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Non-linear Least Mean Squares Prediction Based on Non-Gaussian Mixtures

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Advances in Computational Intelligence (IWANN 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10305))

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Abstract

Independent Component Analyzers Mixture Models (ICAMM) are versatile and general models for a large variety of probability density functions. In this paper, we assume ICAMM to derive a closed-form solution to the optimal Least Mean Squared Error predictor, which we have named E-ICAMM. The new predictor is compared with four classical alternatives (Kriging, Wiener, Matrix Completion, and Splines) which are representative of the large amount of existing approaches. The prediction performance of the considered methods was estimated using four performance indicators on simulated and real data. The experiment on real data consisted in the recovering of missing seismic traces in a real seismology survey. E-ICAMM outperformed the other methods in all cases, displaying the potential of the derived predictor.

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References

  1. Einicke, G.: Smoothing, Filtering and Prediction - Estimating The Past, Present and Future. InTech, Rijeka (2012)

    Google Scholar 

  2. Lee, T., Lewicki, S., Sejnowski, T.: ICA mixture models for unsupervised classification of non-gaussian classes and automatic context switching in blind signal separation. IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1078–1089 (2000)

    Article  Google Scholar 

  3. Salazar, A., Vergara, L., Serrano, A., Igual, J.: A general procedure for learning mixtures of independent component analyzers. Pattern Recognit. 43(1), 69–85 (2010)

    Article  MATH  Google Scholar 

  4. Salazar, A.: On Statistical Pattern Recognition in Independent Component Analysis Mixture Modelling. Springer, Heidelberg (2013)

    Book  MATH  Google Scholar 

  5. Safont, G., Salazar, A., Vergara, L., Gomez, E., Villanueva, V.: Probabilistic distance for mixtures of independent component analyzers. IEEE Trans. Neural Netw. Learn. Syst. (2017, in press). doi:10.1109/TNNLS.2017.2663843

  6. Stein, M.: Interpolation of Spatial Data: Some Theory for Kriging. Springer, New York (2012)

    Google Scholar 

  7. Wiener, N.: Nonlinear Problems in Random Theory. M.I.T. Press, New York (1958)

    MATH  Google Scholar 

  8. Candès, E., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717–722 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, Y.: Smoothing Splines: Methods and Applications. Taylor and Francis, Boca Raton (2011)

    Book  MATH  Google Scholar 

  10. Common, P., Jutten, C.: Handbook of Blind Source Separation: Independent Component Analysis and Applications. Academic Press, Waltham (2010)

    Google Scholar 

  11. Jung, T., Lee, T.: Applications of independent component analysis to electroencephalography. In: Wenger, M., Schuster, C. (eds.) Statistical and Process Models for Cognitive Neuroscience and Aging. Psychology Press, Hove (2012)

    Google Scholar 

  12. Vergara, L., Bernabeu, P.: Simple approach to nonlinear prediction. Electron. Lett. 37, 926–928 (2001)

    Article  Google Scholar 

  13. Ghasemi, H., Malek-Mohammadi, M., Babaie-Zadeh, M., Jutten, C.: SRF: matrix completion based on smoothed rank function, In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2011)

    Google Scholar 

  14. Wang, Z., Bovik, A., Sheikh, H., Simoncelli, E.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  15. Gadallah, M., Fisher, R.: Applied Seismology: A Comprehensive Guide to Seismic Theory and Application. PennWell Books, Tulsa (2005)

    Google Scholar 

  16. Zhou, H.: Practical Seismic Data Analysis. Cambridge University Press, New York (2014)

    Google Scholar 

  17. Cheraghi, S., Craven, J., Bellefleur, G.: Feasibility of virtual source reflection seismology using interferometry for mineral exploration: a test study in the lalor lake volcanogenic massive sulphide mining area, Manitoba, Canada. Geophys. Prospect. 63(4), 833–848 (2015)

    Article  Google Scholar 

  18. Etgen, J., Regone, C.: Strike shooting, dip shooting, widepatch shooting-does prestack depth migration care? A model study, In: 58th Annual SEG International Meeting and Exposition, pp. 66–69 (1998)

    Google Scholar 

  19. Li, X.: Patch-based image processing: from dictionary learning to structural clustering. In: Lukac, R. (ed.) Perceptual Digital Imaging: Methods, and Applications, pp. 223–250. CRC Press, Boca Raton (2012)

    Google Scholar 

  20. Llinares, R., Igual, J., Salazar, A., Camacho, A.: Semi-blind source extraction of atrial activity by combining statistical and spectral features. Digital Signal Process.: Rev. J. 21(2), 391–403 (2011)

    Article  Google Scholar 

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Acknowledgment

This work was supported by Spanish Administration and European Union under grant TEC2014-58438-R, and Generalitat Valenciana under grant PROMETEO II/2014/032.

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Authors and Affiliations

  1. Institute of Telecommunications and Multimedia Applications, Universitat Politècnica de València, València, Spain

    Gonzalo Safont, Addisson Salazar & Luis Vergara

  2. Department of Communications Engineering, University Miguel Hernández de Elche, Elche, Spain

    Alberto Rodríguez

Authors
  1. Gonzalo Safont
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  2. Addisson Salazar
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  3. Alberto Rodríguez
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  4. Luis Vergara
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Corresponding author

Correspondence to Gonzalo Safont .

Editor information

Editors and Affiliations

  1. Universidad de Granada , Granada, Spain

    Ignacio Rojas

  2. University of Malaga , Malaga, Spain

    Gonzalo Joya

  3. Polytechnic University of Catalonia, Vilanova i la Geltrú, Barcelona, Spain

    Andreu Catala

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Safont, G., Salazar, A., Rodríguez, A., Vergara, L. (2017). Non-linear Least Mean Squares Prediction Based on Non-Gaussian Mixtures. In: Rojas, I., Joya, G., Catala, A. (eds) Advances in Computational Intelligence. IWANN 2017. Lecture Notes in Computer Science(), vol 10305. Springer, Cham. https://doi.org/10.1007/978-3-319-59153-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-59153-7_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59152-0

  • Online ISBN: 978-3-319-59153-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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