Abstract 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.

中文翻译：

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无监督特征选择的联合自适应流形和嵌入学习

摘要 由于数据总是位于低维空间，特征选择已成为计算机视觉、机器学习和数据挖掘的重要步骤。由于缺乏类信息，无监督特征选择的性能取决于如何表征和保留数据之间的流形结构。在本文中，我们提出了一种新的无监督特征选择框架，称为无监督特征选择的联合自适应流形和嵌入学习（JAMEL）。它迭代自适应地学习数据的低维嵌入以保留数据之间的流形结构，将数据回归到嵌入以衡量特征的重要性，并根据内在空间中的数据密度学习数据之间的流形结构，其中冗余和噪声特征被消除。此外，我们提出了一种有效的算法来解决所提出的问题，并进行收敛分析。最后，使用 12 个数据集上的所选特征对 k 均值、谱聚类和最近邻分类任务的评估结果表明了我们方法的有效性和效率。