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Data-Dimension Reductions: A Comparison

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Mapping Financial Stability

Part of the book series: Computational Risk Management ((Comp. Risk Mgmt))

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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.

This chapter is partly based upon previous research. Please see the following work for further information: Sarlin (2014)

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Notes

  1. 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. 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.

References

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Bertin, J. (1983). Semiology of graphics. WI: The University of Wisconsin Press.

    Google Scholar 

  • Bezdek, J. C., & Pal, N. R. (1995). An index of topological preservation for feature extraction. Pattern Recognition, 28(3), 381–391.

    Article  Google Scholar 

  • Bishop, C., Svensson, M., & Williams, C. (1998). Developments of the generative topographic mapping. Neurocomputing, 21(1–3), 203–224.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • CIELab. (1986). Colorimetry. CIE Publication, No. , 15, 2.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Deakin, E. (1976). Distributions of financial accounting ratios: some empirical evidence. The Accounting Review, 51, 90–96.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Flexer, A. (2001). On the use of self-organizing maps for clustering and visualization. Intelligent Data Analysis, 5(5), 373–384.

    Google Scholar 

  • Harrower, M., & Brewer, C. (2003). Colorbrewer.org: an online tool for selecting color schemes for maps. The Cartographic Journal, 40(1), 27–37.

    Article  Google Scholar 

  • Himberg, J. (2004). From insights to innovations: data mining, visualization, and user interfaces. Ph.D. thesis, Helsinki University of Technology, Espoo, Finland.

    Google Scholar 

  • Kaski, S. (1997). Data exploration using self-organizing maps. Ph.D. thesis, Helsinki University of Technology, Espoo, Finland.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43, 59–69.

    Article  Google Scholar 

  • Kohonen, T. (2001). Self-organizing maps (3rd ed.). Berlin: Springer.

    Book  Google Scholar 

  • 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.

    Google Scholar 

  • Lee, J., & Verleysen, M. (2007). Nonlinear dimensionality reduction. Heidelberg, Germany: Springer, Information Science and Statistics Series.

    Google Scholar 

  • Lee, J., & Verleysen, M. (2009). Quality assessment of dimensionality reduction: rank-based criteria. Neurocomputing, 72(7–9), 1431–1443.

    Article  Google Scholar 

  • Linde, Y., Buzo, A., & Gray, R. (1980). An algorithm for vector quantizer design. IEEE Transactions on Communications, 28(1), 702–710.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • van der Maaten, L., & Hinton, G. (2008). Visualizing high-dimensional data using t-sne. Journal of Machine Learning Research, 9, 2579–2605.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Pölzlbauer, G., Dittenbach, M., & Rauber, A. (2006). Advanced visualization of self-organizing maps with vector fields. Neural Networks, 19(6–7), 911–922.

    Article  Google Scholar 

  • Purves, D., Augustine, G., Fitzpatrick, D., Hall, W., LaMantila, A., McNamara, J., et al. (Eds.). (2004). Neuroscience. Massachusetts: Sinauer Associates.

    Google Scholar 

  • Rauber, A., Paralic, J., & Pampalk, E. (2000). Empirical evaluation of clustering algorithms. Journal of Information and Organizational Sciences, 24(2), 195–209.

    Google Scholar 

  • 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.

    Google Scholar 

  • Samad, T., & Harp, S. (1992). Self-organization with partial data. Network: Computation in Neural Systems, 3, 205–212.

    Article  Google Scholar 

  • Sammon, J. (1969). A non-linear mapping for data structure analysis. IEEE Transactions on Computers, 18(5), 401–409.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sarlin, P. (2014). Data and dimension reduction for visual financial performance analysis. Information Visualization (forthcoming). doi:10.1177/1473871613504102

  • 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.

    Google Scholar 

  • Serrano-Cinca, C. (1996). Self organizing neural networks for financial diagnosis. Decision Support Systems, 17, 227–238.

    Article  Google Scholar 

  • Sun, Y., Tino, P., & Nabney, I. (2001). GTM-based data visualisation with incomplete data. Technical Report. Birmingham, UK: Neural Computing Research Group.

    Google Scholar 

  • Torgerson, W. S. (1952). Multidimensional scaling: i. theory and method. Psychometrika, 17, 401–419.

    Article  Google Scholar 

  • Trosset, M. (2008). Representing clusters: K-means clustering, self-organizing maps, and multidimensional scaling. Technical Report 08–03. Department of Statistics, Indiana University.

    Google Scholar 

  • Tufte, E. (1983). The visual display of quantitative information. Cheshire, CT: Graphics Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Venna, J., & Kaski, S. (2006). Local multidimensional scaling. Neural Networks, 19, 889–899.

    Article  Google Scholar 

  • Venna, J., & Kaski, S. (2007). Comparison of visualization methods for an atlas of gene expression data sets. Information Visualization, 6(2), 139–154.

    Article  Google Scholar 

  • Vesanto, J. (1999). Som-based data visualization methods. Intelligent Data Analysis, 3(2), 111–126.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Vesanto, J., & Alhoniemi, E. (2000). Clustering of the self-organizing map. IEEE Transactions on Neural Networks, 11(3), 586–600.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Ward, J. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 236–244.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Centre of Excellence SAFE, Goethe University Frankfurt, Grüneburgplatz 1, 60323, Frankfurt am Main, Germany

    Peter Sarlin

  2. RiskLab Finland, IAMSR Åbo Akademi University, Turku, Finland

    Peter Sarlin

  3. Arcada University of Applied Sciences, Helsinki, Finland

    Peter Sarlin

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  1. Peter Sarlin
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Correspondence to Peter Sarlin .

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Sarlin, P. (2014). Data-Dimension Reductions: A Comparison. In: Mapping Financial Stability. Computational Risk Management. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54956-4_5

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

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