Beyond Supervised Classification: Extreme Minimal Supervision with the Graph 1-Laplacian

Angelica I. Aviles-Rivero , Nicolas Papadakis (1) , Ruoteng Li , Samar M Alsaleh , Robby T Tan , Carola-Bibiane Schönlieb (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 DAMTP - Department of Applied Mathematics and Theoretical Physics

We consider the task of classifying when an extremely reduced amount of labelled data is available. This problem is of a great interest, in several real-world problems, as obtaining large amounts of labelled data is expensive and time consuming. We present a novel semi-supervised framework for multi-class classification that is based on the normalised and non-smooth graph 1-Laplacian. Our transductive framework is framed under a novel functional with carefully selected class priors - that enforces a sufficiently smooth solution that strengthens the intrinsic relation between the labelled and unlabelled data. We demonstrate through extensive experimental results on large datasets CIFAR-10 and ChestX-ray14, that our method outperforms classic methods and readily competes with recent deep-learning approaches.

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

Angelica I. Aviles-Rivero, Nicolas Papadakis, Ruoteng Li, Samar M Alsaleh, Robby T Tan, et al.. Beyond Supervised Classification: Extreme Minimal Supervision with the Graph 1-Laplacian. 2019. ⟨hal-02170176⟩