可自适应分组的超球多任务学习算法

针对现有回归多任务学习中各任务独立评估风险、缺乏统一约束条件的缺点，提出了一种具有自适应分组能力的超球多任务学习算法。该算法以极限学习机(ELM)为基础形式，首先引入超球损失函数对所有任务的风险进行统一评估，并采用迭代再权最小二乘法求解；其次，考虑到任务之间关联度存在差异，基于相关性强的任务其权重向量也较相似的假设，构建带分组结构的正则项，使得同组内的任务独立进行训练，最终将优化目标转为混合0-1规划问题，并采用多目标优化方法自动确定模型参数和最优分组结构。基于仿真数据和圆柱壳振动信号数据的测试结果表明，该算法可有效识别出任务中的分组结构，同时与现有算法相比，可明显提高回归模型的泛化能力。

Hyper-spherical multi-task learning algorithm with adaptive grouping

To solve the problem in most of conventional multi-task learning algorithms which evaluate risk independently for single task and lack uniform constraint across all tasks, a new hyper-spherical multi-task learning algorithm with adaptive grouping was proposed in this paper. Based on Extreme Learning Machine (ELM) as basic framework, this algorithm introduced hyper-spherical loss function to evaluate the risks of all tasks uniformly, and got decision model via iterative reweighted least squares solution. Furthermore, considering the existence of relatedness between tasks, this paper also constructed regularizer with grouping structure based on the assumption that related tasks had more similar weight vector, which would make the tasks in same group be trained independently. Finally, the optimization object was transformed into a mixed 0-1 programming problem, and a multi-objective method was utilized to identify optimal grouping structure and get model parameters. The simulation results on toy data and cylindrical vibration signal data show that the proposed algorithm outperforms state-of-the-art methods in terms of generalization performance and the ability of identifying inner structure in tasks.