  The popularity of algorithms based on Extreme Learning Machine (ELM), which
can be used to train Single Layer Feedforward Neural Networks (SLFN), has
increased in the past years. They have been successfully applied to a wide
range of classification and regression tasks. The most commonly used methods
are the ones based on minimizing the $\ell_2$ norm of the error, which is not
suitable to deal with outliers, essentially in regression tasks. The use of
$\ell_1$ norm was proposed in Outlier Robust ELM (OR-ELM), which is defined to
one-dimensional outputs. In this paper, we generalize OR-ELM to deal with
multi-target regression problems, using the error $\ell_{2,1}$ norm and the
Elastic Net theory, which can result in a more sparse network, resulting in our
method, Generalized Outlier Robust ELM (GOR-ELM). We use Alternating Direction
Method of Multipliers (ADMM) to solve the resulting optimization problem. An
incremental version of GOR-ELM is also proposed. We chose 15 public real-world
multi-target regression datasets to test our methods. Our conducted experiments
show that they are statistically better than other ELM-based techniques, when
considering data contaminated with outliers, and equivalent to them, otherwise.
