l1-spectral clustering algorithm: a robust spectral clustering using Lasso regularization

Camille Champion (1, 2) , Magali Champion (3) , Mélanie Blazère (1) , Jean-Michel Loubes (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 I2MC - Institut des Maladies Métaboliques et Cardiovasculaires
3 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

Detecting cluster structure is a fundamental task to understand and visualize functional characteristics of a graph. Among the different clustering methods available, spectral clustering is one of the most widely used due to its speed and simplicity, while still being sensitive to perturbations imposed on the graph. This paper presents a robust variant of spectral clustering, called l1-spectral clustering, based on Lasso regularization and adapted to perturbed graph models. By promoting sparse eigenbases solutions of specific l1-minimization problems, it detects the hidden natural cluster structure of the graph. The effectiveness and robustness to noise perturbations of the l1-spectral clustering algorithm is confirmed through a collection of simulated and real biological data.

Mots clés: Unsupervised learning; Spectral clustering; l1-penalty; Biological networks

Domaines: Statistiques [math.ST]

Camille Champion, Magali Champion, Mélanie Blazère, Jean-Michel Loubes. l1-spectral clustering algorithm: a robust spectral clustering using Lasso regularization. 2021. ⟨hal-03095805v1⟩