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2014 | OriginalPaper | Chapter

5. Data-Dimension Reductions: A Comparison

Author : Peter Sarlin

Published in: Mapping Financial Stability

Publisher: Springer Berlin Heidelberg

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Abstract

Data and dimension reduction techniques, and particularly their combination for Data-Dimension Reductions (DDR), have in many fields and tasks held promise for representing data in an easily understandable format. However, comparing methods and finding the most suitable one is a challenging task. In the previous chapter, we discussed the aim of dimension reduction in terms of three tasks. This chapter compares DDR combinations to financial performance analysis. To this end, after a general review of the literature on comparisons of data and dimension reduction methods, we discuss the aims and needs of DDR combinations in general and for the task at hand in particular.

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previous chapter Data and Dimension Reduction
next chapter Extending the SOM
Footnotes
1
While Relative MDS (Naud and Duch 2000) allows to add new data to the basis of an old MDS, it does still not update all distances within the mapping.
 
2
When training SOMs, one has to set a number of free parameters. A set of quality measures is used to track the topographic and quantization accuracy as well as clustering of the map. Given the purpose herein, details about the parametrization of the models in the experiments are not presented in depth.
 
Literature
Bação, F., & Sousa Lobo, V. (2005). Self-organizing maps as substitutes for k-means clustering. Proceedings of the International Conference on Computational Science (ICCS 02) (pp. 476–483). Amsterdam: The Netherlands.
Balakrishnan, P., Martha, C., Varghese, S., & Phillip, A. (1994). A study of the classification capabilities of neural networks using unsupervised learning: a comparison with k-means clustering. Psychometrika, 59, 509–525.CrossRef
Bertin, J. (1983). Semiology of graphics. WI: The University of Wisconsin Press.
Bezdek, J. C., & Pal, N. R. (1995). An index of topological preservation for feature extraction. Pattern Recognition, 28(3), 381–391.CrossRef
Bishop, C., Svensson, M., & Williams, C. (1998). Developments of the generative topographic mapping. Neurocomputing, 21(1–3), 203–224.CrossRef
Carreira-Perpiñan, M. (2000). Reconstruction of sequential data with probabilistic models and continuity constraints. In S. Solla, T. Leen, & K. Müller (Eds.), Advances in neural information processing systems (Vol. 12, pp. 414–420)., MIT Press MA: Cambridge.
Chen, L., & Buja, A. (2009). Local multidimensional scaling for nonlinear dimension reduction, graph drawing, and proximity analysis. Journal of the American Statistical Association, 104, 209–219.CrossRef
CIELab. (1986). Colorimetry. CIE Publication, No. , 15, 2.
Cottrell, M., & Letrémy, P. (2005). Missing values: processing with the kohonen algorithm. Proceedings of Applied Stochastic Models and Data Analysis (ASMDA 05) (pp. 489–496). France: Brest.
de Bodt, E., Cottrell, M., & Verleysen, M., (1999). Using the Kohonen algorithm for quick initialization of simple competitive learning algorithms. In Proceedings of the European Symposium on Artificial Neural Networks (ESANN 99). Bruges, Belgium.
de Vel, O., Lee, S., & Coomans, D. (1996). Comparative performance analysis of non-linear dimensionality reduction methods. In D. Fischer & L. H-J. (Eds.), Learning from data: Artificial intelligence and statistics (pp. 320–345). Heidelberg, Germany: Springer.
Deakin, E. (1976). Distributions of financial accounting ratios: some empirical evidence. The Accounting Review, 51, 90–96.
Denny Squire, D., 2005. Visualization of cluster changes by comparing self-organizing maps. In: Proceedings of the Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD 05). Hanoi, Vietnam, pp. 410–419.
Duch, W., & Naud, A. (1996). Multidimensional scaling and kohonen’s self-organizing maps. Proceedings of the Conference on Neural Networks and their Applications (CNNA 16) (pp. 138–143). Poland: Szczyrk.
Flexer, A. (1997). Limitations of self-organizing maps for vector quantization and multidimensional scaling. In M. Mozer (Ed.), Advances in Neural Information Processing Systems (Vol. 9, pp. 445–451). Cambridge, MA: MIT Press.
Flexer, A. (2001). On the use of self-organizing maps for clustering and visualization. Intelligent Data Analysis, 5(5), 373–384.
