**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Inverse distance weighting

Summary

Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I).
The name given to this type of method was motivated by the weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights.
The expected result is a discrete assignment of the unknown function in a study region:
where is the study region.
The set of known data points can be described as a list of tuples:
The function is to be "smooth" (continuous and once differentiable), to be exact () and to meet the user's intuitive expectations about the phenomenon under investigation. Furthermore, the function should be suitable for a computer application at a reasonable cost (nowadays, a basic implementation will probably make use of parallel resources).
At the Harvard Laboratory for Computer Graphics and Spatial Analysis, beginning in 1965, a varied collection of scientists converged to rethink, among other things, what are now called geographic information systems.
The motive force behind the Laboratory, Howard Fisher, conceived an improved computer mapping program that he called SYMAP, which, from the start, Fisher wanted to improve on the interpolation. He showed Harvard College freshmen his work on SYMAP, and many of them participated in Laboratory events. One freshman, Donald Shepard, decided to overhaul the interpolation in SYMAP, resulting in his famous article from 1968.
Shepard's algorithm was also influenced by the theoretical approach of William Warntz and others at the Lab who worked with spatial analysis. He conducted a number of experiments with the exponent of distance, deciding on something closer to the gravity model (exponent of -2).

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (32)

Related people (1)

Related concepts (5)

Tobler's first law of geography

The First Law of Geography, according to Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things." This first law is the foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method for spatial interpolation and to support the regionalized variable theory for kriging. The first law of geography is the fundamental assumption used in all spatial analysis.

Spatial analysis

Spatial analysis is any of the formal techniques which studies entities using their topological, geometric, or geographic properties. Spatial analysis includes a variety of techniques using different analytic approaches, especially spatial statistics. It may be applied in fields as diverse as astronomy, with its studies of the placement of galaxies in the cosmos, or to chip fabrication engineering, with its use of "place and route" algorithms to build complex wiring structures.

Tobler's second law of geography

The second law of geography, according to Waldo Tobler, is "the phenomenon external to a geographic area of interest affects what goes on inside." This is an extension of his first. He first published it in 1999 in reply to a paper titled "Linear pycnophylactic reallocation comment on a paper by D. Martin" and then again in response to criticism of his first law of geography titled "On the First Law of Geography: A Reply." Much of this criticism was centered on the question of if laws were meaningful in geography or any of the social sciences.

Related lectures (12)

Spatial Autocorrelation: Significance Analysis

Explains the significance analysis of spatial autocorrelation using Moran's I and random permutations, emphasizing the importance of spatial weighting.

Spatial Autocorrelation: Moran's I

Explores Moran's I for assessing spatial clustering in geographical data using precipitation as an example.

Geographically Weighted Regression

Introduces Geographically Weighted Regression, a spatially explicit approach to measure relationships between variables with location-specific outputs.

Objectives : This study aimed to examine associations between mood disorders and cognitive impairments with environmental neighborhood attributes and evaluate their effects on brain plasticity. Setting: Lausanne and Outskirts. Methods: Multiscale and simpl ...

2020In the literature, the plane-strain assumption usually forms the basis of inverse analyses of excavations, mainly due to the high computational cost of 3D analyses. In this paper, a procedure that quantifies three-dimensional effects of excavation is propo ...

Eugen Brühwiler, Emmanuel Denarié, Xiujiang Shen

The equi-biaxial tensile properties of strain-hardening UHPFRC are determined and investigated based on an original analytical inverse analysis of results from ring-on-ring tests. First, the analytical inverse analysis method is developed based on the elas ...

2020