fuzcluster: Clustering for Continuous Fuzzy Data

Description

This function performs clustering for continuous fuzzy data for which membership functions are assumed to be Gaussian (Denoeux, 2013). The mixture is also assumed to be Gaussian and (conditionally cluster membership) independent.

Usage

fuzcluster(dat_m, dat_s, K = 2, nstarts = 7, seed = NULL, maxiter = 100,  parmconv = 0.001, fac.oldxsi=0.75, progress = TRUE)
"summary"(object,...)

Arguments

dat_m

Centers for individual item specific membership functions

dat_s

Standard deviations for individual item specific membership functions

Number of latent classes

nstarts

Number of random starts. The default is 7 random starts.

seed

Simulation seed. If one value is provided, then only one start is performed.

maxiter

Maximum number of iterations

parmconv

Maximum absolute change in parameters

fac.oldxsi

Convergence acceleration factor which should take values between 0 and 1. The default is 0.75.

progress

An optional logical indicating whether iteration progress should be displayed.

object

Object of class fuzcluster

...

Further arguments to be passed

Value

A list with following entries

References

Denoeux, T. (2013). Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Transactions on Knowledge and Data Engineering, 25, 119-130.

Examples

Run this code

## Not run: 
# #############################################################################
# # EXAMPLE 1: 2 classes and 3 items
# #############################################################################
# 
# #*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
# # simulate data (2 classes and 3 items)
# set.seed(876)
# library(mvtnorm)
# Ntot <- 1000  # number of subjects
# # define SDs for simulating uncertainty
# sd_uncertain <- c( .2 , 1 , 2 )
# 
# dat_m <- NULL   # data frame containing mean of membership function
# dat_s <- NULL   # data frame containing SD of membership function
# 
# # *** Class 1
# pi_class <- .6
# Nclass <- Ntot * pi_class
# mu <- c(3,1,0)
# Sigma <- diag(3)
# # simulate data
# dat_m1 <- mvtnorm::rmvnorm( Nclass , mean=mu , sigma = Sigma )
# dat_s1 <- matrix( stats::runif( Nclass * 3 ) , nrow=Nclass )
# for ( ii in 1:3){ dat_s1[,ii] <- dat_s1[,ii] * sd_uncertain[ii] }
# dat_m <- rbind( dat_m , dat_m1 )
# dat_s <- rbind( dat_s , dat_s1 )
# 
# # *** Class 2
# pi_class <- .4
# Nclass <- Ntot * pi_class
# mu <- c(0,-2,0.4)
# Sigma <- diag(c(0.5 , 2 , 2 ) )
# # simulate data
# dat_m1 <- mvtnorm::rmvnorm( Nclass , mean=mu , sigma = Sigma )
# dat_s1 <- matrix( stats::runif( Nclass * 3 ) , nrow=Nclass )
# for ( ii in 1:3){ dat_s1[,ii] <- dat_s1[,ii] * sd_uncertain[ii] }
# dat_m <- rbind( dat_m , dat_m1 )
# dat_s <- rbind( dat_s , dat_s1 )
# colnames(dat_s) <- colnames(dat_m) <- paste0("I" , 1:3 )
# 
# #*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
# # estimation
# 
# #*** Model 1: Clustering with 8 random starts
# res1 <- fuzcluster(K=2,dat_m , dat_s , nstarts = 8 , maxiter=25)
# summary(res1)
#   ##  Number of iterations = 22 (Seed = 5090 ) 
#   ##  --------------------------------------------------- 
#   ##  Class probabilities (2 Classes) 
#   ##  [1] 0.4083 0.5917
#   ##  
#   ##  Means
#   ##           I1      I2     I3
#   ##  [1,] 0.0595 -1.9070 0.4011
#   ##  [2,] 3.0682  1.0233 0.0359
#   ##  
#   ##  Standard deviations
#   ##         [,1]   [,2]   [,3]
#   ##  [1,] 0.7238 1.3712 1.2647
#   ##  [2,] 0.9740 0.8500 0.7523
# 
# #*** Model 2: Clustering with one start with seed 4550
# res2 <- fuzcluster(K=2,dat_m , dat_s , nstarts = 1 , seed= 5090 )
# summary(res2)
# 
# #*** Model 3: Clustering for crisp data 
# #             (assuming no uncertainty, i.e. dat_s = 0)
# res3 <- fuzcluster(K=2,dat_m , dat_s=0*dat_s , nstarts = 30 , maxiter=25)
# summary(res3)
#   ##  Class probabilities (2 Classes) 
#   ##  [1] 0.3645 0.6355
#   ##  
#   ##  Means
#   ##           I1      I2      I3
#   ##  [1,] 0.0463 -1.9221  0.4481
#   ##  [2,] 3.0527  1.0241 -0.0008
#   ##  
#   ##  Standard deviations
#   ##         [,1]   [,2]   [,3]
#   ##  [1,] 0.7261 1.4541 1.4586
#   ##  [2,] 0.9933 0.9592 0.9535
# 
# #*** Model 4: kmeans cluster analysis
# res4 <- stats::kmeans( dat_m , centers = 2 )
#   ##   K-means clustering with 2 clusters of sizes 607, 393
#   ##   Cluster means:
#   ##             I1        I2          I3
#   ##   1 3.01550780  1.035848 -0.01662275
#   ##   2 0.03448309 -2.008209  0.48295067
# ## End(Not run)