Joint adaptive manifold and embedding learning for unsupervised feature selection

As data always lie on a lower-dimensional space, feature selection has become an important step in computer vision, machine learning and data mining. Due to the lack of class information, the performance of unsupervised feature selection depends on how to characterize and preserve the manifold structure among data. In this paper, we propose a novel unsupervised feature selection framework, named as joint adaptive manifold and embedding learning for unsupervised feature selection (JAMEL). It iteratively and adaptively learns lower-dimensional embeddings for data to preserve the manifold structure among data, regresses data to embeddings to measure the importance of features, and learns the manifold structure among data according to the data density in the intrinsic space, where the redundant and noisy features are eliminated. In addition, we present an efficient algorithm to solve the proposed problem, together with the convergence analysis. Finally, the evaluation results with the tasks of k-means, spectral clustering and nearest neighbor classification using the selected features on 12 datasets show the effectiveness and efficiency of our approach. (C) 2020 Elsevier Ltd. All rights reserved.