Ising Model for Interpolation of Spatial Data on Regular Grids
We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well a...
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MDPI AG
2021-09-01
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| Online Access: | https://www.mdpi.com/1099-4300/23/10/1270 |
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| author | Milan Žukovič Dionissios T. Hristopulos |
| author_facet | Milan Žukovič Dionissios T. Hristopulos |
| author_sort | Milan Žukovič |
| collection | DOAJ |
| description | We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images. |
| first_indexed | 2024-03-10T06:34:32Z |
| format | Article |
| id | doaj.art-478cb0ac6b2b433696dd5e973b17af1d |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T06:34:32Z |
| publishDate | 2021-09-01 |
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| spelling | doaj.art-478cb0ac6b2b433696dd5e973b17af1d2023-11-22T18:10:25ZengMDPI AGEntropy1099-43002021-09-012310127010.3390/e23101270Ising Model for Interpolation of Spatial Data on Regular GridsMilan Žukovič0Dionissios T. Hristopulos1Department of Theoretical Physics and Astrophysics, Faculty of Science, Pavol Jozef Šafárik University in Košice, Park Angelinum 9, 04154 Košice, SlovakiaSchool of Electrical & Computer Engineering, Technical University of Crete, 73100 Chania, GreeceWe apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images.https://www.mdpi.com/1099-4300/23/10/1270Ising modelspatial classificationinterpolationnon-Gaussian dataearth observationfast algorithm |
| spellingShingle | Milan Žukovič Dionissios T. Hristopulos Ising Model for Interpolation of Spatial Data on Regular Grids Entropy Ising model spatial classification interpolation non-Gaussian data earth observation fast algorithm |
| title | Ising Model for Interpolation of Spatial Data on Regular Grids |
| title_full | Ising Model for Interpolation of Spatial Data on Regular Grids |
| title_fullStr | Ising Model for Interpolation of Spatial Data on Regular Grids |
| title_full_unstemmed | Ising Model for Interpolation of Spatial Data on Regular Grids |
| title_short | Ising Model for Interpolation of Spatial Data on Regular Grids |
| title_sort | ising model for interpolation of spatial data on regular grids |
| topic | Ising model spatial classification interpolation non-Gaussian data earth observation fast algorithm |
| url | https://www.mdpi.com/1099-4300/23/10/1270 |
| work_keys_str_mv | AT milanzukovic isingmodelforinterpolationofspatialdataonregulargrids AT dionissiosthristopulos isingmodelforinterpolationofspatialdataonregulargrids |