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Neural Information ProcessingLearning Vector Quantization and Self-organizing Maps

Neuronale Informationsverarbeitung

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Learning Vector Quantization and Self-organizing Maps

Self-organizing maps, often termed Kohonen maps, are a versatile and widely used tool for exploratory data analysis. Here we were interested in mathematically characterizing the embedding properties of the Self-organizing Map. We proposed robust learning schemes using deterministic annealing and we investigated extensions of the Self-organizing Map to relational data representations which included pairwise data as a special case. Emphasis was given to formulations which are based on cost-functions and optimization, and we investigated, how the different variants of the Self-organizing map relate to each other and to the original Kohonen map. We also studied prototype-based classifiers related to Learning Vector Quantization with a particular focus on improved learning schemes. Self-organizing maps were also investigated in the context of understanding self-organization and pattern formation in neural development. For details see "Research" page "Models of Neural Development".

Acknowledgement: Research was funded by the Technische Universität Berlin.

Lupe

Selected Publications:

Seo, S. and Obermayer, K. (2004). Self-Organizing Maps and Clustering Methods for Matrix Data. Neural Networks Special Issue, 17, 1211 – 1229.


Seo, S., Bode, M. and Obermayer, K. (2003). Soft Nearest Prototype Classification. IEEE Transactions on Neural Networks, 14, 390 – 398.


Seo, S. and Obermayer, K. (2003). Soft Learning Vector Quantization. Neural Computation, 15, 1589 – 1604.


Graepel, T. and Obermayer, K. (1999). A Self-Organizing Map for Proximity Data. Neural Computation, 11, 139 – 155.


Hasenjäger, M., Ritter, H. and Obermayer, K. (1999). Active Learning in Self-Organizing Maps. Kohonen Maps. Elsevier, 57–70.,


Graepel, T., Burger, M. and Obermayer, K. (1998). Self-Organizing Maps: Generalizations and New Optimization Techniques. Neurocomputing, 20, 173 – 190.


Graepel, T., Burger, M. and Obermayer, K. (1997). Phase Transitions in Stochastic Self-Organizing Maps. PHYSICAL REVIEW E, 56, 3876 – 3890.


Erwin, E., Obermayer, K. and Schulten, K. (1992). Self-Organizing Maps: Ordering, Convergence Properties and Energy Functions. Biological Cybernetics, 67, 47 – 55.


Erwin, E., Obermayer, K. and Schulten, K. (1992). Self-Organizing Maps: Stationary States, Metastability and Convergence Rate. Biological Cybernetics, 67, 35 – 45.


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