Joint dictionary and graph learning for unsupervised feature selection

With the explosion of unlabelled and high-dimensional data, unsupervised feature selection has become an critical and challenging problem in machine learning. Recently, data representation based model has been successfully deployed for unsupervised feature selection, which defines feature importance as the capability to represent original data via a reconstruction function. However, most existing algorithms conduct feature selection on original feature space, which will be affected by the noisy and redundant features of original feature space. In this paper, we investigate how to conduct feature selection on the dictionary basis space of the data, which can capture higher level and more abstract representation than original low-level representation. In addition, a similarity graph is learned simultaneously to preserve the local geometrical data structure which has been confirmed critical for unsupervised feature selection. In summary, we propose a model (referred to as DGL-UFS briefly) to integrate dictionary learning, similarity graph learning and feature selection into a uniform framework. Experiments on various types of real world datasets demonstrate the effectiveness of the proposed framework DGL-UFS.