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.

number of components.

number of dimensions.

sph

covariance matrix structure (FALSE - non-spherical, 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

Pivector of mixing proportions.
Mumatrix consisting of components' mean vectors (K * p).
Sset of components' covariance matrices (p * p * K).
OmegaMapmatrix 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.
BarOmegavalue of average overlap.
MaxOmegavalue of maximum overlap.
rcMaxrow and column numbers for the pair of components producing maximum overlap 'MaxOmega'.
failflag 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 to Study Performance of Clustering Algorithms'', Journal of Statistical Software, (accepted).

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

Examples

Run this code

set.seed(1234)

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

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

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

Run the code above in your browser using DataLab