A low cost and highly accurate technique for big data spatial-temporal interpolation

M. Esmaeilbeigi, O. Chatrabgoun, A. Hosseinian-Far, R. Montasari, A. Daneshkhah

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)
    73 Downloads (Pure)


    The high velocity, variety and volume of data generation by today's systems have necessitated Big Data (BD) analytic techniques. This has penetrated a wide range of industries; BD as a notion has various types and characteristics, and therefore a variety of analytic techniques would be required. The traditional analysis methods are typically unable to analyse spatial-temporal BD. Interpolation is required to approximate the values between the already existing data points, yet since there exist both location and time dimensions, only a multivariate interpolation would be appropriate. Nevertheless, existing software are unable to perform such complex interpolations. To overcome this challenge, this paper presents a layer by layer interpolation approach for spatial-temporal BD. Developing this layered structure provides the opportunity for working with much smaller linear system of equations. Consequently, this structure increases the accuracy and stability of numerical structure of the considered BD interpolation. To construct this layer by layer interpolation, we have used the good properties of Radial Basis Functions (RBFs). The proposed new approach is applied to numerical examples in spatial-temporal big data and the obtained results confirm the high accuracy and low computational cost. Finally, our approach is applied to explore one of the air pollution indices, i.e. daily PM2.5 concentration, based on different stations in the contiguous United States, and it is evaluated by leave-one-out cross validation.

    Original languageEnglish
    Pages (from-to)492-502
    Number of pages11
    JournalApplied Numerical Mathematics
    Early online date13 Mar 2020
    Publication statusPublished - 1 Jul 2020

    Bibliographical note

    NOTICE: this is the author’s version of a work that was accepted for publication in Applied Numerical Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Numerical Mathematics, 153, (2020) DOI: 10.1016/j.apnum.2020.03.009

    © 2020, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/


    UK Engineering & Physical Sciences Research Council (Strategic Package: Centre for Predictive Modelling in Science and Engineering - Grant No. EP/L027682/1)


    • Big data
    • Layer by layer interpolation
    • Radial basis functions
    • Spatial-temporal interpolation

    ASJC Scopus subject areas

    • Numerical Analysis
    • Computational Mathematics
    • Applied Mathematics


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