Symmetrical Self-Representation and Data-Grouping Strategy for Unsupervised Feature Selection

Unsupervised feature selection (UFS) is an important technology for dimensionality reduction and has gained great interest in a wide range of fields. Recently, most popular methods are spectral-based which frequently use adaptive graph constraints to promote performance. However, no literature has considered the grouping characteristic of the data features, which is the most basic and important characteristic for arbitrary data. In this paper, based on the spectral analysis method, we first simulate the data feature grouping characteristic. Then, the similarity between data is adaptively reconstructed through the similarity between groups, which can explore the more fine-grained relationship between data than the previous adaptive graph methods. In order to achieve the aforementioned goal, the local similarity matrix and the global similarity matrix are defined, and the weighted KL entropy is used to constrain the relationship between the global similarity matrix and the local similarity matrices. Furthermore, the symmetrical self-representation structure is used to improve the performance of the reconstruction error term in the conventional spectral-based methods. After the model is constructed, a simple but efficient algorithm is proposed to solve the full model. Extensive experiments on 8 benchmark dataset with different types to show the effectiveness of the proposed method.