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) objectives to address the problems. The first one aims to learn a shared feature representation, which can be seen as a technical combination of the convex multitask feature learning and the convex Multiclass Maximum Margin Clustering (M3C). The second one aims to learn the task relationship, which can be seen as a combination of the convex multitask relationship learning and M3C. The objectives of the two algorithms are solved in a uniform procedure by the efficient cutting-plane algorithm and further unified in the Bayesian framework. Experimental results on a toy problem and two benchmark data sets demonstrate the effectiveness of the proposed algorithms.