlinear PCA as performed with generic neural networks
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
PRSOM: a new visualization method by hybridizing multidimensional scaling and self-organizing map
IEEE Transactions on Neural Networks
Quantifying the neighborhood preservation of self-organizing feature maps
IEEE Transactions on Neural Networks
Artificial neural networks for feature extraction and multivariate data projection
IEEE Transactions on Neural Networks
Decoding Population Neuronal Responses by Topological Clustering
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part II
Nonlinear Principal Manifolds --- Adaptive Hybrid Learning Approaches
HAIS '08 Proceedings of the 3rd international workshop on Hybrid Artificial Intelligence Systems
ViSOM for Dimensionality Reduction in Face Recognition
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
PolSOM: A new method for multidimensional data visualization
Pattern Recognition
Nonlinear dimensionality reduction for face recognition
IDEAL'09 Proceedings of the 10th international conference on Intelligent data engineering and automated learning
Adaptive nonlinear manifolds and their applications to pattern recognition
Information Sciences: an International Journal
Integrated Computer-Aided Engineering
Incremental manifold learning by spectral embedding methods
Pattern Recognition Letters
On nonlinear dimensionality reduction for face recognition
Image and Vision Computing
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The self-organising map (SOM) and its variant, visualisation induced SOM (ViSOM), have been known to yield similar results to multidimensional scaling (MDS). However, the exact connection has not been established. In this paper, a review on the SOM and its cost function and topological measures is provided first. We then examine the exact scaling effect of the SOM and ViSOM from their objective functions. The SOM is shown to produce a qualitative, nonmetric scaling, while the local distance-preserving ViSOM produces a quantitative or metric scaling. Their relationship with the principal manifold is also discussed. The SOM-based methods not only produce topological or metric scaling but also provide a principal manifold. Furthermore a growing ViSOM is proposed to aid the adaptive embedding of highly nonlinear manifolds. Examples and comparisons with other embedding methods such as Isomap and local linear embedding are also presented.