Spectral feature selection (SFS) is superior to conventional feature selection methods in many aspects, by extra importing a graph matrix to preserve the subspace structure of data. However, the graph matrix of classical SFS that is generally constructed by original data easily outputs a suboptimal performance of feature selection because of the redundancy. To address this, this paper proposes a novel feature selection method via coupling the graph matrix learning and feature data learning into a unified framework, where both steps can be iteratively update until achieving the stable solution. We also apply a low-rank constraint to obtain the intrinsic structure of data to improve the robustness of learning model. Besides, an optimization algorithm is proposed to solve the proposed problem and to have fast convergence. Compared to classical and state-of-the-art feature selection methods, the proposed method achieved the competitive results on twelve real data sets.

通过额外导入图形矩阵以保留数据的子空间结构，光谱特征选择（SFS）在许多方面都优于常规特征选择方法。然而，由于冗余，通常由原始数据构成的经典SFS的图矩阵很容易输出特征选择的次优性能。为了解决这个问题，本文通过将图矩阵学习和特征数据学习耦合到一个统一的框架中，提出了一种新颖的特征选择方法，其中两个步骤都可以迭代更新，直到获得稳定的解决方案。我们还应用低秩约束来获取数据的固有结构，以提高学习模型的鲁棒性。此外，提出了一种优化算法来解决所提出的问题并具有快速收敛性。