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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.

### Selected Publications:

Citation key | Seo2004 |
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Author | Seo, S. and Obermayer, K. |

Pages | 1211 – 1229 |

Year | 2004 |

DOI | doi:10.1016/j.neunet.2004.06.012 |

Journal | Neural Networks Special Issue |

Volume | 17 |

Number | 8-9 |

Publisher | Elsevier |

Abstract | In this contribution we present extensions of the Self Organizing Map and clustering methods for the categorization and visualization of data which are described by matrices rather than feature vectors. Rows and columns of these matrices correspond to objects which may or may not belong to the same set, and the entries in the matrix describe the relationships between them. The clustering task is formulated as an optimization problem: Model complexity is minimized under the constraint, that the error one makes when reconstructing objects from class information is fixed, usually to a small value. The data is then visualized with help of modified Self Organizing Maps methods, i.e. by constructing a neighborhood preserving non-linear projection into a low-dimensional ``map-space''. Grouping of data objects is done using an improved optimization technique, which combines deterministic annealing with ``growing'' techniques. Performance of the new methods is evaluated by applying them to two kinds of matrix data: (i) pairwise data, where row and column objects are from the same set and where matrix elements denote dissimilarity values and $(ii)$ co-occurrence data, where row and column objects are from different sets and where the matrix elements describe how often object pairs occur. |

Bibtex Type of Publication | Selected:quantization |