Scale-space module detection for irregular graphs

Bernard Chalmond (1) , Xiaoyi Chen (2)

1 CMLA - Centre de Mathématiques et de Leurs Applications
2 IP - Institut Pasteur [Paris]

In the spirit of Lindeberg's approach for image analysis on regular lattice, we adapt the blob detection procedure to irregular graphs from a statistical point of view. We treat data observed on an undirected graph in the goal of detecting salient modules. This task consists in seeking subgraphs whose activity is strong or weak compared to those of their neighbors. This is performed by analyzing nodes activity at multi-scale levels. To do that, data are seen as the occurrence of a random field, for which we propose a multi-scale graphical modeling. In the framework of diffusion processes, the covariance matrix of the random field is decomposed into a sum of weighted graph Laplacians at different scales. Under the assumption of Gaussian law, the maximum likelihood estimation of the weights is performed that provides a set of relevant scales. As a result, we obtain a multi-scale decomposition of the random field on which the module detection is based. This method is experimentally analyzed on simulated data and biological networks.

Mots clés: Blob Detection; Module Detection; Network Activity; Graphical Modeling; Scale-space Random Field; Graph Laplacian; Diffusion Kernel; Multi-scale Decomposition; Scale Selection

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Bernard Chalmond, Xiaoyi Chen. Scale-space module detection for irregular graphs. 2013. ⟨hal-00947472v1⟩