A topological index-based new smoother for spatial interpolation

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 topological-index 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 spatial-dependence based interpolation is performed by the topological information and structure-descriptive matrices. The determinant-based 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.