CLUSTERING VARIABLES WITH DAG STRUCTURE

A gene regulatory network (GRN) is a directed graph in which each node corresponds to a gene and each edge to a direct regulatory interaction. Clustering techniques have been largely used with the main purpose of identified clusters of genes that constitutes relevant functional structures. We represents the GRN by means of directed acyclic graph (DAG) model and examine the identification of transcriptions by using different measures based on Wilks' Lambda in a hierarchical clustering context. These measures are based on the determinant of the correlation matrix of the two groups of variables compared and are in relationship with the canonical correlations. It follows that they stress the multivariate dependence relationships between sets of variables removing the within-group correlation. We focus on some particular DAG structures and investigate the properties of these measures comparing them with those of the average linkage rule based on the "1 - squared correlation coefficient''.