Rademacher Complexity Bounds for a Penalized Multiclass Semi-Supervised Algorithm

TL;DR

This paper derives Rademacher complexity bounds for a semi-supervised multiclass classification algorithm that uses clustering and margin-based training, providing theoretical convergence rates and empirical validation.

Contribution

It introduces novel Rademacher complexity bounds for a two-step semi-supervised multiclass classifier with clustering and margin penalization, extending binary case results.

Findings

Theoretical generalization error bounds involving margin distribution and clustering stability.

Convergence rates that extend previous binary case results.

Empirical evidence supporting the theoretical bounds on multiclass classification tasks.

Abstract

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.