Abstract Most of manifold learning based feature extraction methods are two-step methods, which first construct a weighted neighborhood graph and then use the pre-constructed graph to perform subspace learning. As a result, these methods fail to use the underlying correlation structure of data to learn an adaptive graph to preciously characterize the similarity relationship between samples. To address this problem, we propose a novel unsupervised feature extraction method called low-rank adaptive graph embedding (LRAGE), which can perform subspace learning and adaptive probabilistic neighborhood graph embedding simultaneously based on reconstruction error minimization. The proposed LRAGE is imposed with low-rank constraint for the sake of exploring the underlying correlation structure of data and learning more informative projection. Moreover, the L 2 , 1 -norm penalty is imposed on the regularization to further enhance the robustness of LRAGE. Since the resulting objective function has no closed-form solutions, an iterative optimization algorithm is elaborately designed. The convergence of the proposed algorithm is proved and the corresponding computational complexity analysis is also presented. In addition, we explore the potential properties of the proposed LRAGE by comparing it with several similar models on both synthetic and real-world data sets. Extensive experiments on five well-known face data sets and three non-face data sets demonstrate the superiority of the proposed LRAGE.

中文翻译：

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用于无监督特征提取的低秩自适应图嵌入

摘要 基于流形学习的特征提取方法大多是两步法，先构造加权邻域图，然后利用预先构造的图进行子空间学习。结果，这些方法未能利用数据的底层相关结构来学习自适应图来珍贵地表征样本之间的相似关系。为了解决这个问题，我们提出了一种新的无监督特征提取方法，称为低秩自适应图嵌入（LRAGE），它可以基于重构误差最小化同时执行子空间学习和自适应概率邻域图嵌入。为了探索数据的潜在相关结构并学习更多信息投影，建议的 LRAGE 被强加低秩约束。而且，对正则化施加 L 2 , 1 -范数惩罚以进一步增强 LRAGE 的鲁棒性。由于得到的目标函数没有封闭形式的解，所以精心设计了迭代优化算法。证明了所提算法的收敛性，并给出了相应的计算复杂度分析。此外，我们通过在合成数据集和真实数据集上将其与几个类似的模型进行比较来探索所提出的 LRAGE 的潜在特性。在五个众所周知的人脸数据集和三个非人脸数据集上进行的大量实验证明了所提出的 LRAGE 的优越性。精心设计了迭代优化算法。证明了所提算法的收敛性，并给出了相应的计算复杂度分析。此外，我们通过在合成数据集和真实数据集上将其与几个类似的模型进行比较来探索所提出的 LRAGE 的潜在特性。在五个众所周知的人脸数据集和三个非人脸数据集上进行的大量实验证明了所提出的 LRAGE 的优越性。精心设计了迭代优化算法。证明了所提算法的收敛性，并给出了相应的计算复杂度分析。此外，我们通过在合成数据集和真实数据集上将其与几个类似的模型进行比较来探索所提出的 LRAGE 的潜在特性。在五个众所周知的人脸数据集和三个非人脸数据集上进行的大量实验证明了所提出的 LRAGE 的优越性。