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Inverse Distance Weighting as a sum of all weighting functions for each sample point. Each function has the value of one of the samples at its sample point and zero at every other sample point. Inverse distance weighting ( IDW ) is a type of deterministic method for multivariate interpolation with a known scattered set of points.
Natural neighbor interpolation with Sibson weights. The area of the green circles are the interpolating weights, w i.The purple-shaded region is the new Voronoi cell, after inserting the point to be interpolated (black dot).
Inverse distance weighting; Radial basis function (RBF) — a function of the form ƒ(x) = φ(|x−x 0 |) Polyharmonic spline — a commonly used radial basis function; Thin plate spline — a specific polyharmonic spline: r 2 log r; Hierarchical RBF; Subdivision surface — constructed by recursively subdividing a piecewise linear interpolant
Compute the Euclidean or Mahalanobis distance from the query example to the labeled examples. Order the labeled examples by increasing distance. Find a heuristically optimal number k of nearest neighbors, based on RMSE. This is done using cross validation. Calculate an inverse distance weighted average with the k-nearest multivariate neighbors.
Inverse distance weighting; ABOS - approximation based on smoothing; Kriging; Gradient-enhanced kriging (GEK) Thin plate spline; Polyharmonic spline (the thin-plate-spline is a special case of a polyharmonic spline) Radial basis function (Polyharmonic splines are a special case of radial basis functions with low degree polynomial terms) Least ...
The concept of a spatial weight is used in spatial analysis to describe neighbor relations between regions on a map. [1] If location i {\displaystyle i} is a neighbor of location j {\displaystyle j} then w i j ≠ 0 {\displaystyle w_{ij}\neq 0} otherwise w i j = 0 {\displaystyle w_{ij}=0} .
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Elastic map (a discrete version of the thin plate approximation for manifold learning) Inverse distance weighting; Polyharmonic spline (the thin plate spline is a special case of a polyharmonic spline) Radial basis function; Smoothing spline; Spline; Subdivision surface (emerging alternative to spline-based surfaces)