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Multitask feature selection (MTFS) methods have become more important for many real world applications, especially in a high-dimensional setting. The most widely used assumption is that all tasks share the same features, and the l2,1 regularization method is usually applied. However, this assumption may not hold when the correlations among tasks are not obvious. Learning with unrelated tasks together may result in negative transfer and degrade the performance. In this paper, we present a flexible MTFS by graph-clustered feature sharing approach. To avoid the above limitation, we adopt a graph to represent the relevance among tasks instead of adopting a hard task set partition. Furthermore, we propose a graph-guided regularization approach such that the sparsity of the solution can be achieved on both the task level and the feature level, and a variant of the smooth proximal gradient method is developed to solve the corresponding optimization problem. An evaluation of the proposed method on multitask regression and multitask binary classification problem has been performed. Extensive experiments on synthetic datasets and real-world datasets demonstrate the effectiveness of the proposed approach to capture task structure.

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