Generalized Uncorrelated Regression with Adaptive Graph for Unsupervised Feature Selection

Unsupervised feature selection always occupies a key position as a preprocessing in the tasks of classification or clustering due to the existence of extra essential features within high-dimensional data. Although lots of efforts have been made, the existing methods neglect to consider the redundancy of features, and thus select redundant features. In this brief, by virtue of a generalized uncorrelated constraint, we present an improved sparse regression model [generalized uncorrelated regression model (GURM)] for seeking the uncorrelated yet discriminative features. Benefited from this, the structure of data is kept in the Stiefel manifold, which avoids the potential trivial solution triggered by a conventional ridge regression model. Besides that, the uncorrelated constraint equips the model with the closed-form solution. In addition, we also incorporate a graph regularization term based on the principle of maximum entropy into the GURM model (URAFS), so as to embed the local geometric structure of data into the manifold learning. An efficient algorithm is designed to perform URAFS by virtue of the existing generalized powered iteration method. Extensive experiments on eight benchmark data sets among seven state-of-the-art methods on the task of clustering are conducted to verify the effectiveness and superiority of the proposed method.