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2016 | OriginalPaper | Chapter

Fast Two-Dimensional Smoothing with Discrete Cosine Transform

Authors : Pavel Lyubin, Eugeny Shchetinin

Published in: Distributed Computer and Communication Networks

Publisher: Springer International Publishing

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Abstract

Smoothing is the process of removing “noise” and “insignificant” fragments while preserving the most important properties of the data structure. We propose a fast spline method for two-dimensional smoothing. Data smoothing usually attained by parametric and nonparametric regression. The nonparametric regression requires a prior knowledge of the regression equation form. However, most of the investigated data can’t be parameterized simply. From this point of view, our algorithm belongs to nonparametric regression. Our simulation study shows that smoothing with discrete cosine transform is orders of magnitude faster to compute than other two-dimensional spline smoothers.

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Whittaker, E.T.: On a new method of graduation. Proc. Edinb. Math. Soc. 41, 62–75 (1923)

Wahba, G.: Spline Models for Observational Data. Society for Industrial Mathematics, Philadelphia (1990)CrossRefMATH

Schoenberg, I.J.: Spline functions and the problem of graduation. Proc. Natl. Acad. Sci. USA 52, 947–950 (1964)MathSciNetCrossRefMATH

Takezawa, K.: Introduction to Nonparametric Regression. Wiley, New York (2005)CrossRefMATH

Weinert, H.L.: Efficient computation for whittaker-henderson smoothing. Comput. Stat. Data Anal. 52, 959–974 (2007)MathSciNetCrossRefMATH

Yu, S.E., Lyubin, P.G.: Robust smoothing with splines. Sci. Rev. 1, 86–94 (2015)

Lyubin, P.G., Shetinin, E.Y.: Stochastic models of mortality estimation. Sci. Rev. 18, 147–155 (2015)

Xiao, L., Li, Y., Ruppert, D.: Fast bivariate p-splines: the sandwich smoother. J. Roy. Stat. Soc. 75, 577–599 (2013)MathSciNetCrossRef

Garcia, D.: Robust smoothing of gridded data in one and higher dimensions with missing values. Comput. Stat. Data Anal. 54, 1167–1178 (2010)MathSciNetCrossRefMATH

10.

Seber, G.: A Matrix Handbook for Statisticians. Wiley-Interscience, Hoboken (2007)CrossRef

11.

Wood, S.: mgcv: mixed gam computation vehicle with gcv/aic/reml smoothness estimation. R package version 1.8.10

12.

\(\tilde{\text{D}}\)epartment of Demography at the University of California. The human mortality database. Last visited on 25.02.2016

13.

Wood, S.N.: Thin plate regression splines. R. Stat. Soc. B 65, 95–114 (2003)MathSciNetCrossRefMATH

14.

Ruppert, D.: Selecting the number of knots for penalized splines. Comput. Graph. Stat. 1, 735–757 (2006)MathSciNet

15.

Li, Y., Ruppert, D.: On the asymptotics of penalized splines. Biometrika 95, 415–436 (2008)MathSciNetCrossRefMATH

16.

Dierckx, P.: A fast algorithm for smoothing data on a rectangular grid while using spline functions. SIAM J. Numer. Anal. 19(6), 1286–1304 (1982)MathSciNetCrossRefMATH

17.

Wood, S.N., Smith, L., Hyndman, R.J.: Spline interpolation for demographic variables: the monotonicity problem. J. Popul. Res. 21(1), 95–98 (2004)CrossRef

18.

Eilers, P.H.C., Marx, B.D.: Generalized linear additive smooth structures. J. Comput. Graph. Stat. 11(4), 758–783 (2002)MathSciNetCrossRef

19.

Eilers, P.H.C., Marx, B.D.: Multidimensional penalized signal regression. Technometrics 47(1), 13–22 (2005)MathSciNetCrossRef

20.

Hyndman, R.J., Booth, H., Tickle, L., Maindonald, J.: Demography: forecasting mortality, fertility, migration and population data, R package version 1.18 (2014)

21.

Yueh, W.C.: Eigenvalues of several tridiagonal matrices. Appl. Math. E-Not. 5, 66–74 (2005)MathSciNetMATH

22.

Hoaglin, D.C., Welsch, R.E.: The hat matrix in regression and ANOVA. Am. Stat. 32, 17–22 (1978)MATH

23.

Eilers, P.H.C., Marx, B.D.: Splines, knots, and penalties. Wiley Interdisc. Rev. Comput. Stat. 2, 637–653 (2010)CrossRef

Title: Fast Two-Dimensional Smoothing with Discrete Cosine Transform
Authors: Pavel Lyubin
Eugeny Shchetinin
Publisher: Springer International Publishing
Book: Distributed Computer and Communication Networks
Print ISBN: 978-3-319-51916-6

Electronic ISBN: 978-3-319-51917-3

Copyright Year: 2016
DOI: https://doi.org/10.1007/978-3-319-51917-3_55

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