MixSim (version 1.1-8)

MixGOM: Mixture Simulation based on generalized overlap of Maitra

Description

Generates a finite mixture model with Gaussian components for a prespecified level of goMega (generalized overlap of Maitra).

Usage

MixGOM(goMega = 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)

Value

Pi

vector of mixing proportions.

Mu

matrix consisting of components' mean vectors (K * p).

S

set of components' covariance matrices (p * p * K).

goMega

value of generalized overlap of Maitra.

fail

flag value; 0 represents successful mixture generation, 1 represents failure.

Arguments

goMega

value of desired generalized overlap of Maitra.

K

number of components.

p

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).

Author

Volodymyr Melnykov, Wei-Chen Chen, and Ranjan Maitra.

Details

Returns mixture parameters satisfying the prespecified level of goMega.

References

Maitra, R. (2010) ``A re-defined and generalized percent-overlap-of-activation measure for studies of fMRI reproducibility and its use in identifying outlier activation maps'', NeuroImage, 50, 124-135.

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, 51:12, 1-25.

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

See Also

overlapGOM, MixSim, and simdataset.

Examples

set.seed(1234)

# controls average and maximum overlaps
(ex.1 <- MixGOM(goMega = 0.05, K = 4, p = 5))

# controls maximum overlap
(ex.2 <- MixGOM(goMega = 0.15, K = 4, p = 5, sph = TRUE))