In multi-task learning, multiple related tasks are considered simultaneously, with the goal to improve the generalization performance by utilizing the intrinsic sharing of information across tasks. This paper presents a multi-task learning approach by modeling the task-feature relationships. Specifically, instead of assuming that similar tasks have similar weights on all the features, we start with the motivation that the tasks should be related in terms of subsets of features, which implies a co-cluster structure. We design a novel regularization term to capture this task-feature co-cluster structure. A proximal algorithm is adopted to solve the optimization problem. Convincing experimental results demonstrate the effectiveness of the proposed algorithm and justify the idea of exploiting the task-feature relationships.

The task of feature selection is to select a subset of the original features according to certain predefined criterion with the goal to remove irrelevant and redundant features, improve the prediction performance and reduce the computational costs of data mining algorithms. In this paper, we integrate feature relevance and redundancy explicitly in the feature selection criterion. Spectral feature analysis is applied here which can fit into both supervised and unsupervised learning problems. Specifically, we formulate the problem into a combinatorial problem to maximize the relevance and minimize the redundancy of the selected subset of features at the same time. The problem can be relaxed and solved with an efficient extended power method with global convergence guaranteed. Extensive experiments demonstrate the advantages of the proposed technique in terms of improving the prediction performance and reducing redundancy in data.

Trajectory regression, which aims to predict the travel time of arbitrary trajectories on road networks, attracts significant attention in various applications of traffic systems these years. In this paper, we tackle this problem with a multitask learning (MTL) framework. To take the temporal nature of the problem into consideration, we divide the regression problem into a set of sub-tasks of distinct time periods, then the problem can be treated in a multi-task learning framework. Further, we propose a novel regularization term in which we exploit the block sparse structure to augment the robustness of the model. In addition, we incorporate the spatial smoothness over road links and thus achieve a spatial-temporal framework. An accelerated proximal algorithm is adopted to solve the convex but non-smooth problem, which will converge to the global optimum. Experiments on both synthetic and real data sets demonstrate the effectiveness of the proposed method.