Model selection for Gaussian mixture model based on desirability level criterion

The expectation maximization (EM) algorithm is the most enduring way to estimate the parameters of Gaussian mixture models. However, use the EM algorithm needs to know in advance the true number of mixing components. Therefore, unless this key information is available, it is usually not straightforward to perform this algorithm. On the other hand, its performance highly depends on the initial parameters. To alleviate these problems, a new model selection criterion, i.e., the desirability level criterion, is proposed to choose the number of components. In particular, we proposed a variable step until find either coincides with the actual number or slightly exceeds it, which maximize the value of the desirability level criterion that provides an efficient index to quantify the distance between the Gaussian mixture model fits the observation data. Furthermore, unwanted components can be suppressed by setting the threshold of the desirability level criterion. Numerical examples are provided to illustrate the effectiveness of our desirability level criterion.