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Kriging Model with Fractional Euclidean Distance Matrices
Volume 30, Issue 2 (2019), pp. 367–390
Pub. online: 1 January 2019      Type: Research Article      Open accessOpen Access
Received
1 August 2018
Accepted
1 February 2019
Published
1 January 2019

Abstract

The multidimensional data model for kriging is developed using fractional Euclidean distance matrices (FEDM). The properties of FEDM are studied by means of the kernel matrix mehod. It has been shown that the factorization of kernel matrix enables us to create the embedded set being a nonsingular simplex. Using the properties of FEDM the Gaussian random field (GRF) is constructed doing it without positive definite correlation functions usually applied for such a purpose. Created GRF can be considered as a multidimensional analogue of the Wiener process, for instance, line realizations of this GRF are namely Wiener processes. Next, the kriging method is developed based on FEDM. The method is rather simple and depends on parameters that are simply estimated by the maximum likelihood method. Computer simulation of the developed kriging extrapolator has shown that it outperforms the well known Shepard inverse distance extrapolator. Practical application of the developed approach to surrogate modelling of wastewater treatment is discussed. Theoretical investigation, computer simulation, and a practical example demonstrate that the proposed kriging model, using FEDM, can be efficiently applied to multidimensional data modelling and processing.

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Biographies

Pozniak Natalija
natalija.pozniak@gmail.com

N. Pozniak is an external PhD student at Vilnius University Institute of Data Science and Digital Technologies.

Sakalauskas Leonidas
leonidas.sakalauskas@mii.vu.lt

L. Sakalauskas, Prof. Dr. Habil., is a principal researcher at Vilnius University Institute of Data Science and Digital Technologies. He is an associate professor at Vilnius Gediminas Technical University.

Saltyte Laura
laura.saltyte@ku.lt

L. Saltyte is an associate professor at Klaipėda University. Her research interests belong to statistical data analysis and artificial intelligence.


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© 2019 Vilnius University
Open access article under the CC BY license.

Keywords
scattered data fractional Euclidean distance matrices multivariate normal distribution homogeneous Gaussian field maximum likelihood

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