Abstract: To solve the problem that the traditional unsupervised feature selection cannot fully take into account the local structure of samples and features, and does not consider that the non-convex regular term brings sparse solutions and can select more discriminant features, an unsupervised feature selection method based on adaptive graph embedding and non-convex regular feature self-expression is proposed. Firstly, the dimensions of features are reduced by the graph embedding technology, and a sample similarity matrix is obtained to guide feature selection. Secondly, the feature self-expression strategy is introduced to represent each feature linearly by the other features, and the similarity relationship between features is considered to maintain the local structure of features. Thirdly, a non-convex regular term is added to the feature self-expression to obtain a more sparse weight matrix for feature selection. In the process of feature selection, the adaptive graph embedding technology is performed to learn the local structure of data and select the optimal feature subset. Finally, to solve non-convex sparse problems, a new unsupervised feature selection algorithm is designed by using the alternate iterative method to optimize this solution model. Compared with other methods on six datasets, the experimental results show that the proposed method is effective.

Key words: unsupervised feature selection, graph embedding, feature self-expression, non-convex regular term, self-adaptation

摘要： 针对传统的无监督特征选择不能充分兼顾样本及特征的局部结构，以及没有考虑非凸正则项带来更稀疏的解并能够选择出更具判别性特征等问题，提出了自适应图嵌入和非凸正则特征自表达的无监督特征选择方法。通过图嵌入降低特征维度，获得样本相似度矩阵，引导特征选择；引入特征自表达策略，用其余特征线性表示每一个特征，考虑特征间的相似性关系，保持特征局部结构；在特征自表达中添加非凸正则项，获得行更稀疏的权重矩阵，实现特征选择；在特征选择过程中执行自适应图嵌入对数据局部结构进行学习，选择最优特征子集；为求解非凸稀疏问题，使用交替迭代方法优化求解模型，设计了一种新的无监督特征选择算法。在6个数据集上与其他算法进行实验对比分析，实验结果表明所提算法是有效的。

关键词: 无监督特征选择, 图嵌入, 特征自表达, 非凸正则项, 自适应