Robust classification using ℓ2,1-norm based regression model

A novel classification method using ℓ2,1ℓ2,1-norm based regression is proposed in this paper. The ℓ2,1ℓ2,1-norm based loss function is robust to outliers or large variations distributed in the given data, and the ℓ2,1ℓ2,1-norm regularization term selects correlated samples across the whole training set with grouped sparsity. A probabilistic interpretation under the multiple task learning framework presents theoretical foundation for the optimal solution. Complexity analysis of our proposed classification algorithm is also presented. Several benchmark data sets including facial images and gene expression data are used for evaluating the effectiveness of the new proposed algorithm, and the results show competitive performance particularly better than those using dummy matrix as the response variables. This result is very useful since it is important for selecting appropriate response variables in classification oriented regression models.

► A ℓ2,1ℓ2,1-norm based regression model is proposed.
► The loss function is robust to outliers or large variations.
► The regularization term selects correlated samples with grouped sparsity.
► A probabilistic interpretation under a multiple task learning framework is given.