A Joint Markov Model for Communities, Connectivity and Signals Defined Over Graphs

Stefania Colonnese (1) , Paolo Di Lorenzo (1) , Tiziana Cattai (2, 3, 4, 5, 1) , Gaetano Scarano (1) , Fabrizio de Vico Fallani (2, 3, 4, 5)

1 DIET - Dipartimento di Ingegneria dell'Informazione, Elettronica e Telecomunicazioni [Roma]
2 ARAMIS - Algorithms, models and methods for images and signals of the human brain = Algorithmes, modèles et méthodes pour les images et les signaux du cerveau humain [ICM Paris]
3 ICM - Institut du Cerveau = Paris Brain Institute
4 INSERM - Institut National de la Santé et de la Recherche Médicale
5 SU - Sorbonne Université

Real-world networks are typically described in terms of nodes, links, and communities, having signal values often associated with them. The aim of this letter is to introduce a novel Compound Markov random field model (Compound MRF, or CMRF) for signals defined over graphs, encompassing jointly signal values at nodes, edge weights, and community labels. The proposed CMRF generalizes Markovian models previously proposed in the literature, since it accounts for different kinds of interactions between communities and signal smoothness constraints. Finally, the proposed approach is applied to (joint) graph learning and signal recovery. Numerical results on synthetic and real data illustrate the competitive performance of our method with respect to other state-of-the-art approaches.

Mots clés: Graph signal processing; Markov random field; Graph community; Gaph learning; Graph signal denoisin

Domaines: Traitement du signal et de l'image [eess.SP]

Stefania Colonnese, Paolo Di Lorenzo, Tiziana Cattai, Gaetano Scarano, Fabrizio de Vico Fallani. A Joint Markov Model for Communities, Connectivity and Signals Defined Over Graphs. IEEE Signal Processing Letters, 2020, 27, pp.1160-1164. ⟨10.1109/LSP.2020.3005053⟩. ⟨hal-03139296⟩