MixGOM: Mixture Simulation based on generalized overlap of Maitra

In MixSim: Simulating Data to Study Performance of Clustering Algorithms

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).

Details

Returns mixture parameters satisfying the prespecified level of goMega.

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.

Author(s)

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

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))

MixSim documentation built on Sept. 11, 2024, 9:08 p.m.