a principal cluster. We identified as significant, all those peaks with a surface density above 1.0 stars per sq. arcmin (see $\S$\[s:analysis:ss:ysodist:sss:gather\], below).

### Identification of Principal Clusters \[s:analysis:ss:ysodist:sss:GMM\]

In order to delimit individual clusters, we employed a Gaussian Mixture Model (GMM) analysis via the `mclust` package on the `R` code [@Banfield:1993xy; @Fraley:2002qf; @Raftery:2012nr]. The package provides a model-based clustering analysis of any population, based on covariance parametrization and an Expectation-Minimization (EM) algorithm. It can also divide a population in an optimized number of clusters by means of the Bayesian Information Criterion (BIC). The BIC is the value of the maximized log-likelihood with a penalty on the number of model parameters, and allows comparison of models with different parameter sets as well as solutions with different numbers of clusters.

![Identification of principal clusters in the W3 region using a Gaussian Model Mixture (GMM). This five cluster model, applied to projected distribution of the population of Class II YSO candidates in the region provides the optimal mixture based on a Bayesian Information Criterion (BIC). The circles are placed at the cluster centers determined by the GMM analysis and have radii equal to the Gaussian $\sigma$. \[fig:GMM\]](./f6.eps){width="6.2in"}

We chose the Class II 