Abstract
Classical clustering algorithms as well as intrinsic evaluation criteria impose predefined structures onto a data set. If the structures do not fit the data, the clustering will fail and the evaluation criteria will lead to erroneous conclusions. Recently, the abstract U-matrix has been defined for emergent self-organizing maps (ESOM). In this work the abstract forms of the P- and the U* are defined in analogy to the P- and the U*-matrix on ESOM. The abstract U*-matrix can be used for AU*-clustering of data by taking account of density and distance structures. For AU*-clustering the structures seen on the ESOM serve as a supervising quality measure. In this way it can be determined whether an AU*-clustering represents important structures inherent to the high dimensional data. Importantly, AU*-clustering does not impose a geometric cluster shape, which may not fit the underlying data structure, onto the data set. The approach is demonstrated on benchmark data as well as real world data from spatial science.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ultsch, A.: Clustering with SOM: U*C. Workshop on Self-Organizing Maps, pp. 75–82. Paris (2005)
Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern. 43, 59–69 (1982)
Ultsch, A.: Maps for Visualization of High-Dimensional Data Spaces. WSOM, pp. 225–230, Kyushu, Japan (2003)
Lötsch, J., Ultsch, A.: A machine-learned knowledge discovery method for associating complex phenotypes with complex genotypes. application to pain. J. Biomed. Inf. 46, 921–928 (2013)
Lötsch, J., Ultsch, A.: Exploiting the structures of the U-matrix. In: Villmann, T., Schleif, F.-M., Kaden, M., Lange, M. (eds.) Adv. Intell. Syst. Comput., vol. 295, pp. 248–257. Springer, Heidelberg (2014)
Cottrell, M, de Bodt, E.: A Kohonen Map Representation to Avoid Misleading Interpretations, ESANN’96, pp. 103–110. DeFacto, Bruges, Belgium (1996)
Tademir, K., Mernyi, E.: Exploiting data topology in visualization and clustering of self-organizing Maps. IEEE Trans. Neural Netw. 20(4), 549–562 (2009)
Merényi, E., Tasdemir, K., Zhang, L.: Learning highly structured manifolds: harnessing the power of SOMs. In: Biehl, M., Hammer, B., Verleysen, M., Villmann, T. (eds.) Similarity Based Clustering. Lecture Notes in Computer Science, LNAI 5400, pp. 138–168. Springer, Berlin (2009)
Tasdemir, K., Merényi, E.: A validity index for prototype based clustering of data sets with complex structures. IEEE Trans. Syst. Man Cybern. Part B. 02/2011 41(4), 1039–1053 (2011)
Ultsch, A.: Clustering with SOM: U*C. In: Proceedings Workshop on Self-Organizing Maps WSOM, pp. 75–82. Paris, France (2005)
Kroll, F., Haase, D.A.: Does demographic change affect land use patterns? a case study from Germany. Land Use Policy 27, 726–737 (2010)
Hietel, E., Waldhardt, R., Otte, A.: Analysing land-cover changes in relation to environmental variables in Hesse Germany. Landsc. Ecol. 19(5), 473–489 (2004). Springer, New York
Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Comput. Appl. Math. 20, 53–65 (1987)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Ultsch, A., Behnisch, M., Lötsch, J. (2016). ESOM Visualizations for Quality Assessment in Clustering. In: Merényi, E., Mendenhall, M., O'Driscoll, P. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-319-28518-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-28518-4_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28517-7
Online ISBN: 978-3-319-28518-4
eBook Packages: EngineeringEngineering (R0)