#' Fuzzy Geographically Weighted Clustering (FGWC) optimized by Gravitational Search Algorithm
#'
#' @description 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
#'
#' @param X data frame n x p
#' @param population dataset 1 x n number of population each region (row)
#' @param distance shapefile or distance matrik n x n
#' @param K specific number of cluster (must be >1)
#' @param m fuzzifier / degree of fuzziness
#' @param beta proportion of geographically effect (if 0 equal Fuzzy C-Means)
#' @param a power for increase population effect
#' @param b power for increase distance effect
#' @param max.iteration maximum iteration to convergence
#' @param threshold threshold of convergence
#' @param RandomNumber specific seed
#'
#' @return func.obj objective function that calculated.
#' @return U matrix n x K consist fuzzy membership matrix
#' @return V matrix K x p consist fuzzy centroid
#' @return D matrix n x K consist distance of data to centroid that calculated
#' @return Clust.desc cluster description (dataset with additional column of cluster label)
#'
#' @examples
#' #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)
#'
#' @details 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.
#'
#' @details 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.
#'
#' @seealso \code{\link{fgwc}} for standard Fuzzy Geographically Weighted Clustering,
#' \code{\link{spClustIndex}} for cluser validation,
#' \code{\link{visualize}} for cluster visualizatiion,
#' \code{\link{scale}} for data scalling
#'
#' @references 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
#' @references Bezdek, J. C., Ehrlich, R., & Full, W. (1984). FCM: The Fuzzy C-Means Clustering Algorithm. Computers and Geosciences Vol 10, 191-203
#' @references Rashedi, E., Nezamabadi-pour, H., & S. Saryazdi. (2009). GSA: A Gravitational Search Algorithm. Information Sciences, vol. 179, no. 13, pp. 2232-224
#'
#' @import rgeos
#' @importFrom stats runif
#' @export
#'
fgwc.gsa<- function(X,population,distance,K=2,m=2,beta=0.5,a=1,b=1,max.iteration=100,threshold=10^-5,
RandomNumber=0) {
## Set data
data.X <- as.matrix(X)
population <- as.matrix(population)
n <- nrow(data.X)
p <- ncol(data.X)
alfa <- 1- beta
map <- NULL
if(is.matrix(distance)){
distance <- as.matrix(distance)
}else{
if (!requireNamespace("rgeos", quietly = TRUE)) {
stop("rgeos needed for this function to work. Please install it.",
call. = FALSE)
}
centroid <- gCentroid(distance,byid = T)
map <- distance
distance <- as.matrix(spDists(centroid, longlat=T))
}
##Initiation Parameter##
if ((K <= 1) || !(is.numeric(K)) || (K %% ceiling(K) > 0))
K = 2
if ( (m <= 1) || !(is.numeric(m)))
m = 2
if (RandomNumber > 0)
set.seed(RandomNumber)
## Membership Matrix U (n x K)
U <- matrix(runif(n * K,0,1),n,K)
## Prerequirement of U:
## Sum of membership on datum is 1
U <- U / rowSums(U)
## Centroid Matrix V (K x p)
V <- matrix(0,K,p)
## Distance Matrix
D <- matrix(0,n,K)
#GSA
pop <- nrow(data.X)
const <- 650
#velocity
Velocity <- matrix(0,n,K)
Vm <- Velocity
force <- matrix(0,K,pop)
#candidate solution
fitness <- vector("numeric")
CurrentFitness <- vector("numeric")
best <- vector("numeric")
worst <- vector("numeric")
mass <- vector("numeric")
Mass <- vector("numeric")
arrayBestfit <- vector("numeric")
fit <- vector("numeric")
#weighted membership matrix
mi.mj <- (population %*% t(population)) ^ b
diag(distance) <- Inf
