Convex Discriminative Multitask Clustering

Multitask clustering tries to improve the clustering performance of multiple tasks simultaneously by taking their relationship into account. Most existing multitask clustering algorithms fall into the type of generative clustering, and none are formulated as convex optimization problems. In this paper, we propose two convex Discriminative Multitask Clustering (DMTC) algorithms to address the problems. Specifically, we first propose a Bayesian DMTC framework. Then, we propose two convex DMTC objectives within the framework. The first one, which can be seen as a technical combination of the convex multitask feature learning and the convex Multiclass Maximum Margin Clustering (M3C), aims to learn a shared feature representation. The second one, which can be seen as a combination of the convex multitask relationship learning and M3C, aims to learn the task relationship. The two objectives are solved in a uniform procedure by the efficient cutting-plane algorithm. Experimental results on a toy problem and two benchmark datasets demonstrate the effectiveness of the proposed algorithms.