Feature selection based on non-negative spectral feature learning and adaptive rank constraint

Abstract

Unsupervised feature selection plays a significant role in data classification and clustering. General regression models cannot directly exploit the information on the feature space and fail to accurately describe the local geometric structure of data during feature selection. To address these problems, this paper proposes the feature selection algorithm, which is based on non-negative spectral feature learning and adaptive rank constraint (NNSAFS). First, the algorithm utilizes the residual term in sparse regression to ensure that the learned low-dimensional subspaces have greater fault tolerance and introduces a feature graph on the sparse transformation matrix to reveal the manifold information on the feature space. This sparse transformation matrix is the projection matrix because the introduction of feature graphs on this matrix can connect manifold learning to feature selection. In addition, traditional spectral clustering algorithms usually construct fixed similarity graphs for clustering analysis. The NNSAFS algorithm imposes a rank constraint on the clustering indicator matrix, which is equivalent to the graph regularization that can recover accurate local structure information. Moreover, the similarity matrix in the regularization term is constructed by using the maximum entropy theory, which can increase the adaptability of manifold learning. Finally, the algorithm imposes the l1-norm constraint on the projection matrix, which makes the selected features more conducive to clustering performance. The clustering performance of the NNSAFS algorithm is evaluated against seven other unsupervised feature selection algorithms on nine benchmark datasets. The experimental results show that the features selected by the proposed algorithm are more discriminative and outperform other algorithms in the clustering task.11The code of the proposed algorithm has been uploaded and available at the following link: https://github.com/Vita427/NNSAFS.git.