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International Journal for Uncertainty Quantification
インパクトファクター: 4.911 5年インパクトファクター: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 印刷: 2152-5080
ISSN オンライン: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2019028125
pages 569-587

MULTIVARIATE ANALYSIS OF EXTRAPOLATING TIME-INVARIANT DATA WITH UNCERTAINTY

Die Joseph Hassan Millogo
Department of Mechanical Engineering, National Taiwan University, Taiwan
Kuei-Yuan Chan
Department of Mechanical Engineering, National Taiwan University, Taiwan

要約

Data analysis deciphers phenomena and system behaviors within a large number of experimental realizations. Transforming these massive quantities of raw data into knowledge about the data is made possible thanks to continuously improved computing techniques. In science and engineering, a particular interest lies within surrogate models for system behaviour prediction and data extrapolation. These models could, however, be under- or over- fitted when confronted to a complex dataset or one embedded with uncertainty. In this paper, we suggest a treatment approach of experimental data under uncertainty prior to its surrogate model creation. We specially focus on extrapolation an attempt to estimate the true underlying phenomena. We quantify the uncertainty quantity through eigenvalues, copy the behavior of the data through its covariance matrix, and reproduce an almost identical dataset whose particularity is a perfectly correlated inputs and output. This new dataset is then used as the basis for the creation of a surrogate model. Our approach shows consistency and a clear opportunity to obtain better predictions under uncertainty as it focuses on the overall dataset's behavior and stays faithful to each data.

参考

  1. Letouz, E., Big Data for Development: Challenges and Opportunities, UN Global Pulse, from http://www.unglobalpulse.org big data for Development-GlobalPulseMay2012.pdf, 2012.

  2. Wasserman, L., Nonparametric Statistics, in All ofNonparametric Regression, New York: Springer, pp. 63-66, 2005.

  3. MathWorks, Least-Squares Curve Fitting, accessed May 2016, from http://www.mathworks.com/help/curvefit/least-squares-fitting.html, 2019.

  4. MathWorks, Polynomial Curve Fitting, accessed May 2016, from https://www.mathworks.com/help/matlab/ref/polyfit.html, 2019.

  5. OriginLAB, Curve Fitting, accessed May 2016, https://wwworiginlab.com/index.aspx?go=Products/Origin/DataAnalysis/ CurveFitting, 2019.

  6. University of Wisconsin-Madison, A Basic Introduction to Neural Networks, accessed May 2016, from http://pages.cs.wisc.edu/~bolo/shipyard/neural/local.html, 2019.

  7. Stefano, J.D., A Confidence Interval Approach to Data Analysis, Forest Ecol. Manag, 187(2-3):173-183,2004.

  8. Bylander, T., Estimating Generalization Error on Two-Class Datasets Using Out-of-Bag Estimates, Mach. Learn., 48(1):287-297, 2002.

  9. Taiana, M., Nascimento, J., and Bernardino, A., On the Purity of Training and Testing Data for Learning: The Case of Pedestrian Detection, Neurocomputing, 150(Part A):214-226, 2015.

  10. Browne, M.W., Cross-Validation Methods, J. Math. Psychol, 44(1):108-132, 2000.

  11. Cawley, G.C. and Talbot, N.L., Efficient Leave-One-Out Cross-Validation of Kernel Fisher Discriminant Classifiers, Pattern Recognit., 36(11):2585-2592, 2003.

  12. Sokolova, M. and Lapalme, G., A Systematic Analysis of Performance Measures for Classification Tasks, Inf. Process. Manag, 45(4):427-437, 2009.

  13. Davis, T.G., Total Least Squares Spiral Curve Fitting, J. Surv. Eng., 125(4):159-176, 1999.

  14. Golub, G.H. and Loan, C.F.V., An Analysis of the Total Least Squares Problem, Numer. Anal., 17:883-893,1980.

  15. Plesinger, M., The Total Least Squares Problem and Reduction of Data in AX = B, PhD, TU of Liberec and Institute of Computer Science, Liberec, Czech Republic, pp. 883-893,2008.

  16. Hnetynkova, I., Pleeinger, M., Sima, D.M., Strakos, Z., and Huffel, S.V., The Total Least Squares Problem in AX = B. A New Classification with the Relationship to the Classical Works, SIAMJ. Matrix Anal. Appl., 32:748-770, 2011.

  17. Jolliffe, I., Mathematical and Statistical Properties of Population Principal Components, in Principal Component Analysis, New York: Springer Verlag, pp. 27-28, 2002.

  18. Bishop, C.M. and Roach, C.M., Fast Curve Fitting Using Neural Networks, Rev. Sci. Instrum., 63(10):4450-4456, 1992.

  19. MathWorks, Deep Learning ToolboxTM (Formerly Neural Network ToolboxTM), accessed May 2016, from https://www.mathworks.com/products/deep-learning.html, 2019.

  20. Box, G.E.P., Science and Statistics, J. Am. Stat. Assoc, 71(356):791-799, 1976.

  21. He, Y., Mirzargar, M., Hudson, S., Kirby, R.M., and Whitaker, R.T., An Uncertainty Visualization Technique Using Possibility Theory: Possibilistic Marching Cubes, Int. J. Uncertainty Quantif., 5:433-451, 2015.

  22. Wu, K. and Zhang, S., A Contour Tree based Visualization for Exploring Data with Uncertainty, Int. J. Uncertainty Quantif, 3:203-223,2013.

  23. Crespo, L.G., Kenny, S.P., and Giesy, D.P., Random Predictor Models for Rigorous Uncertainty Quantification, Int. J. Uncertainty Quantif, 5:469-489, 2016.

  24. Yang, C., Xiu, D., and Kirby, R.M., Visualization of Covariance and Cross-Covariance Fields, Int. J. Uncertainty Quantif, 3:25-38,2013.

  25. Correa, D.C. and Lindstrom, P., The Mutual Information Diagram for Uncertainty Visualization, Int. J. Uncertainty Quantif, 3:187-201,2013.


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