基于自适应图学习的多目标特征选择算法

针对多目标回归中的特征选择问题,提出一种基于自适应图学习的多目标特征选择算法,在单个框架中同时考虑3种关系结构:输入特征与目标输出、不同目标输出以及样本间的相关结构,并基于上述结构信息进行特征选择.首先,在传统稀疏回归模型中对系数矩阵施加低秩约束,利用低秩学习对特征间相关性以及目标间的依赖关系进行解耦学习;然后,构建基于样本局部结构信息的自适应图学习项,充分利用样本间的相似结构进行特征选择;进一步地,引入基于输出相关性的结构矩阵优化项,使模型能够更加充分地考虑目标间的相关性;最后,提出一种交替优化算法求解目标函数,并从理论上证明算法的收敛性.在公开数据集上的实验表明,所提方法相较于现有主流的多目标特征选择方法具有更好的性能和适用性.

Multi-target feature selection algorithm based on adaptive graph learning

Feature selection not only enhances the efficiency of regression modelling but also reduces the detrimental effects of feature redundancy and noises. This paper proposes a multi-target feature selection algorithm based on adaptive graph learning. Specifically, the method imposes a low-rank constraint on the regression matrix, enabling simultaneous modelling of inter-target, input-output and inter-sample relationships within a general framework. The similarity-induced graph matrix is learned to adaptively preserve samples'' similarity structure to alleviate the influence of noises and outliers. Furthermore, we introduce a manifold regularizer to preserve the global target correlations to ensure the global target correlations structure of data in the subsequent learning process. An alternative optimization algorithm is presented to solve the final objective function. Extensive experiments conducted on real-world data sets demonstrate that the proposed method is superior to state-of-the-art multi-target feature selection methods.