MixSim (version 1.0-3)

MixSim: Mixture Simulation

Description

Generates a finite mixture model with Gaussian components for prespecified levels of maximum and/or average overlaps.

Usage

MixSim(BarOmega = NULL, MaxOmega = NULL, K, p, sph = FALSE, hom = FALSE,
       ecc = 0.90, PiLow = 1.0, int = c(0.0, 1.0), resN = 100,
       eps = 1e-06, lim = 1e06)

Arguments

BarOmega

value of desired average overlap.

MaxOmega

value of desired maximum overlap.

K

number of components.

p

number of dimensions.

sph

covariance matrix structure (FALSE - nonspherical, TRUE - spherical).

hom

heterogeneous or homogeneous clusters (FALSE - heterogeneous, TRUE - homogeneous).

ecc

maximum eccentricity.

PiLow

value of the smallest mixing proportion (if 'PiLow' is not reachable with respect to K, equal proportions are taken; PiLow = 1.0 implies equal proportions by default).

int

mean vectors are simulated uniformly on a hypercube with sides specified by int = (lower.bound, upper.bound).

resN

maximum number of mixture resimulations.

eps

error bound for overlap computation.

lim

maximum number of integration terms (Davies, 1980).

Value

• Pi
  vector of mixing proprtions.
• Mu
  matrix consisting of components' mean vectors (K * p).
• S
  set of components' covariance matrices (p * p * K).
• OmegaMap
  matrix of misclassification probabilities (K * K); OmegaMap[i,j] is the probability that X coming from the i-th component is classified to the j-th component.
• BarOmega
  value of average overap.
• MaxOmega
  value of maximum overap.
• rcMax
  row and column numbers for the pair of components producing maximum overlap 'MaxOmega'.
• fail
  flag value; 0 represents successful mixture generation, 1 represents failure.

Details

If 'BarOmega' is not specified, the function generates a mixture solely based on 'MaxOmega'; if 'MaxOmega' is not specified, the function generates a mixture solely based on 'BarOmega'.

References

Maitra, R. and Melnykov, V. (2010) ``Simulating data to study performance of finite mixture modeling and clustering algorithms'', The Journal of Computational and Graphical Statistics, 2:19, 354-376.

Melnykov, V., Chen, W.-C., and Maitra, R. (2012) ``MixSim: An R Package for Simulating Data from Finite Gaussian Mixtures to Study Performance of Clustering Algorithms'', Journal of Statistical Software, (submitted).

Davies, R. (1980) ``The distribution of a linear combination of chi-square random variables'', Applied Statistics, 29, 323-333.

See Also

overlap, pdplot, and simdataset.

Examples

set.seed(1234)

# controls average and maximum overlaps
ex.1 <- MixSim(BarOmega = 0.05, MaxOmega = 0.15, K = 4, p = 5)
print(ex.1)
summary(ex.1)

# controls average overlap
ex.2 <- MixSim(BarOmega = 0.05, K = 4, p = 5, hom = TRUE)
print(ex.2)
summary(ex.2)

# controls maximum overlap
ex.3 <- MixSim(MaxOmega = 0.15, K = 4, p = 5, sph = TRUE)
print(ex.3)
summary(ex.3)