Smart Multitask Bregman Clustering and Multitask Kernel Clustering

Traditional clustering algorithms deal with a single clustering task on a single dataset. However, there are many related tasks in the real world, which motivates multitask clustering. Recently some multitask clustering algorithms have been proposed, and among them multitask Bregman clustering (MBC) is a very applicable method. MBC alternatively updates clusters and learns relationships between clusters of different tasks, and the two phases boost each other. However, the boosting does not always have positive effects on improving the clustering performance, it may also cause negative effects. Another issue of MBC is that it cannot deal with nonlinear separable data. In this article, we show that in MBC, the process of using cluster relationship to boost the cluster updating phase may cause negative effects, that is, cluster centroids may be skewed under some conditions. We propose a smart multitask Bregman clustering (S-MBC) algorithm which can identify the negative effects of the boosting and avoid the negative effects if they occur. We then propose a multitask kernel clustering (MKC) framework for nonlinear separable data by using a similar framework like MBC in the kernel space. We also propose a specific optimization method, which is quite different from that of MBC, to implement the MKC framework. Since MKC can also cause negative effects like MBC, we further extend the framework of MKC to a smart multitask kernel clustering (S-MKC) framework in a similar way that S-MBC is extended from MBC. We conduct experiments on 10 real world multitask clustering datasets to evaluate the performance of S-MBC and S-MKC. The results on clustering accuracy show that: (1) compared with the original MBC algorithm MBC, S-MBC and S-MKC perform much better; (2) compared with the convex discriminative multitask relationship clustering (DMTRC) algorithms DMTRC-L and DMTRC-R which also avoid negative transfer, S-MBC and S-MKC perform worse in the (ideal) case in which different tasks have the same cluster number and the empirical label marginal distribution in each task distributes evenly, but better or comparable in other (more general) cases. Moreover, S-MBC and S-MKC can work on the datasets in which different tasks have different number of clusters, violating the assumptions of DMTRC-L and DMTRC-R. The results on efficiency show that S-MBC and S-MKC consume more computational time than MBC and less computational time than DMTRC-L and DMTRC-R. Overall S-MBC and S-MKC are competitive compared with the state-of-the-art multitask clustering algorithms in synthetical terms of accuracy, efficiency and applicability.