Unconfused ultraconservative multiclass algorithms

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 where the proposed approaches to combat 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 Unconfused Multiclass additive Algorithm (UMA) 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.