IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp893-902.html
   My bibliography  Save this article

Modified moving least squares with polynomial bases for scattered data approximation

Author

Listed:
  • Joldes, Grand Roman
  • Chowdhury, Habibullah Amin
  • Wittek, Adam
  • Doyle, Barry
  • Miller, Karol

Abstract

One common problem encountered in many fields is the generation of surfaces based on values at irregularly distributed nodes. To tackle such problems, we present a modified, robust moving least squares (MLS) method for scattered data smoothing and approximation. The error functional used in the derivation of the classical MLS approximation is augmented with additional terms based on the coefficients of the polynomial base functions. This allows quadratic base functions to be used with the same size of the support domain as linear base functions, resulting in better approximation capability. The increased robustness of the modified MLS method to irregular nodal distributions makes it suitable for use across many fields. The analysis is supported by several univariate and bivariate examples.

Suggested Citation

  • Joldes, Grand Roman & Chowdhury, Habibullah Amin & Wittek, Adam & Doyle, Barry & Miller, Karol, 2015. "Modified moving least squares with polynomial bases for scattered data approximation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 893-902.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:893-902
    DOI: 10.1016/j.amc.2015.05.150
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315007924
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.05.150?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Xia Jin & Grand Roman Joldes & Karol Miller & King H. Yang & Adam Wittek, 2014. "Meshless algorithm for soft tissue cutting in surgical simulation," Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis Journals, vol. 17(7), pages 800-811, May.
    2. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    2. Bauer, Benedikt & Devroye, Luc & Kohler, Michael & Krzyżak, Adam & Walk, Harro, 2017. "Nonparametric estimation of a function from noiseless observations at random points," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 93-104.
    3. Francomano, Elisa & Hilker, Frank M. & Paliaga, Marta & Venturino, Ezio, 2018. "Separatrix reconstruction to identify tipping points in an eco-epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 80-91.
    4. Hongtao Yang & Hao Wang & Bo Li, 2024. "Analysis of Meshfree Galerkin Methods Based on Moving Least Squares and Local Maximum-Entropy Approximation Schemes," Mathematics, MDPI, vol. 12(3), pages 1-20, February.
    5. Mustafa, Ghulam & Hameed, Rabia, 2019. "Families of non-linear subdivision schemes for scattered data fitting and their non-tensor product extensions," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 214-240.
    6. Wang, Qiao & Zhou, Wei & Feng, Y.T. & Ma, Gang & Cheng, Yonggang & Chang, Xiaolin, 2019. "An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 347-370.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. Carstensen, Kai & Heinrich, Markus & Reif, Magnus & Wolters, Maik H., 2020. "Predicting ordinary and severe recessions with a three-state Markov-switching dynamic factor model," International Journal of Forecasting, Elsevier, vol. 36(3), pages 829-850.
    3. Hou-Tai Chang & Ping-Huai Wang & Wei-Fang Chen & Chen-Ju Lin, 2022. "Risk Assessment of Early Lung Cancer with LDCT and Health Examinations," IJERPH, MDPI, vol. 19(8), pages 1-12, April.
    4. Wang, Qiao & Zhou, Wei & Cheng, Yonggang & Ma, Gang & Chang, Xiaolin & Miao, Yu & Chen, E, 2018. "Regularized moving least-square method and regularized improved interpolating moving least-square method with nonsingular moment matrices," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 120-145.
    5. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    6. Lucian Belascu & Alexandra Horobet & Georgiana Vrinceanu & Consuela Popescu, 2021. "Performance Dissimilarities in European Union Manufacturing: The Effect of Ownership and Technological Intensity," Sustainability, MDPI, vol. 13(18), pages 1-19, September.
    7. Candelon, B. & Hurlin, C. & Tokpavi, S., 2012. "Sampling error and double shrinkage estimation of minimum variance portfolios," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 511-527.
    8. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Specification Choices in Quantile Regression for Empirical Macroeconomics," Working Papers 22-25, Federal Reserve Bank of Cleveland.
    9. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    10. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    11. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    12. Enrico Bergamini & Georg Zachmann, 2020. "Exploring EU’s Regional Potential in Low-Carbon Technologies," Sustainability, MDPI, vol. 13(1), pages 1-28, December.
    13. Qianyun Li & Runmin Shi & Faming Liang, 2019. "Drug sensitivity prediction with high-dimensional mixture regression," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-18, February.
    14. Jung, Yoon Mo & Whang, Joyce Jiyoung & Yun, Sangwoon, 2020. "Sparse probabilistic K-means," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    15. Christopher J Greenwood & George J Youssef & Primrose Letcher & Jacqui A Macdonald & Lauryn J Hagg & Ann Sanson & Jenn Mcintosh & Delyse M Hutchinson & John W Toumbourou & Matthew Fuller-Tyszkiewicz &, 2020. "A comparison of penalised regression methods for informing the selection of predictive markers," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    16. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    17. Soave, David & Lawless, Jerald F., 2023. "Regularized regression for two phase failure time studies," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    18. Moharil Janhavi & May Paul & Gaile Daniel P. & Blair Rachael Hageman, 2016. "Belief propagation in genotype-phenotype networks," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 15(1), pages 39-53, March.
    19. Won Hee Lee, 2023. "The Choice of Machine Learning Algorithms Impacts the Association between Brain-Predicted Age Difference and Cognitive Function," Mathematics, MDPI, vol. 11(5), pages 1-15, March.
    20. Mohammad Amin Amani & Mohammad Mahdi Nasiri, 2023. "A novel cross docking system for distributing the perishable products considering preemption: a machine learning approach," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-32, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:893-902. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.