Extract eigenfunctions of a connectivity matrix for spatial filtering

make_EV(C, nsa = FALSE, threshold = 0.2, values = FALSE)

Source

Daniel Griffith and Yongwan Chun. 2014. "Spatial Autocorrelation and Spatial Filtering." in M. M. Fischer and P. Nijkamp (eds.), Handbook of Regional Science. Springer.

Arguments

C: A binary spatial weights matrix. See shape2mat.
nsa: Logical. Default of nsa = FALSE excludes eigenvectors capturing negative spatial autocorrelation. Setting nsa = TRUE will result in a candidate set of EVs that contains eigenvectors representing positive and negative SA.
threshold: Defaults to threshold=0.2 to exclude eigenvectors representing spatial autocorrelation levels that are less than threshold times the maximum possible Moran coefficient achievable for the given spatial connectivity matrix. If theshold = 0, all eigenvectors will be returned (however, the eigenvector of constants (with eigenvalue of zero) will be dropped automatically).
values: Should eigenvalues be returned also? Defaults to FALSE.

Value

A data.frame of eigenvectors for spatial filtering. If values=TRUE then a named list is returned with elements eigenvectors and eigenvalues.

Details

Returns a set of eigenvectors related to the Moran coefficient (MC), limited to those eigenvectors with |MC| > threshold if nsa = TRUE or MC > threshold if nsa = FALSE, optionally with corresponding eigenvalues.

Examples

library(ggplot2)
data(georgia)
C <- shape2mat(georgia, style = "B")
EV <- make_EV(C)
head(EV)

ggplot(georgia) +
  geom_sf(aes(fill = EV[,1])) +
  scale_fill_gradient2()