Learning the Shared Subspace for Multi-task Clustering and Transductive Transfer Classification

There are many clustering tasks which are closely related in the real world, e.g. clustering the Web pages of different universities. However, existing clustering approaches neglect the underlying relation and treat these clustering tasks either individually or simply together. In this paper, we will study a novel clustering paradigm, namely multi-task clustering, which performs multiple related clustering tasks together and utilizes the relation of these tasks to enhance the clustering performance. We aim to learn a subspace shared by all the tasks, through which the knowledge of the tasks can be transferred to each other. The objective of our approach consists of two parts: (1) Within-task clustering: clustering the data of each task in its input space individually; and (2) Cross-task clustering: simultaneous learning the shared subspace and clustering the data of all the tasks together. We will show that it can be solved by alternating minimization, and its convergence is theoretically guaranteed. Furthermore, we will show that given the labels of one task, our multi-task clustering method can be extended to transductive transfer classification (a.k.a. cross-domain classification, domain adaption). Experiments on several cross-domain text data sets demonstrate that the proposed multi-task clustering outperforms traditional single-task clustering methods greatly. And the transductive transfer classification method is comparable to or even better than several existing transductive transfer classification approaches.