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Machine Learning

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Active Learning in Self-Organizing Maps
Citation key Hasenjaeger1999a
Author Hasenjäger, M. and Ritter, H. and Obermayer, K.
Title of Book Kohonen Maps
Pages 57–70
Year 1999
ISBN 978-0-444-50270-4
Publisher Elsevier
Abstract The self-organizing map (SOM) was originally proposed by T. Kohonen in 1982 on biological grounds and has since then become a widespread tool for explanatory data analysis. Although introduced as a heuristic, SOMs have been related to statistical methods in recent years, which led to a theoretical foundation in terms of cost functions as well as to extensions to the analysis of pairwise data, in particular of dissimilarity data. In our contribution, we first relate SOMs to probabilistic autoencoders, re-derive the SOM version for dissimilarity data, and review part of the above-mentioned work. Then we turn our attention to the fact, that dissimilarity-based algorithms scale with O($D^2$), where D denotes the number of data items, and may therefore become impractical for real-world datasets. We find that the majority of the elements of a dissimilarity matrix are redundant and that a sparsse matrix with more than 80\\\\\\\\% missing values suffices to learn a SOM representation of low cost. We then describe a strategy how to select the most informative dissimilarities for a given set of objects. We suggest to select (and measure) only those elements whose knowledge maximizes the expected reduction in the SOM cost function. We find that active data selection is computationally expensive, but may reduce the number of necessary dissimilarities by more than a factor of two compared to a random selection strategy. This makes active data selection a viable alternative when the cost of actually measuring dissimilarities between data objects comes high.
Bibtex Type of Publication Selected:quantization
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