  We tackle the problem of learning linear classifiers from noisy datasets in a
multiclass setting. The two-class version of this problem was studied a few
years ago by, e.g. Bylander (1994) and Blum et al. (1996): in these
contributions, the proposed approaches to fight the noise revolve around a
Perceptron learning scheme fed with peculiar examples computed through a
weighted average of points from the noisy training set. We propose to build
upon these approaches and we introduce a new algorithm called UMA (for
Unconfused Multiclass additive Algorithm) which may be seen as a generalization
to the multiclass setting of the previous approaches. In order to characterize
the noise we use the confusion matrix as a multiclass extension of the
classification noise studied in the aforementioned literature. Theoretically
well-founded, UMA furthermore displays very good empirical noise robustness, as
evidenced by numerical simulations conducted on both synthetic and real data.
Keywords: Multiclass classification, Perceptron, Noisy labels, Confusion Matrix
