The success of existing unsupervised feature selection (UFS) methods heavily relies on the assumption that the intrinsic relationships among original high-dimensional (HD) data samples exist in the discriminative low-dimension (LD) subspace. However, previous UFS methods commonly construct pairwise graphs and employ ℓ2,1\ell _{2,1} -norm regularization to severally preserve the local structure and calculate the score of features, which is computationally complex and easy to get stuck into local optimum, so that those approaches cannot be applied in dealing with large-scale datasets in practice. To overcome this challenge, we propose a novel UFS method, in which a novel anchor graph embedding paradigm is designed to extract the local neighborhood relationships among data samples by reducing the computational complexity of graph construction to be linear in the number of data. Moreover, to improve the optimality of selected features as well as the performance of downstream tasks, we propose a discrete feature scoring mechanism, which imposes orthogonal ℓ2,0\ell _{2,0} -norm constraints on learned projections, in order to enhance the distinction of feature scores as well as reduce the probability of falling into local optimum. In addition, solving the proposed nonconvex and nonsmooth NP-hard problem is challenging, and we present an efficient optimization algorithm to address it and acquire a closed-form solution of the transformation matrix. Extensive experiments demonstrate the effectiveness and efficiency of the proposed UFS by comparison with several state-of-the-art approaches to clustering and image segmentation tasks.

中文翻译：

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用于无监督特征选择的联合锚图嵌入和离散特征评分


现有无监督特征选择（UFS）方法的成功在很大程度上依赖于这样的假设：原始高维（HD）数据样本之间的内在关系存在于判别性低维（LD）子空间中。然而，以往的UFS方法通常构建成对图，并采用ℓ2,1\ell _{2,1} -范数正则化分别保留局部结构并计算特征得分，计算复杂且容易陷入局部最优，因此这些方法无法应用于实际处理大规模数据集。为了克服这一挑战，我们提出了一种新颖的 UFS 方法，其中设计了一种新颖的锚图嵌入范式，通过将图构造的计算复杂度降低到与数据数量呈线性关系来提取数据样本之间的局部邻域关系。此外，为了提高所选特征的最优性以及下游任务的性能，我们提出了一种离散特征评分机制，该机制对学习的投影施加正交 ℓ2,0\ell _{2,0} -范数约束，以便增强特征得分的区分度并降低陷入局部最优的概率。此外，解决所提出的非凸非光滑 NP 难问题具有挑战性，我们提出了一种有效的优化算法来解决它并获得变换矩阵的闭式解。通过与几种最先进的聚类和图像分割任务方法进行比较，大量的实验证明了所提出的 UFS 的有效性和效率。