MixSim (version 0.1-02)

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 = 0, ecc = 0.90, PiLow = 1.0, Ubound = 1.0, resN = 100, eps = 1e-06, acc = 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 (0 - nonspherical, 1 - spherical)

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)

Ubound

upper bound for mean vectors; coordinates are simulated according to Uniform(0, Ubound)

resN

maximum number of dataset resimulations

eps

error bound for overlap computation

acc

error bound for integration (Davies, 1980)

lim

maximum number of integration terms (Davies, 1980)

Value

• Pi
  vector of mixing proprtions
• Mu
  matrix consisting of components' mean vectors (K x p)
• S
  set of components' covariance matrices (p x p x K)
• OmegaMap
  matrix of misclassification probabilities (K x 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 overap
• MaxOmega
  value of maximum overap
• 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

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. (200?) "Simulating data to study performance of finite mixture modeling and clustering algorithms", The Journal of Computational and Graphical Statistics.

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

See Also

overlap, pdplot, simdataset

Examples

# controls average and maximum overlaps
MixSim(BarOmega = 0.05, MaxOmega = 0.15, K = 4, p = 5) 

# controls average overlap
MixSim(BarOmega = 0.05, , K = 4, p = 5)

# controls maximum overlap
MixSim( , MaxOmega = 0.15, K = 4, p = 5)