MixSim (version 1.1-2)

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)

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).

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.

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))