Abstract
The PCASOM is a novel self-organizing neural model that performs Principal Components Analysis (PCA). It is also related to the ASSOM network, but its training equations are simpler. The PCASOM has the ability to learn self-organizing maps of the means and correlations of complex input distributions. Here we propose a method to extend this capability to build intrinsic dimensionality maps. These maps model the underlaying structure of the input. Experimental results are reported, which show the self-organizing map formation performed by the proposed network.
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References
Chen, H.-W., et al.: Early-type galaxy progenitors beyond z=1. Astrophysical Journal 560, L131 (2001)
Fukunaga, K., Olsen, D.R.: An Algorithm for Finding Intrinsic Dimensionality of Data. IEEE Trans. Computers 20(2), 176–183 (1971)
Kambhatla, N., Leen, T.K.: Dimension Reduction by Local Principal Component Analysis. Neural Computation 9(7), 1493–1516 (1997)
Kohonen, T.: The Self-Organizing Map. Proc. IEEE 78, 1464–1480 (1990)
Kohonen, T.: The Adaptive-Subspace SOM (ASSOM) and its Use for the Implementation of Invariant Feature detection. In: Fogelman-Soulié, F., Galniari, P. (eds.) Proc. ICANN 1995, International Conference on Artificial Neural Networks, vol. 1, pp. 3–10 (1995)
López-Rubio, E., Muñoz-Pérez, J., Gómez-Ruiz, J.A.: A Principal Components Analysis Self-Organizing Map. Neural Networks 17(2), 261–270 (2004)
López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., Muñoz-Pérez, J., Gómez-Ruiz, J.A.: Principal Components Analysis Competitive Learning. Neural Computation 16(11), 2459–2481 (2004)
NASA Earth Observatory, Data & Images, November 28 (2002), [online] Available at http://earthobservatory.nasa.gov/Observatory/datasets.html
Roweis, S., Ghahramani, Z.: A Unifying Review of Linear Gaussian Models. Neural Computation 11, 305–345 (1999)
Tipping, M.E., Bishop, C.M.: Mixtures of Probabilistic Principal Components Analyzers. Neural Computation 11, 443–482 (1999)
Verveer, P.J., Duin, R.P.W.: An Evaluation of Intrinsic Dimensionality Estimators. IEEE Trans. Pattern Analysis and Machine Intelligence 17(1), 81–86 (1995)
VizieR service March 29 (2004), [online] Available at http://vizier.cfa.harvard.edu/viz-bin/VizieR
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López-Rubio, E., Ortiz-de-Lazcano-Lobato, J.M., del Carmen Vargas-González, M., López-Rubio, J.M. (2005). Intrinsic Dimensionality Maps with the PCASOM. In: Cabestany, J., Prieto, A., Sandoval, F. (eds) Computational Intelligence and Bioinspired Systems. IWANN 2005. Lecture Notes in Computer Science, vol 3512. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494669_92
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DOI: https://doi.org/10.1007/11494669_92
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26208-4
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