  Multi-task learning (MTL) aims to improve the performance of multiple related
prediction tasks by leveraging useful information from them. Due to their
flexibility and ability to reduce unknown coefficients substantially, the
task-clustering-based MTL approaches have attracted considerable attention.
Motivated by the idea of semisoft clustering of data, we propose a semisoft
task clustering approach, which can simultaneously reveal the task cluster
structure for both pure and mixed tasks as well as select the relevant
features. The main assumption behind our approach is that each cluster has some
pure tasks, and each mixed task can be represented by a linear combination of
pure tasks in different clusters. To solve the resulting non-convex constrained
optimization problem, we design an efficient three-step algorithm. The
experimental results based on synthetic and real-world datasets validate the
effectiveness and efficiency of the proposed approach. Finally, we extend the
proposed approach to a robust task clustering problem.
