Modelling contextual constraints in probabilistic relaxation for multi-class semi-supervised learning

This paper proposes a semi-supervised approach based on probabilistic relaxation theory. The algorithm performs a consistent multi-class assignment of labels according to the contextual information constraints. We start from a fully connected graph where each initial sample of the input data is a node of the graph and where only a few nodes have been labelled. A local propagation process is then performed by means of a support function where a new compatibility measure has been proposed. Contributions also include a comparative study of a wide variety of data sets with recent and well-known state-of-the-art algorithms for semi-supervised learning. The results have been provided by an analysis of their statistical significance. Our methodology has demonstrated a noticeably better performance in multi-class classification tasks. Experiments will also show that the proposed technique could be especially useful for applications such as hyperspectral image classification.The authors would like to thank Prof. Pelillo for his help on the proof of convergence in Probabilistic Relaxation approaches and also to Dr. Aykut Erdem for his help with the SSL–GTG algorithm. We deeply thank Dr. Pedro Garcia-Sevilla for his help on the calculation of the algorithms complexity. This work was supported by the Spanish Ministry of Science and Innovation under the Projects Consolider Ingenio 2010 CSD2007-00018, AYA2008-05965-C04-04/ESP and by Caixa-Castelló foundation under the Project P1 1B2007-48