Advertisement

Inverse Data Visualization Framework (IDVF): Towards a Prior-Knowledge-Driven Data Visualization

  • M. Vélez-FalconíEmail author
  • J. González-Vergara
  • D. H. Peluffo-Ordóñez
Conference paper
  • 120 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1277)

Abstract

Broadly, the area of dimensionality reduction (DR) is aimed at providing ways to harness high dimensional (HD) information through the generation of lower dimensional (LD) representations, by following a certain data-structure-preservation criterion. In literature there have been reported dozens of DR techniques, which are commonly used as a pre-processing stage withing exploratory data analyses for either machine learning or information visualization (IV) purposes. Nonetheless, the selection of a proper method is a nontrivial and -very often- toilsome task. In this sense, a readily and natural way to incorporate an expert’s criterion into the analysis process, while making this task more tractable is the use of interactive IV approaches. Regarding the incorporation of experts’ prior knowledge there still exists a range of open issues. In this work, we introduce a here-named Inverse Data Visualization Framework (IDVF), which is an initial approach to make the input prior knowledge directly interpretable. Our framework is based on 2D-scatter-plots visuals and spectral kernel-driven DR techniques. To capture either the user’s knowledge or requirements, users are requested to provide changes or movements of data points in such a manner that resulting points are located where best convenient according to the user’s criterion. Next, following a Kernel Principal Component Analysis approach and a mixture of kernel matrices, our framework accordingly estimates an approximate LD space. Then, the rationale behind the proposed IDVF is to adjust as accurate as possible the resulting LD space to the representation fulfilling users’ knowledge and requirements. Results are greatly promising and open the possibility to novel DR-based visualizations approaches.

Keywords

Dimensionality reduction Interaction model Kernel functions Data visualization 

Notes

Acknowledgment

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. 180 November 1st, 2016 by VIPRI from Universidad de Nariño.

Authors thank the valuable support given by the SDAS Research Group (www.sdas-group.com).

