Joint Self-expression with Adaptive Graph for Unsupervised Feature Selection

Feature selection usually takes unsupervised way to preprocess the data before clustering. In the unsupervised feature selection, the embedding based method can capture more discriminative information contained in data compared to the other methods. Considering many existing methods learn a cluster indicator matrix which may bring noise, and at the same time, these kinds of methods does not make good use of the geometry structure of the data. In order to address the existing problems, we propose a novel model based on joint self-expression model with adaptive graph constraint. The joint self-expression module is utilized to explore the relationship between features. Different from the conventional self-expression, our joint self-expression module contains two types self-expression, i.e., conventional self-expression and the convex non-negative matrix factorization (CNMF) which can extract more representative features. Furthermore, we introduce manifold learning to maintain the structural characteristics of the original data. Adaptive graph regularization term is also incorporated based on the principle of maximum entropy into our model. In order to solve the final model, an alternative algorithm is well designed. Finally, experiment is well designed on five benchmark datasets and the experimental results show that the model proposed in this paper is more effectiveness than the state-of-the-art comparison models.