This article provides an original understanding of the behavior of a class of
graph-oriented semi-supervised learning algorithms in the limit of large and
numerous data. It is demonstrated that the intuition at the root of these
methods collapses in this limit and that, as a result, most of them become
inconsistent. Corrective measures and a new data-driven parametrization scheme
are proposed along with a theoretical analysis of the asymptotic performances
of the resulting approach. A surprisingly close behavior between theoretical
performances on Gaussian mixture models and on real datasets is also
illustrated throughout the article, thereby suggesting the importance of the
proposed analysis for dealing with practical data. As a result, significant
performance gains are observed on practical data classification using the
proposed parametrization