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.

中文翻译：

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基于拓扑索引的用于空间插值的新平滑器

确定性插值可以通过仅调整有限数量的参数来自动应用。尽管使用映射是一种简单的方法，但是数据集中潜在的空间关系被广泛省略。为了表示空间关系，已经引入了基于拓扑索引的插值（TIBI）。基于权重的平滑使用图论，它可以像在有机化学中使用的分子图一样对空间结构进行数字化表征。作为图不变式，拓扑索引具有使用矩阵运算获得结构上的关系（如邻域和距离）的能力。因此，通过拓扑信息和结构描述矩阵执行基于空间依赖性的插值。基于行列式的逆加权为全局和局部解提供了机会。与加权确定性模型（例如ISDW）相比，TIBI方法的主要优势在于它能够基于生成拓扑搜索来提供区域变化的间接信息。的TIBI方法不需要像k- NN中那样的用户定义的邻居数，也不需要严格的权重求和条件。实验研究和比较评估表明该方法具有鲁棒性和透明性。