weighted <- mi.mj / distance
#give weighted for membership
membership <- weighted%*%U
summ <- as.matrix(rowSums(membership))
#bagi tiap baris matriks U dengan pembagi
for(j in 1:K){
for(i in 1:n){
U[i,j] <- (alfa*U[i,j])+(beta*(membership[i,j]/summ[i,1]))
}
}
noAgen <- 0
t <- 0
while(t < max.iteration){
t <- t + 1
#acceleration
A <- matrix(0,nrow = pop,ncol = K)
#best fitness (minimal)
fmin <- Inf
for(iter in 1:pop){
#jumlah agen
noAgen <- (t-1)*pop+iter
G <- 1*exp(-5*iter)
#matrik partisi
U.old <- U
#calculate centroid
V <- t(U.old ^ m) %*% data.X / colSums(U.old ^ m)
for (k in 1:K)
{
#Distance calculation
for (i in 1:n)
{
D[i,k] = t(data.X[i,] - V[k,]) %*%
(data.X[i,] -V[k,])
}
}
#hitung jarak data ke pusat klaster
f <- sum(U.old ^ m * D)
fit[iter] <- f
CurrentFitness[noAgen] <- fit[iter]
fitness[noAgen] <- fit[iter]
if(fmin > fitness[noAgen]){
fmin <- fitness[noAgen]
}
arrayBestfit[noAgen] <- fmin
if(noAgen > 1){
if(abs(arrayBestfit[noAgen] - arrayBestfit[noAgen-1]) < threshold){
break
}
}
best[noAgen] <- min(CurrentFitness)
worst[noAgen] <- max(CurrentFitness)
for(i in 1:noAgen){
if( i == 1){
mass[noAgen] <- 0
}else{
mass[i] <- (CurrentFitness[i] - worst[noAgen])/(best[noAgen]-worst[noAgen])
}
}
for(i in 1:noAgen){
if( i == 1){
Mass[noAgen] <- 0
}else{
Mass[i] <- mass[i]*const/sum(mass)
}
}
#calculate force
if (noAgen==1){
force <- matrix(0,pop,K)
}else{
for(i in 2:iter){
for(j in 1:K){
for (l in 2:iter){
if (U.old[l,j]!=U.old[i,j]){
force[i,j] <- force[i,j]+ 0.9999 * G * (( Mass[l]* Mass[i] )/ ((U.old[l,j]-U.old[i,j])+0.000001 ))*(U.old[l,j]-U.old[i,j])
}
}
}
}
}
#calculate acceleration
for(i in 1:iter){
for (j in 1:K){
if (Mass[i] != 0){
A[i,j] <- force[i,j]/Mass[i]
}
}
}
#calculate velocity
for(i in 1:iter){
for (j in 1:K){
Vm[i,j] <- Velocity[i,j]
Velocity[i,j] <- Velocity[i,j]+A[i,j]
}
}
#new membership
for(i in 1:n){
for(l in 1:K){
pembilang <- 0
for(j in 1:p){
pembilang <- pembilang + abs(data.X[i,j] - V[l,j]) ^ 2
}
D[i,l] <- pembilang
}
}
# distout<-sqrt(dist)
# objVal<- membership0*dist
D <- (D)^(-1/(m-1))
U.old <- D/rowSums(D)%*%t(matrix(1,K))
#weigthing membership
membership <- weighted%*%U.old
summ <- as.matrix(rowSums(membership))
#bagi tiap baris matriks U dengan pembagi
for(j in 1:K){
for(i in 1:n){
U.old[i,j] <- (alfa*U.old[i,j])+(beta*(membership[i,j]/summ[i,1]))
}
}
U <- abs(U.old-Velocity)
}
if(noAgen > 1){
if(abs(arrayBestfit[noAgen] - arrayBestfit[noAgen-1]) < threshold){
break
}
}
}
#new membership
for(i in 1:n){
for(l in 1:K){
pembilang <- 0
for(j in 1:p){
pembilang <- pembilang + abs(data.X[i,j] - V[l,j]) ^ 2
}
D[i,l] <- pembilang
}
}
# distout<-sqrt(dist)
# objVal<- membership0*dist
D <- (D)^(-1/(m-1))
U <- D/rowSums(D)%*%t(matrix(1,K))
func.obj <- sum(U ^ m * D)
func.obj -> func.obj.opt
U -> U.opt
V -> V.opt
D -> D.opt
###Labelling###
colnames(U.opt) = paste("Clust",1:K,sep = " ")
Clust.desc <- matrix(0,n,p + 1)
rownames(Clust.desc) <- rownames(X)
colnames(Clust.desc) <- c(colnames(X),"cluster")
Clust.desc[,1:p] <- data.X
for (i in 1:n)
Clust.desc[i,p + 1] <- which.max(U.opt[i,])
result <- list()
result$func.obj <- func.obj.opt
result$U <- U.opt
result$V <- V.opt
result$D <- D.opt
result$m <- m
result$data <- data.X
result$call<-match.call()
result$Clust.desc <- Clust.desc
class(result)<-"fgwc-gsa"
print(result$U)
result$map <- map
return(result)
}
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