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Angle-Based Model for Interactive Dimensionality Reduction and Data Visualization

  • Cielo K. Basante-Villota
  • Carlos M. Ortega-Castillo
  • Diego F. Peña-Unigarro
  • E. Javier Revelo-Fuelagán
  • Jose A. Salazar-Castro
  • MacArthur Ortega-Bustamante
  • Paul Rosero-Montalvo
  • Laura Stella Vega-Escobar
  • Diego H. Peluffo-Ordóñez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11047)

Abstract

In recent times, an undeniable fact is that the amount of data available has increased dramatically due mainly to the advance of new technologies allowing for storage and communication of enormous volumes of information. In consequence, there is an important need for finding the relevant information within the raw data through the application of novel data visualization techniques that permit the correct manipulation of data. This issue has motivated the development of graphic forms for visually representing and analyzing high-dimensional data. Particularly, in this work, we propose a graphical approach, which, allows the combination of dimensionality reduction (DR) methods using an angle-based model, making the data visualization more intelligible. Such approach is designed for a readily use, so that the input parameters are interactively given by the user within a user-friendly environment. The proposed approach enables users (even those being non-experts) to intuitively select a particular DR method or perform a mixture of methods. The experimental results prove that the interactive manipulation enabled by the here-proposed model-due to its ability of displaying a variety of embedded spaces-makes the task of selecting a embedded space simpler and more adequately fitted for a specific need.

Keywords

Dimensionality reduction Data visualization Kernel PCA Pairwise similarity 

Notes

Acknowledgments

This work is supported by the Smart Data Analysis Systems (SDAS) Research Group (http://sdas-group.com), as well as the “Grupo de Investigación en Ingeniería Eléctrica y Electrónica - GIIEE” from Universidad de Nariño. Also, the authors acknowledge to the research project: “Desarrollo de una metodología de visualización interactiva y eficaz de información en Big Data” supported by Agreement No. 18 November 1st, 2016 by VIPRI from Universidad de Nariño.

References

  1. 1.
    Asuncion, A., Newman, D.: UCI machine learning repository. University of california, School of Information and Computer Science, Irvine, CA (2007). http://www.ics.uci.edu/~mlearn/MLRepository.html
  2. 2.
    Belkin, M., Niyogi, P.: Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)CrossRefGoogle Scholar
  3. 3.
    Borg, I.: Modern Multidimensional Scaling: Theory And Applications. Springer, New York (2005).  https://doi.org/10.1007/0-387-28981-XCrossRefzbMATHGoogle Scholar
  4. 4.
    Cook, J., Sutskever, I., Mnih, A., Hinton, G.: Visualizing similarity data with a mixture of maps. In: International Conference on Artificial Intelligence and Statistics, pp. 67–74 (2007)Google Scholar
  5. 5.
    Ham, J., Lee, D.D., Mika, S., Schölkopf, B.: A Kernel view of the dimensionality reduction of manifolds. In: Proceedings of the Twenty-First International Conference on Machine learning, p. 47. ACM (2004)Google Scholar
  6. 6.
    Lee, J.A., Renard, E., Bernard, G., Dupont, P., Verleysen, M.: Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation. Neurocomputing 112, 92–108 (2013)CrossRefGoogle Scholar
  7. 7.
    Peluffo-Ordonez, D.H., Aldo Lee, J., Verleysen, M.: Generalized Kernel framework for unsupervised spectral methods of dimensionality reduction. In: 2014 IEEE Symposium on Computational Intelligence and Data Mining (CIDM), pp. 171–177. IEEE (2014)Google Scholar
  8. 8.
    Peluffo-Ordóñez, D.H., Castro-Ospina, A.E., Alvarado-Pérez, J.C., Revelo-Fuelagán, E.J.: Multiple Kernel learning for spectral dimensionality reduction. Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. LNCS, vol. 9423, pp. 626–634. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-25751-8_75CrossRefGoogle Scholar
  9. 9.
    Peluffo-Ordóñez, D.H., Lee, J.A., Verleysen, M.: Recent methods for dimensionality reduction: a brief comparative analysis. In: European Symposium on Artificial Neural Networks (ESANN). Citeseer (2014)Google Scholar
  10. 10.
    Peluffo-Ordóñez, D.H., Lee, J.A., Verleysen, M.: Short review of dimensionality reduction methods based on stochastic neighbour embedding. In: Villmann, T., Schleif, F.-M., Kaden, M., Lange, M. (eds.) Advances in Self-Organizing Maps and Learning Vector Quantization. AISC, vol. 295, pp. 65–74. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-07695-9_6CrossRefGoogle Scholar
  11. 11.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)CrossRefGoogle Scholar
  12. 12.
    Sedlmair, M., Aupetit, M.: Data-driven evaluation of visual quality measures. Comput. Graph. Forum 34, 201–210 (2015)CrossRefGoogle Scholar
  13. 13.
    Sedlmair, M., Brehmer, M., Ingram, S., Munzner, T.: Dimensionality reduction in the wild: gaps and guidance. Department of Computer Science, University of British Columbia, Vancouver, BC, Canada, Technical report TR-2012-03 (2012)Google Scholar
  14. 14.
    Peña-Unigarro, D.F., et al.: Interactive data visualization using dimensionality reduction and dissimilarity-based representations. In: Yin, H., et al. (eds.) IDEAL 2017. LNCS, vol. 10585, pp. 461–469. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-68935-7_50CrossRefGoogle Scholar
  15. 15.
    Rosero-Montalvo, P.D., Peña-Unigarro, D.F., Peluffo, D.H., Castro-Silva, J.A., Umaquinga, A., Rosero-Rosero, E.A.: Interactive visualization methodology of high-dimensional data with a color-based model for dimensionality reduction. Biomed. Appl. Based Nat. Artif. Comput. 10338, 289 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Cielo K. Basante-Villota
    • 1
  • Carlos M. Ortega-Castillo
    • 1
  • Diego F. Peña-Unigarro
    • 1
  • E. Javier Revelo-Fuelagán
    • 1
  • Jose A. Salazar-Castro
    • 1
    • 2
  • MacArthur Ortega-Bustamante
    • 3
  • Paul Rosero-Montalvo
    • 3
    • 4
    • 5
  • Laura Stella Vega-Escobar
    • 6
  • Diego H. Peluffo-Ordóñez
    • 2
    • 7
  1. 1.Universidad de NariñoPastoColombia
  2. 2.Corporación Universitaria Autónoma de NariñoPastoColombia
  3. 3.Universidad Técnica del NorteIbarraEcuador
  4. 4.Universidad de SalamancaSalamancaSpain
  5. 5.Instituto Tecnológico Superior 17 de JulioIbarraEcuador
  6. 6.Instituto Tecnológico Metropolitano (ITM)MedellínColombia
  7. 7.Yachay TechUrcuquíEcuador

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