# Geographically Weighted Principal Components Analysis

# Module Description

This module implements basic or robust Geographically Weighted Principal Components Analysis[1]

# Argument

The arguments were taken from Gollini et al.[2]

`Variables`: a vector of variable names to be evaluated

`k`: the number of retained components; k must be less than the number of variable

`Kernel` : A set of five commonly used kernel functions;

`Robust`: if TRUE, robust GWPCA will be applied; otherwise basic GWPCA will be applied.

`Adaptive`: If TRUE, find an adaptive kernel with a bandwidth proportional to the number of nearest neighbors (i.e. adaptive distance); otherwise, find a fixed kernel (bandwidth is a fixed distance).

`longlat` : if TRUE, great circle distances will be calculated.

`Distance bandwidth`: bandwidth used in the weighting function. It has two options, `automatic` which is calculated in the Bandwidth selection module and `manual` in which the user enter the value.

`Power`: the power of the Minkowski distance,default is 2, i.e. the Euclidean distance.

`Theta (Angle in radians)`: an angle in radians to rotate the coordinate system, default is 0

# Value

Returns a list of class “gwpca” as Gwmodel Package [2]: * a list class object including the model fitting parameters for generating the report file;

- the localised loadings;

- a SpatialPointsDataFrame or SpatialPolygonsDataFrame object (see package “sp”) integrated with local proportions of variance for each principle components, cumulative proportion and winning variable for the first principle component in its “data” slot.

# Video

Video 1 : Geographically Weighted Principal Components Analysis

# References

[1] Harris P, Brunsdon C, Charlton M (2011) Geographically weighted principal components analysis. International Journal of Geographical Information Science 25:1717-1736. https://doi.org/10.1080/13658816.2011.554838

[2] Gollini, I., Lu, B., Charlton, M., Brunsdon, C., & Harris, P. (2015). GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models. Journal of Statistical Software, 63(17), 1–50. https://doi.org/10.18637/jss.v063.i17

[3] Harris P, Brunsdon C, Charlton M, Juggins S, Clarke A (2014) Multivariate spatial outlier detection using robust geographically weighted methods. Mathematical Geosciences 46(1) 1-31. https://doi.org/10.1007/s11004-013-9491-0

[4] Harris P, Clarke A, Juggins S, Brunsdon C, Charlton M (2015) Enhancements to a geographically weighted principal components analysis in the context of an application to an environmental data set. Geographical Analysis 47: 146-172. https://doi.org/10.1111/gean.12048