Finite mixture models with log-normal and normal distributions among the optimization methods

Music City Center 

Finite mixture models have been used to cluster data into different groups based on statistical distribution. In flow cytometry, for example, we applied finite mixture model using a multivariate log-normal distribution and normal distributions to identify the cell populations of mixture of pollen. an expectation–maximization (EM) algorithm is used to approximate parameters by maximum likelihood estimation. Maximum likelihood estimation is used on the M step, so we apply other optimization methods such as Gradient descent, Stochastic gradient descent and Newton-Raphson to estimate the parameters of the finite mixture models.
In terms of comparison, we simulated a data set that has three clusters. Samples in the first cluster have a multivariate log-normal distribution while samples in other clusters have multivariate normal distributions with different mean. Processing of time, accuracy, bias, and MSE will be provided to compare to performance of these optimization methods.

Finite mixture models

EM algorithm

Optimization 

Section on Statistical Learning and Data Science