Abstract
The visual interpretation of data is an essential step to guide any further processing or decision making. Dimensionality reduction (or manifold learning) tools may be used for visualization if the resulting dimension is constrained to be 2 or 3. The field of machine learning has developed numerous nonlinear dimensionality reduction tools in the last decades. However, the diversity of methods reflects the diversity of quality criteria used both for optimizing the algorithms, and for assessing their performances. In addition, these criteria are not always compatible with subjective visual quality. Finally, the dimensionality reduction methods themselves do not always possess computational properties that are compatible with interactive data visualization. This paper presents current and future developments to use dimensionality reduction methods for data visualization.
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References
Lee, J.A., Verleysen, M.: Nonlinear dimensionality reduction. Springer (2007)
Keim, D.A., Mansmann, F., Schneidewind, J., Thomas, J., Ziegler, H.: Visual analytics: Scope and challenges. In: Simoff, S.J., Böhlen, M.H., Mazeika, A. (eds.) Visual Data Mining. LNCS, vol. 4404, pp. 76–90. Springer, Heidelberg (2008)
Jolliffe, I.T.: Principal Component Analysis. Springer-Verlag, New York, NY (1986)
Sammon, J.W.: A nonlinear mapping algorithm for data structure analysis. IEEE Transactions on Computers, CC-18(5), 401–409 (1969)
Demartines, P., Hérault, J.: Curvilinear component analysis: A self-organizing neural network for nonlinear mapping of data sets. IEEE Transactions on Neural Networks 8(1), 148–154 (1997)
Lee, J.A., Verleysen, M.: Curvilinear distance analysis versus isomap. Neurocomputing 57, 49–76 (2004)
Tenenbaum, J.B., de Silva, V., Langford, J.C.: A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science 290(5500), 2319–2323 (2000)
Donoho, D.L.: High-Dimensional Data Analysis: The Curse and Blessings of Dimensionality. Lecture for the American Math. Society Math. Challenges of the 21st Century (2000)
Venna, J., Peltonen, J., Nybo, K., Aidos, H., Kaski, S.: Information retrieval perspective to nonlinear dimensionality reduction for data visualization. Journal of Machine Learning Research 11, 451–490 (2010)
Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing 72(7-9), 1431–1443 (2009)
Hinton, G., Roweis, S.T.: Stochastic neighbor embedding. In: Becker, S., Thrun, S., Obermayer, K. (eds.) Advances in Neural Information Processing Systems (NIPS 2002), vol. 15, pp. 833–840. MIT Press (2003)
van der Maaten, L., Hinton, G.: Visualizing data using t-SNE. Journal of Machine Learning Research 9, 2579–2605 (2008)
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Verleysen, M., Lee, J.A. (2013). Nonlinear Dimensionality Reduction for Visualization. In: Lee, M., Hirose, A., Hou, ZG., Kil, R.M. (eds) Neural Information Processing. ICONIP 2013. Lecture Notes in Computer Science, vol 8226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-42054-2_77
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DOI: https://doi.org/10.1007/978-3-642-42054-2_77
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