Local matrix learning in clustering and applications for manifold visualization

Arnonkijpanich B, Hasenfuss A, Hammer B (2010)
In: Neural Networks. 23. Elsevier: 476-486.

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Abstract
Electronic data sets are increasing rapidly with respect to both, size of the data sets and data resolution, i.e. dimensionality, such that adequate data inspection and data visualization have become central issues of data mining. In this article, we present an extension of classical clustering schemes by local matrix adaptation, which allows a better representation of data by means of clusters with an arbitrary spherical shape. Unlike previous proposals, the method is derived from a global cost function. The focus of this article is to demonstrate the applicability of this matrix clustering scheme to low-dimensional data embedding for data inspection. The proposed method is based on matrix learning for neural gas and manifold charting. This provides an explicit mapping of a given high-dimensional data space to low dimensionality. We demonstrate the usefulness of this method for data inspection and manifold visualization. (C) 2009 Elsevier Ltd. All rights reserved.
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The 18th International Conference on Artificial Neural Networks, ICANN 2008
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Arnonkijpanich B, Hasenfuss A, Hammer B. Local matrix learning in clustering and applications for manifold visualization. In: Neural Networks. Vol 23. Elsevier; 2010: 476-486.
Arnonkijpanich, B., Hasenfuss, A., & Hammer, B. (2010). Local matrix learning in clustering and applications for manifold visualization. Neural Networks, 23(4), 476-486.
Arnonkijpanich, B., Hasenfuss, A., and Hammer, B. (2010). “Local matrix learning in clustering and applications for manifold visualization” in Neural Networks, vol. 23, (Elsevier), 476-486.
Arnonkijpanich, B., Hasenfuss, A., & Hammer, B., 2010. Local matrix learning in clustering and applications for manifold visualization. In Neural Networks. no.23 Elsevier, pp. 476-486.
B. Arnonkijpanich, A. Hasenfuss, and B. Hammer, “Local matrix learning in clustering and applications for manifold visualization”, Neural Networks, vol. 23, Elsevier, 2010, pp.476-486.
Arnonkijpanich, B., Hasenfuss, A., Hammer, B.: Local matrix learning in clustering and applications for manifold visualization. Neural Networks. 23, p. 476-486. Elsevier (2010).
Arnonkijpanich, Banchar, Hasenfuss, Alexander, and Hammer, Barbara. “Local matrix learning in clustering and applications for manifold visualization”. Neural Networks. Elsevier, 2010.Vol. 23. 476-486.
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