On the stationary state of Kohonen's self-organizing sensory mapping
Biological Cybernetics
Neural computation and self-organizing maps: an introduction
Neural computation and self-organizing maps: an introduction
Co-occurrence map: quantizing multidimensional texture histograms
Pattern Recognition Letters
Reduced Multidimensional Co-Occurrence Histograms in Texture Classification
IEEE Transactions on Pattern Analysis and Machine Intelligence
GTM: the generative topographic mapping
Neural Computation
Unsupervised visual learning of three-dimensional objects using a modular network architecture
Neural Networks - Special issue on organisation of computation in brain-like systems
Supervised Neural Gas with General Similarity Measure
Neural Processing Letters
Magnification Control in Self-Organizing Maps and Neural Gas
Neural Computation
TreeSOM: cluster analysis in the self-organizing map
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Neural Networks
SOM of SOMs: self-organizing map which maps a group of self-organizing maps
ICANN'05 Proceedings of the 15th international conference on Artificial Neural Networks: biological Inspirations - Volume Part I
SOM of SOMs: an extension of SOM from ‘map' to ‘homotopy'
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Handwritten digit recognition by adaptive-subspace self-organizing map (ASSOM)
IEEE Transactions on Neural Networks
`Neural-gas' network for vector quantization and its application to time-series prediction
IEEE Transactions on Neural Networks
Line Image Classification by NG×SOM: Application to Handwritten Character Recognition
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Applying self-organizing mapping neural network for discovery market behavior of equity fund
WSEAS Transactions on Information Science and Applications
ICONIP'10 Proceedings of the 17th international conference on Neural information processing: theory and algorithms - Volume Part I
Requirements for the learning of multiple dynamics
WSOM'11 Proceedings of the 8th international conference on Advances in self-organizing maps
Text clustering based on granular computing and wikipedia
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Shape space estimation by SOM2
ICONIP'11 Proceedings of the 18th international conference on Neural Information Processing - Volume Part II
Cartogram visualization for nonlinear manifold learning models
Data Mining and Knowledge Discovery
Patient's motion recognition based on SOM-decision tree
WASA'13 Proceedings of the 8th international conference on Wireless Algorithms, Systems, and Applications
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This paper proposes an extension of the self-organizing map (SOM), in which the mapping objects themselves are self-organizing maps. Thus a ''SOM of SOMs'' is presented, which we refer to as a SOM^2. A SOM^2 has a hierarchical structure consisting of a single parent SOM and a set of child SOMs. Each child SOM is trained to represent the distribution of a data class in a manifold, while the parent SOM generates a self-organizing map of the group of manifolds modeled by the child SOMs. Thus a SOM^2 is an architecture that organizes a product manifold represented as (child SOM) x (parent SOM). Such a product manifold is called a fiber bundle in terms of the topology. This extension of a SOM is easily generalized to any combination of SOM families, including cases of neural gas (NG) in which, for example, '' NG^2 (=NGxNG) as an NG of NGs'' and ''NGxSOM as a SOM of NGs'' are possible. Furthermore, a SOM^2 can be extended to a SOM^n, such as SOM^3=SOMxSOMxSOM defined as a ''SOM of SOM^2''. In this paper, the algorithms for the SOM^2 and its variations are introduced, and some simulation results are reported.