通过图滤波与自表示捕捉数据高阶结构，实现无监督特征选择。
Unsupervised Feature Selection Algorithm Based on Graph Filtering and Self-representation
- 利用高阶图滤波提取数据平滑表示，融合高阶邻域信息。
- 设计正则项增强模型对噪声的鲁棒性与特征行稀疏性。
- 适用于高维数据降维，适合无标签场景下的特征筛选。
针对现有方法在未考虑数据高阶邻域信息时难以充分捕捉数据内在结构的问题，提出一种基于图滤波与自表示的无监督特征选择算法。首先，采用高阶图滤波处理数据以获得其平滑表示，并设计正则项将高阶图信息融入自表示矩阵学习中，以捕捉数据内在结构。其次，使用l2,1范数重构误差项和特征选择矩阵，提升模型对噪声的鲁棒性及特征的行稀疏性，从而选取具有判别性的特征。最后，采用迭代算法有效求解所提出的优化目标函数，并通过仿真实验验证了该算法的有效性。
原文摘要 · Abstract (English)
Aiming at the problem that existing methods could not fully capture the intrinsic structure of data without considering the higher-order neighborhood information of the data, we proposed an unsupervised feature selection algorithm based on graph filtering and self-representation. Firstly,a higher-order graph filter was applied to the data to obtain its smooth representation,and a regularizer was designed to combine the higher-order graph information for the self-representation matrix learning to capture the intrinsic structure of the data. Secondly,l2,1 norm was used to reconstruct the error term and feature selection matrix to enhance the robustness and row sparsity of the model to select the discriminant features. Finally, an iterative algorithm was applied to effectively solve the proposed objective function and simulation experiments were carried out to verify the effectiveness of the proposed algorithm.
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