References

  1. 1.
    Peluffo Ordoñez, D.H., Lee, J.A., Verleysen, M.: Recent methods for dimensionality reduction: a brief comparative analysis. In: 2014 European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN 2014) (2014)Google Scholar
  2. 2.
    Peluffo-Ordóñez, D.H., Castro-Ospina, A.E., Alvarado-Pérez, J.C., Revelo-Fuelagán, E.J.: Multiple kernel learning for spectral dimensionality reduction. CIARP 2015. LNCS, vol. 9423, pp. 626–634. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-25751-8_75
  3. 3.
    Liu, S., Maljovec, D., Wang, B., Bremer, P.T., Pascucci, V.: Visualizing high-dimensional data: advances in the past decade. IEEE Trans. Vis. Comput. Graph. 23(3), 1249–1268 (2016)Google Scholar
  4. 4.
    Ortega-Bustamante, M.C., et al.: Introducing the concept of interaction model for interactive dimensionality reduction and data visualization. In: Gervasi, O., et al. (eds.) Computational Science and its Applications - ICCSA 2020. ICCSA 2020. Lecture Notes in Computer Science, vol. 12250. Springer, Cham (2020).  https://doi.org/10.1007/978-3-030-58802-1_14
  5. 5.
    Salazar-Castro, J., Rosas-Narváez, Y., Pantoja, A., Alvarado-Pérez, J.C., Peluffo-Ordóñez, D.H.: Interactive interface for efficient data visualization via a geometric approach. In: 2015 20th Symposium on Signal Processing, Images and Computer Vision (STSIVA), pp. 1–6. IEEE (2015)Google Scholar
  6. 6.
    Rosero-Montalvo, P., et al.: Interactive data visualization using dimensionality reduction and similarity-based representations. In: Beltrán-Castañón, C., Nyström, I., Famili, F. (eds.) CIARP 2016. LNCS, vol. 10125, pp. 334–342. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-52277-7_41CrossRefGoogle Scholar
  7. 7.
    Peña-ünigarro, D.F., et al.: Interactive visualization methodology of high-dimensional data with a color-based model for dimensionality reduction. In: XXI Symposium on Signal Processing, vol. 2016, pp. 1–7 (2016)Google Scholar
  8. 8.
    Salazar-Castro, J.A., et al.: Dimensionality reduction for interactive data visualization via a Geo-Desic approach. In: 2016 IEEE Latin American Conference on Computational Intelligence (LA-CCI), pp. 1–6. IEEE (2016)Google Scholar
  9. 9.
    Umaquinga-Criollo, A.C., Peluffo-Ordóñez, D.H., Rosero-Montalvo, P.D., Godoy-Trujillo, P.E., Benítez-Pereira, H.: Interactive visualization interfaces for big data analysis using combination of dimensionality reduction methods: a brief review. In: Basantes-Andrade, A., Naranjo-Toro, M., Zambrano Vizuete, M., Botto-Tobar, M. (eds.) TSIE 2019. AISC, vol. 1110, pp. 193–203. Springer, Cham (2020).  https://doi.org/10.1007/978-3-030-37221-7_17CrossRefGoogle Scholar
  10. 10.
    Weinberger, K.Q., Sha, F., Saul, L.K.: Learning a kernel matrix for nonlinear dimensionality reduction. In: Proceedings of the Twenty-First International Conference on Machine Learning, p. 106. ACM (2004)Google Scholar
  11. 11.
    Choi, H., Choi, S.: Kernel ISOMAP. Electron. Lett. 40(1), 1612–1613 (2004)zbMATHGoogle Scholar
  12. 12.
    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, vol. 47. ACM (2004)Google Scholar
  13. 13.
    Mika, S., Schölkopf, B., Smola, A.J., Müller, K.R., Scholz, M., Rätsch, G.: Kernel PCA and de-noising in feature spaces. In: Advances in Neural Information Processing Systems, pp. 536–542 (1999)Google Scholar
  14. 14.
    Washizawa, Y.: Subset basis approximation of kernel principal component analysis. Principal Component Analysis, vol. 67 (2012)Google Scholar
  15. 15.
    Bengio, Y., Vincent, P., Paiement, J.F., Delalleau, O., Ouimet, M., LeRoux, N.: Learning eigenfunctions of similarity: linking spectral clustering and kernel PCA. Technical report, Technical report 1232, Departement d’Informatique et Recherche Oprationnelle (2003)Google Scholar
  16. 16.
    Peluffo-Ordóñez, D.H., Lee, J.A., 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
  17. 17.
    Lanckriet, G.R., Cristianini, N., Bartlett, P., Ghaoui, L.E., Jordan, M.I.: Learning the kernel matrix with semidefinite programming. J. Mach. Learn. Res. 5(Jan), 27–72 (2004)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Information Science and Statistics. Springer, New York (2006).  https://doi.org/10.1007/978-1-4615-7566-5. Softcover published in 2016CrossRefzbMATHGoogle Scholar
  19. 19.
    Salazar-Castro, J.A., et al.: A novel color-based data visualization approach using a circular interaction model and dimensionality reduction. In: Huang, T., Lv, J., Sun, C., Tuzikov, A.V. (eds.) ISNN 2018. LNCS, vol. 10878, pp. 557–567. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-92537-0_64CrossRefGoogle Scholar
  20. 20.
    Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)Google Scholar
  22. 22.
    Choi, H., Choi, S.: Robust kernel ISOMAP. Pattern Recogn. 40(3), 853–862 (2007)zbMATHGoogle Scholar
  23. 23.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, pp. 585–591 (2002)Google Scholar
  24. 24.
    Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)zbMATHGoogle Scholar
  25. 25.
    Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)Google Scholar
  26. 26.
    Donoho, D.L., Grimes, C.: Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci. 100(10), 5591–5596 (2003)MathSciNetzbMATHGoogle Scholar
  27. 27.
    DeCoste, D.: Visualizing mercer kernel feature spaces via kernelized locally-linear embeddings (2001)Google Scholar
  28. 28.
    Belanche Muñoz, L.A.: Developments in kernel design. In: ESANN 2013 proceedings: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges, Belgium, 24–26 April 2013, pp. 369–378 (2013)Google Scholar
  29. 29.
    Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: rank-based criteria. Neurocomputing 72(7–9), 1431–1443 (2009)Google Scholar
  30. 30.
    Mokbel, B., Lueks, W., Gisbrecht, A., Hammer, B.: Visualizing the quality of dimensionality reduction. Neurocomputing 112, 109–123 (2013)Google Scholar
  31. 31.
    Lee, J.A., Verleysen, M.: Scale-independent quality criteria for dimensionality reduction. Pattern Recogn. Lett. 31(14), 2248–2257 (2010)Google Scholar
  32. 32.
    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)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • M. Vélez-Falconí
    • 1
    • 2
    Email author
  • J. González-Vergara
    • 1
    • 2
  • D. H. Peluffo-Ordóñez
    • 1
    • 2
    • 3
  1. 1.Yachay Tech UniversitySan Miguel de UrcuquíEcuador
  2. 2.SDAS Research GroupPastoColombia
  3. 3.Corporación Universitaria Autónoma de NariñoPastoColombia

Personalised recommendations