Adaptive graph-based generalized regression model for unsupervised feature selection

Abstract

Unsupervised feature selection is an important method to reduce dimensions of high-dimensional data without labels, which is beneficial to avoid “curse of dimensionality” and improve the performance of subsequent machine learning tasks, like clustering and retrieval. A lot of methods have been developed in recent years. However, most of them only focus on selecting discriminative features but ignore the redundancy of features. Besides, these methods construct the similarity structure of data in the original input space and remain fixed during feature selection. The similarity structure is easily affected by the noises and outliers. Then the reliability of the similarity structure will be reduced in the procedure of feature selection. In order to address these issues, we present a novel generalized regression model equipped with an uncorrelated constraint and the ℓ2,1-norm regularization. It can simultaneously select the uncorrelated and discriminative features as well as reduce the variance of these data points belonging to the same neighborhood, which is helpful for the clustering task. Furthermore, to obtain the similarity structure of data and alleviate the influence of noises and outliers, we propose to adaptively learn a similarity-induced graph matrix in the reduced space and integrate it into the generalized regression model. An alternative iterative optimization algorithm is developed to solve the final objective function. A series of experiments are carried out on nine real-world data sets to demonstrate the effectiveness of the proposed method in comparison with other competing approaches.