Harrower, M., & Brewer, C. (2003). Colorbrewer.org: an online tool for selecting color schemes for maps. The Cartographic Journal, 40(1), 27–37.CrossRef
Himberg, J. (2004). From insights to innovations: data mining, visualization, and user interfaces. Ph.D. thesis, Helsinki University of Technology, Espoo, Finland.
Kaski, S. (1997). Data exploration using self-organizing maps. Ph.D. thesis, Helsinki University of Technology, Espoo, Finland.
Kaski, S., & Kohonen, T. (1996). Exploratory data analysis by the self-organizing map: structures of welfare and poverty in the world. Proceedings of the International Conference on Neural Networks in the Capital Markets (pp. 498–507). London: World Scientific.
Kaski, S. (1999). Fast winner search for som based monitoring and retrieval of high dimensional data. Proceedings of the IEEE International Conference on Artificial Neural Networks (ICANN 99) (pp. 940–945). London, UK: IEEE Press.CrossRef
Kaski, S., Venna, J., & Kohonen, T. (2001). Coloring that reveals cluster structures in multivariate data. Australian Journal of Intelligent Information Processing Systems, 60, 2–88.
Kiviluoto, K., & Oja, E. (1997). S-map: a network with a simple self-organization algorithm for generative topographic mappings. In M. I. Jordan, M. J. Kearns, & S. A. Solla (Eds.), Advances in Neural Information Processing Systems (Vol. 10, pp. 549–555)., MIT Press MA: Cambridge.
Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59–69.CrossRef
Latif, K., & Mayer, R. (2007). Sky-metaphor visualisation for self-organising maps. In Proceedings of the International Conference on Knowledge Management (I-KNOW 07). Graz, Austria.
Lee, J., & Verleysen, M. (2007). Nonlinear dimensionality reduction. Heidelberg, Germany: Springer, Information Science and Statistics Series.
Lee, J., & Verleysen, M. (2009). Quality assessment of dimensionality reduction: rank-based criteria. Neurocomputing, 72(7–9), 1431–1443.CrossRef
Linde, Y., Buzo, A., & Gray, R. (1980). An algorithm for vector quantizer design. IEEE Transactions on Communications, 28(1), 702–710.CrossRef
Lueks, W., Mokbel, B., Biehl, M., & Hammer, B. (2011). How to evaluate dimensionality reduction? In B. Hammer & T. Villmann (Eds.), Proceedings of the Workshop on New Challenges in Neural Computation. Machine Learning Reports: University of Bielefeld, Department of Technology, Frankfurt, Germany.
van der Maaten, L., & Hinton, G. (2008). Visualizing high-dimensional data using t-sne. Journal of Machine Learning Research, 9, 2579–2605.
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (pp. 281–297). Berkeley, CA: University of California Press.
Merkl, D., & Rauber, A. (1997). Alternative ways for cluster visualization in self-organizing maps. In Proceedings of the Workshop on Self-Organizing Maps (WSOM 97). Helsinki, Finland.
Naud, A., & Duch, W. (2000). Interactive data exploration using MDS mapping. Proceedings of the Conference on Neural Networks and Soft Computing (pp. 255–260). Poland, Zakopane.
Neumayer, N., Mayer, R., Poelzlbauer, G., & Rauber, A. (2007). The metro visualisation of component planes for self-organising maps. In Proceedings of the International Joint Conference on Neural Networks (IJCNN 07). Orlando, FL, USA: IEEE Computer Society.
Nikkilä, J., Törönen, P., Kaski, S., Venna, J., Castrén, E., & Wong, G. (2002). Analysis and visualization of gene expression data using self-organizing maps. Neural Networks, 15(8–9), 953–966.CrossRef
Pampalk, E., Rauber, A., & Merkl, D. (2002). Using smoothed data histograms for cluster visualization in self-organizing maps. In Proceedings of the International Conference on Artificial Neural Networks (ICANN 02) (pp. 871–876). Madrid, Spain.
Pölzlbauer, G., Rauber, A., & Dittenbach, M. (2005). Advanced visualization techniques for self-organizing maps with graph-based methods. Proceedings of the International Symposium on Neural Networks (ISNN 05) (pp. 75–80). Chongqing, China: Springer.
Pölzlbauer, G., Dittenbach, M., & Rauber, A. (2006). Advanced visualization of self-organizing maps with vector fields. Neural Networks, 19(6–7), 911–922.CrossRef
Purves, D., Augustine, G., Fitzpatrick, D., Hall, W., LaMantila, A., McNamara, J., et al. (Eds.). (2004). Neuroscience. Massachusetts: Sinauer Associates.
Rauber, A., Paralic, J., & Pampalk, E. (2000). Empirical evaluation of clustering algorithms. Journal of Information and Organizational Sciences, 24(2), 195–209.
