Semi-Supervised Gaussian Mixture Model with a Missing-Data Mechanism
Classifier based on Bayes rule
Transform a variance matrix into a vector
Discriminant function
Fitting Gaussian mixture models
Error rate of the Bayes rule for two-class Gaussian homoscedastic mode...
Posterior probability
Shannon entropy
Initial values for ECM
Transfer a list into a vector
Full log-likelihood function
Log likelihood for partially classified data with ingoring the missing...
Log likelihood function formed on the basis of the missing-label indic...
log summation of exponential function
Label matrix
Negative objective function for EMMIXSSL
Normalize log-probability
Transfer a vector into a list
Transfer a probability vector into a vector
Generation of a missing-data indicator
Normal mixture model generator.
Transform a vector into a matrix
Transfer an informative vector to a probability vector
The algorithm of semi-supervised learning based on finite Gaussian mixture models with a missing-data mechanism is designed for a fitting g-class Gaussian mixture model via maximum likelihood (ML). It is proposed to treat the labels of the unclassified features as missing-data and to introduce a framework for their missing as in the pioneering work of Rubin (1976) for missing in incomplete data analysis. This dependency in the missingness pattern can be leveraged to provide additional information about the optimal classifier as specified by Bayes’ rule.