MixSim {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 - 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

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'.

If 'hom' is TRUE, only one of 'BarOmega' or 'MaxOmega' can be specified.

Value

Pi

vector of mixing proportions.

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 overlap.

MaxOmega

value of maximum overlap.

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.

Author(s)

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

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, 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

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))
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)