Resta, M. (2009). Early warning systems: an approach via self organizing maps with applications to emergent markets. In B. Apolloni, S. Bassis, & M. Marinaro (Eds.), Proceedings of the 18th Italian Workshop on Neural Networks (pp. 176–184). Amsterdam: IOS Press.
Samad, T., & Harp, S. (1992). Self-organization with partial data. Network: Computation in Neural Systems, 3, 205–212.CrossRef
Sammon, J. (1969). A non-linear mapping for data structure analysis. IEEE Transactions on Computers, 18(5), 401–409.CrossRef
Sarlin, P. (2012a). Chance discovery with self-organizing maps: discovering imbalances in financial networks. In Y. Ohsawa & A. Abe (Eds.), Advances in Chance Discovery (pp. 49–61). Heidelberg, Germany: Springer.
Sarlin, P. (2012b). Visual tracking of the millennium development goals with a fuzzified self-organizing neural network. International Journal of Machine Learning and Cybernetics, 3, 233–245.CrossRef
Sarlin, P., & Rönnqvist, S. (2013). Cluster coloring of the self-organizing map: An information visualization perspective. In Proceedings of the International Conference on Information Visualization (iV 13). London, UK: IEEE Press.
Serrano-Cinca, C. (1996). Self organizing neural networks for financial diagnosis. Decision Support Systems, 17, 227–238.CrossRef
Sun, Y., Tino, P., & Nabney, I. (2001). GTM-based data visualisation with incomplete data. Technical Report. Birmingham, UK: Neural Computing Research Group.
Torgerson, W. S. (1952). Multidimensional scaling: i. theory and method. Psychometrika, 17, 401–419.CrossRef
Trosset, M. (2008). Representing clusters: K-means clustering, self-organizing maps, and multidimensional scaling. Technical Report 08–03. Department of Statistics, Indiana University.
Tufte, E. (1983). The visual display of quantitative information. Cheshire, CT: Graphics Press.
Ultsch, A. (2003b). U*-matrix: A tool to visualize clusters in high dimensional data. Technical Report No. 36. Germany: Deptartment of Mathematics and Computer Science, University of Marburg.
Ultsch, A., & Siemon, H. (1990). Kohonen’s self organizing feature maps for exploratory data analysis. In Proceedings of the International Conference on Neural Networks (ICNN 90) (pp. 305–308). Dordrecht, the Netherlands.
Ultsch, A., & Vetter, C. (1994). Self-organizing feature maps versus statistical clustering methods: A benchmark, University of Marburg. Research Report. FG Neuroinformatik & Kuenstliche Intelligenz. 0994.
Ultsch, A. (2003a). Maps for the visualization of high-dimensional data spaces. Proceedings of the Workshop on Self-Organizing Maps (WSOM 03) (pp. 225–230). Kitakyushu, Japan: Hibikino.
Venna, J., & Kaski, S. (2001). Neighborhood preservation in nonlinear projection methods. an experimental study. In Proceedings of the International Conference on Artificial Neural Networks (ICANN 01) (pp. 485–491). Vienna, Austria: Springer.
Venna, J., & Kaski, S. (2006). Local multidimensional scaling. Neural Networks, 19, 889–899.CrossRef
Venna, J., & Kaski, S. (2007). Comparison of visualization methods for an atlas of gene expression data sets. Information Visualization, 6(2), 139–154.CrossRef
Vesanto, J. (1999). Som-based data visualization methods. Intelligent Data Analysis, 3(2), 111–126.CrossRef
Vesanto, J., & Ahola, J. (1999). Hunting for correlations in data using the self-organizing map. Proceeding of the International ICSC Congress on Computational Intelligence Methods and Applications (CIMA 99) (pp. 279–285). Rochester, NY, USA: ICSC Academic Press.
Vesanto, J., & Alhoniemi, E. (2000). Clustering of the self-organizing map. IEEE Transactions on Neural Networks, 11(3), 586–600.CrossRef
Waller, N., Kaiser, H., Illian, J., & Manry, M. (1998). A comparison of the classification capabilities of the 1-dimensional kohonen neural network with two partitioning and three hierarchical cluster analysis algorithms. Psychometrika, 63, 5–22.CrossRef
Ward, J. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 236–244.CrossRef
Yin, H. (2008). The self-organizing maps: background, theories, extensions and applications. In J. Fulcher & L. Jain (Eds.), Computational intelligence: A compendium (pp. 715–762). Heidelberg, Germany: Springer.CrossRef
Metadata
Title
Data-Dimension Reductions: A Comparison
Author
Peter Sarlin
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
Book
Mapping Financial Stability

Print ISBN: 978-3-642-54955-7

Electronic ISBN: 978-3-642-54956-4

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-642-54956-4_5