Dual space-based fuzzy graphs and orthogonal basis clustering for unsupervised feature selection

Abstract

Unsupervised feature selection (UFS) takes an important position because gaining the class labels is laborious or even impossible. In the domain of UFS, clustering is a major means to exploit label information. The existing methods either could not model a clear clustering structure or could not utilize the local structure of data. Consequently, a new clustering method in combination with graph learning is proposed in this work. Specifically, for clustering, orthogonal basis clustering is introduced, where orthogonal constraints are imposed on the cluster center matrix and the clustering matrix. The clustering indicator matrix is also imposed by a non-negative constraint. A clearer clustering structure and more independent clustering centers are obtained through these constraints. For local preservation, given that traditional graphs for keeping the local manifold are faced with the problem of imbalanced neighbors, the fuzzy graph is introduced to acquire a robust structure, which is applied to both data space and feature space. The topological structure in these spaces can be well maintained. For the choice of salient features, ℓ2,0-norm regularization is imposed on the projection matrix. The object function is solved alternately. Then, a feature selection algorithm is designed. Experiments are designed and performed on nine real-world data sets. The results attest to the effectiveness of the proposed algorithm compared with other relevant algorithms.