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.
D. H. Peluffo-Ordóñez—This work is supported by Yachay Tech University and SDAS research group (www.sdas-group.com).
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References
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)
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
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)
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
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)
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_41
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)
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)
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_17
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)
Choi, H., Choi, S.: Kernel ISOMAP. Electron. Lett. 40(1), 1612–1613 (2004)
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)
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)
Washizawa, Y.: Subset basis approximation of kernel principal component analysis. Principal Component Analysis, vol. 67 (2012)
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)
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)
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)
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 2016
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_64
Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)
Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)
Choi, H., Choi, S.: Robust kernel ISOMAP. Pattern Recogn. 40(3), 853–862 (2007)
Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, pp. 585–591 (2002)
Belkin, M., Niyogi, P.: Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15(6), 1373–1396 (2003)
Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Donoho, D.L., Grimes, C.: Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci. 100(10), 5591–5596 (2003)
DeCoste, D.: Visualizing mercer kernel feature spaces via kernelized locally-linear embeddings (2001)
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)
Lee, J.A., Verleysen, M.: Quality assessment of dimensionality reduction: rank-based criteria. Neurocomputing 72(7–9), 1431–1443 (2009)
Mokbel, B., Lueks, W., Gisbrecht, A., Hammer, B.: Visualizing the quality of dimensionality reduction. Neurocomputing 112, 109–123 (2013)
Lee, J.A., Verleysen, M.: Scale-independent quality criteria for dimensionality reduction. Pattern Recogn. Lett. 31(14), 2248–2257 (2010)
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)
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).
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Vélez-Falconí, M., González-Vergara, J., Peluffo-Ordóñez, D.H. (2020). Inverse Data Visualization Framework (IDVF): Towards a Prior-Knowledge-Driven Data Visualization. In: Florez, H., Misra, S. (eds) Applied Informatics. ICAI 2020. Communications in Computer and Information Science, vol 1277. Springer, Cham. https://doi.org/10.1007/978-3-030-61702-8_19
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