Several measures have been proposed for comparing nonlinear projection methods but so far no comparisons have taken into account one of their most important properties, the trustworthiness of the resulting neighborhood or proximity relationships. One of the main uses of nonlinear mapping methods is to visualize multivariate data, and in such visualizations it is crucial that the visualized proximities can be trusted upon: If two data samples are close to each other on the display they should be close-by in the original space as well. A local measure of trustworthiness is proposed and it is shown for three data sets that neighborhood relationships visualized by the Self-Organizing Map and its variant, the Generative Topographic Mapping, are more trustworthy than visualizations produced by traditional multidimensional scaling-based nonlinear projection methods.
- Data Vector
- Neighborhood Relationship
- Generative Topographic Mapping
- Proximity Relationship
- Visualize Neighborhood
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M. Bishop, M. Svensén, and C. K. I. Williams. GTM: The generative topographic mapping. Neural Computation, 10:215–234, 1998.
G. J. Goodhill and T. J. Sejnowski. A unifying objective function for topographic mappings. Neural Computation, 9:1291–1303, 1997.
H. Hotelling. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology, 24:417–441,498-520, 1933.
S. Kaski and K. Lagus. Comparing self-organizing maps. In C. von der Malsburg, W. von Seelen, J. C. Vorbrüggen, and B. Sendhoff, editors, Proceedings of ICANN’96, International Conference on Neural Networks, pages 809–814, Berlin, 1997. Springer.
K. Kiviluoto. Topology preservation in self-organizing maps. Proceedings of IEEE International Conference on Neural Networks., volume 1, pages 294–299, 1996.
T. Kohonen. Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43:59–69, 1982.
T. Kohonen. Self-Organizing Maps. Springer-Verlag, Berlin, 1995 (third, extended edition 2001).
J. B. Kruskal. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrica, 29(1):1–26, Mar 1964.
J. W. Sammon, Jr. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers, C-18(5):401–409, May 1969.
W. S. Torgerson. Multidimensional scaling I—theory and methods. Psychometrica, 17:401–419, 1952.
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Venna, J., Kaski, S. (2001). Neighborhood Preservation in Nonlinear Projection Methods: An Experimental Study. In: Dorffner, G., Bischof, H., Hornik, K. (eds) Artificial Neural Networks — ICANN 2001. ICANN 2001. Lecture Notes in Computer Science, vol 2130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44668-0_68
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