fgwc.gsa: Fuzzy Geographically Weighted Clustering (FGWC) optimized by...
In spatialClust: Spatial Clustering using Fuzzy Geographically Weighted Clustering

Description Usage Arguments Details Value References See Also Examples

View source: R/fgwcgsa.R

This function used to perform Fuzzy Geographically Weighted Clustering of X dataset. by using this function the initialization phase of FGWC will be optimized using Gravitational Search Algorithm

1 2	fgwc.gsa(X, population, distance, K = 2, m = 2, beta = 0.5, a = 1, b = 1, max.iteration = 100, threshold = 10^-5, RandomNumber = 0)

`X`	data frame n x p
`population`	dataset 1 x n number of population each region (row)
`distance`	shapefile or distance matrik n x n
`K`	specific number of cluster (must be >1)
`m`	fuzzifier / degree of fuzziness
`beta`	proportion of geographically effect (if 0 equal Fuzzy C-Means)
`a`	power for increase population effect
`b`	power for increase distance effect
`max.iteration`	maximum iteration to convergence
`threshold`	threshold of convergence
`RandomNumber`	specific seed

This function perform Fuzzy Geographically Weighted Clustering optimized using Gravitational Search Algorithm(GSA). using this method the initilitation phase will be handle by GSA to get optimal result. Number of cluster (K) must be greater than 1. To control the overlaping or fuzziness of clustering, parameter m must be specified. Maximum iteration and threshold is specific number for convergencing the cluster. Random Number is number that will be used for seeding to firstly generate fuzzy membership matrix. population dataset, shapefile or distance matrix is used to give geographically weighted for membership matrix.

Clustering will produce fuzzy membership matrix (U) and fuzzy cluster centroid (V). The greatest value of membership on data point will determine cluster label. Centroid or cluster center can be use to interpret the cluster. Both membership and centroid produced by calculating mathematical distance. Fuzzy Geographically Weighted Clustering calculate distance with Euclideans norm. So it can be said that cluster will have sperichal shape of geometry.

func.obj objective function that calculated.

U matrix n x K consist fuzzy membership matrix

V matrix K x p consist fuzzy centroid

D matrix n x K consist distance of data to centroid that calculated

Clust.desc cluster description (dataset with additional column of cluster label)

G. A. Mason and R. D. Jacobson.(2007). Fuzzy Geographically Weighted Clustering, in Proceedings of the 9th International Conference on Geocomputation, no. 1998, pp. 1-7

Bezdek, J. C., Ehrlich, R., & Full, W. (1984). FCM: The Fuzzy C-Means Clustering Algorithm. Computers and Geosciences Vol 10, 191-203

Rashedi, E., Nezamabadi-pour, H., & S. Saryazdi. (2009). GSA: A Gravitational Search Algorithm. Information Sciences, vol. 179, no. 13, pp. 2232-224

fgwc for standard Fuzzy Geographically Weighted Clustering, spClustIndex for cluser validation, visualize for cluster visualizatiion, scale for data scalling

#load data example
X <- example

#if using matrix distance
distance <- dist

#if using shapefile
#library(rgdal) for call readOGR
#distance <- readOGR(dsn = 'folder/.',"shapefile name")

#load population data
pop <- population

clust <- fgwc(X,pop,distance,K=2,m=1.5,beta=0.5)