  We propose Rademacher complexity bounds for multiclass classifiers trained
with a two-step semi-supervised model. In the first step, the algorithm
partitions the partially labeled data and then identifies dense clusters
containing $\kappa$ predominant classes using the labeled training examples
such that the proportion of their non-predominant classes is below a fixed
threshold. In the second step, a classifier is trained by minimizing a margin
empirical loss over the labeled training set and a penalization term measuring
the disability of the learner to predict the $\kappa$ predominant classes of
the identified clusters. The resulting data-dependent generalization error
bound involves the margin distribution of the classifier, the stability of the
clustering technique used in the first step and Rademacher complexity terms
corresponding to partially labeled training data. Our theoretical result
exhibit convergence rates extending those proposed in the literature for the
binary case, and experimental results on different multiclass classification
problems show empirical evidence that supports the theory.
