A General Framework for Dimensionality-Reducing Data Visualization Mapping

Bunte K, Biehl M, Hammer B (2012)
Neural Computation 24(3): 771-804.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In recent years, a wealth of dimension-reduction techniques for data visualization and preprocessing has been established. Nonparametric methods require additional effort for out-of-sample extensions, because they provide only a mapping of a given finite set of points. In this letter, we propose a general view on nonparametric dimension reduction based on the concept of cost functions and properties of the data. Based on this general principle, we transfer nonparametric dimension reduction to explicit mappings of the data manifold such that direct out-of-sample extensions become possible. Furthermore, this concept offers the possibility of investigating the generalization ability of data visualization to new data points. We demonstrate the approach based on a simple global linear mapping, as well as prototype-based local linear mappings. In addition, we can bias the functional form according to given auxiliary information. This leads to explicit supervised visualization mappings with discriminative properties comparable to state-of-the-art approaches.
Erscheinungsjahr
Zeitschriftentitel
Neural Computation
Band
24
Zeitschriftennummer
3
Seite
771-804
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Bunte K, Biehl M, Hammer B. A General Framework for Dimensionality-Reducing Data Visualization Mapping. Neural Computation. 2012;24(3):771-804.
Bunte, K., Biehl, M., & Hammer, B. (2012). A General Framework for Dimensionality-Reducing Data Visualization Mapping. Neural Computation, 24(3), 771-804. doi:10.1162/NECO_a_00250
Bunte, K., Biehl, M., and Hammer, B. (2012). A General Framework for Dimensionality-Reducing Data Visualization Mapping. Neural Computation 24, 771-804.
Bunte, K., Biehl, M., & Hammer, B., 2012. A General Framework for Dimensionality-Reducing Data Visualization Mapping. Neural Computation, 24(3), p 771-804.
K. Bunte, M. Biehl, and B. Hammer, “A General Framework for Dimensionality-Reducing Data Visualization Mapping”, Neural Computation, vol. 24, 2012, pp. 771-804.
Bunte, K., Biehl, M., Hammer, B.: A General Framework for Dimensionality-Reducing Data Visualization Mapping. Neural Computation. 24, 771-804 (2012).
Bunte, Kerstin, Biehl, Michael, and Hammer, Barbara. “A General Framework for Dimensionality-Reducing Data Visualization Mapping”. Neural Computation 24.3 (2012): 771-804.