Inverse Distance Weighting

Properties2

Type	Concept
Note created	Feb 17, 2025

Inverse distance weighting is a type of deterministic method for spatial interpolation, even though it also can be used to create spatial weight matrices in spatial autocorrelation methods like Moran’s I.

It is traditionally defined as $u(x)$, where:

$$u(x)=\frac{{\sum }_{i=1}^N{w}_i(x)u_i}{{\sum }_{i=1}^N{w}_i(x)}$$

Where $x$ is an arbitrary point (to interpolate), $x_i$ is a known point (whose value is $u_i$) and $w_i(x)$ is the weight function to the point $x_i$ defined as:

$$w_i(x)=\frac{1}{d(x,x_i{)}^p}$$

Where $d$ is the distance function and $p$ is a positive real number known as the power parameter.