gw_nsprcomp {GWnnegPCA}

Geographically Weighted non-negative Principal Component Analysis

Description

Implementation of geographically weighted non-negative principal component analysis, whcih consists of the fusion of GWPCA and sparse non-negative PCA.

Usage

gw_nsprcomp(data, elocat, vars, bw, k = 2, kernel, adaptive = TRUE,
          p = 2, theta = 0, longlat = FALSE, geodisic_measure = "cheap",
          dMat = NULL, n.obs = NA, n.iter = 1, ncomp = k, nneg = TRUE,
          localcenter = TRUE, localscale = FALSE,...)

Arguments

data

a Spatial*DataFrame either SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp.

elocat

Same as GWmodel::gwpca. two-column numeric array or Spatial*DataFrame object for providing evaluation locations, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp.

vars

the number of retained components; k must be less than the number of variables.

bw

bandwidth used in the weighting function, possibly calculated by bw.gwpca;fixed (distance) or adaptive bandwidth(number of nearest neighbours).

k

the number of retained components; k must be less than the number of variables

kernel

Same as GWmodel::gwpca. Function chosen as follows: gaussian: wgt = exp(-.5*(vdist/bw)^2); exponential: wgt = exp(-vdist/bw); bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise; tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise; boxcar: wgt=1 if dist < bw, wgt=0 otherwise

see help(GWmodel::gw.weight) more detail.

adaptive

if TRUE calculate an adaptive kernel where the bandwidth corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance).

p

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

theta

an angle in radians to rotate the coordinate system, default is 0.

longlat

if TRUE, great circle distances will be calculated.

geodisic_measure

geodisic_measure is used when latlon coordinate. The distance is cauclated by geodist::geodist(). One of "haversine" "vincenty", "geodesic", or "cheap" specifying desired method of geodesic distance calculation. "Cheap" is the fastest way but may have errors if the ROI is large.

dMat

a pre-specified distance matrix, it can be calculated by the function gw.dist .

n.obs

Number of observations used to find the correlation matrix if using a correlation matrix. Used for finding the goodness of fit statistics. Must be specified if using a correlaton matrix and finding confidence intervals.

n.iter

Same as psych::fa. Number of bootstrap interations to do in fa or fa.poly

ncomp

the number of principal components (PCs) to be computed. With the default setting, PCs are computed until x is fully deflated. ncomp can be specified implicitly if k is given as a vector.

nneg

a logical value indicating whether the loadings should be non-negative, i.e. the PAs should be constrained to the non-negative orthant.

localcenter

If TRUE, local weighted x is centered. The default is TRUE.

localscale

If TRUE, local weighted x is scaled. The default is FALSE.

...

arguments passed to or from other methods.

Value

loadings

The localized loadings

score

The PC score by the localized non-negative PCA.

sdev

The localized standard deviation of the principal components.

Author(s)

N. Tsutsumida

References

Tsutsumida N., Murakami D.,Yoshida T., Nakaya T. Exploring geographically weighted non negative principal component analysis for producing index. The 27th meeting of GIS association of Japan, Tokyo, 20-21 October, 2018 (Japanese), http://www.gisa-japan.org/conferences/proceedings/2018/papers/C52.pdf

Tsutsumida N., Murakami D., Yoshida T., Nakaya T., Lu B., and P. Harris. Geographically Weighted Non-negative Principal Component Analysis for Exploring Spatial Variation in Multidimensional Composite Index, Geocomputation 2019, https://doi.org/10.17608/k6.auckland.9850826.v1

Examples

### This example is for demonstrating GWnnegPCA only.
### The application does not imply any reasonable meanings.

library(sp)
library(spData)
library(sf)

boston <- as(st_read(system.file("shapes/boston_tracts.shp",
                                 package="spData")[1]), "Spatial")
Data.scaled <- scale(as.matrix(boston@data[, c("AGE","RAD","TAX")]))
Coords <- as.matrix(cbind(boston$LON, boston$LAT))
Data.scaled.spdf <- SpatialPointsDataFrame(Coords, as.data.frame(Data.scaled))

gwnnegpca_ans <- gw_nsprcomp(
  data = Data.scaled.spdf,
  vars = colnames(Data.scaled.spdf@data),
  bw = 0.25,
  k = 3,
  longlat = TRUE,
  kernel="bisquare",
  adaptive = TRUE,
  nneg=TRUE,
  center=FALSE
)

boston$PC1_load_AGE <- gwnnegpca_ans$loadings[,"AGE","PC1"]
boston$PC1_load_RAD <- gwnnegpca_ans$loadings[,"RAD","PC1"]
boston$PC1_load_TAX <- gwnnegpca_ans$loadings[,"TAX","PC1"]

plot(st_as_sf(boston)[,c("PC1_load_AGE","PC1_load_RAD","PC1_load_TAX")])