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This article provides an original understanding of the behavior of a class ofgraph-oriented semi-supervised learning algorithms in the limit of large andnumerous data. It is demonstrated that the intuition at the root of thesemethods collapses in this limit and that, as a result, most of them becomeinconsistent. Corrective measures and a new data-driven parametrization schemeare proposed along with a theoretical analysis of the asymptotic performancesof the resulting approach. A surprisingly close behavior between theoreticalperformances on Gaussian mixture models and on real datasets is alsoillustrated throughout the article, thereby suggesting the importance of theproposed analysis for dealing with practical data. As a result, significantperformance gains are observed on practical data classification using theproposed parametrization.

A random matrix analysis and improvement of semi-supervised learning for large dimensional data