Clustering for Continuous Fuzzy Data — fuzcluster • sirt

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)

# S3 method for fuzcluster
summary(object,...)

Arguments

dat_m: Centers for individual item specific membership functions
dat_s: Standard deviations for individual item specific membership functions
K: 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

deviance: Deviance
iter: Number of iterations
pi_est: Estimated class probabilities
mu_est: Cluster means
sd_est: Cluster standard deviations
posterior: Individual posterior distributions of cluster membership
seed: Simulation seed for cluster solution
ic: Information criteria

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.

See also

See fuzdiscr for estimating discrete distributions for fuzzy data.

See the fclust package for fuzzy clustering.

Examples

if (FALSE) {
#############################################################################
# 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 <- sirt::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 <- sirt::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 <- sirt::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
}