A topological index-based new smoother for spatial interpolation
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METHODOLOGY ARTICLE
A topological index-based new smoother for spatial interpolation Ibrahim Duman 1 & Bulent Tutmez 1 Received: 29 April 2019 / Accepted: 30 January 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Deterministic interpolation can be applied automatically by tuning only limited number of parameters. Although it is an easy way to use mapping, potential spatial relationships in a data set are widely omitted. To represent spatial relationships, a topologicalindex based interpolation (TIBI) has been introduced. The weighting-based smoothing uses graph theory and it numerically characterizes spatial structures as in molecular graphs utilized in organic chemistry. As a graph invariant, the topological index has ability to obtain the relationships in structure such as neighborhood and distance using matrix operations. Thus, a spatialdependence based interpolation is performed by the topological information and structure-descriptive matrices. The determinantbased inverse weighting provides opportunity for both global and local solutions. The maim superiority of the TIBI method compared with weighted deterministic models such as ISDW is its ability to provide indirect information of areal variability based on generating a topological search. The TIBI method does not require a user-defined number of neighbors like in k-NN and also does not need strict conditions for summation of weights. The experimental studies and comparative evaluations showed that the method has robustness and transparency. Keywords Spatial interpolation . Graph theory . Topological index . Inverse weighting . Search domain
Introduction In spatial science, the selection of a model relies on the interpretation of the spatial data either deterministic or statistics with the excluding science-based physical models. Deterministic interpolation (DI) is a popular method in visualisation and it is easy to use so that it can be practiced automatically by tuning only limit number of parameters. However, the well-known DI methods such as Voronoi polygons and inverse square distance weighting (ISDW) do Highlights - The method has ability to identify spatial structure as in molecular graphs. - Spatial interpolation is performed by the topological index and descriptive matrices. - Determinant-based inverse weighting provides an opportunity for both global and local solution. - The new smoother has robustness and transparency. Communicated by: H. Babaie * Bulent Tutmez [email protected] 1
Department of Mining Engineering, Inonu University, 44280 Malatya, Turkey
not consider spatial correlations in a data set. Further, the smoothing effect has been appeared a problem on local variability. The smoothing created by these methods yield a reverse trend for high and low values recorded in practice (Kanevski et al. 2009). To overcome the structural problems and represent the spatial uncertainty in interpolation, spatial information science require weighting and different model perspectives such as deterministic and geos
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