The traditional label relaxation regression (LRR) algorithm directly fits the original data without considering the local structure information of the data. While the label relaxation regression algorithm of graph regularization takes into account the local geometric information, the performance of the algorithm depends largely on the construction of graph. However, the traditional graph structures have two defects. First of all, it is largely influenced by the parameter values. Second, it relies on the original data when constructing the weight matrix, which usually contains a lot of noise. This makes the constructed graph to be often not optimal, which affects the subsequent work. Therefore, a discriminative label relaxation regression algorithm based on adaptive graph (DLRR_AG) is proposed for feature extraction. DLRR_AG combines manifold learning with label relaxation regression by constructing adaptive weight graph, which can well overcome the problem of label overfitting. Based on a large number of experiments, it can be proved that the proposed method is effective and feasible.

中文翻译：

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自适应图学习的判别标签松弛回归

传统的标签松弛回归（LRR）算法直接拟合原始数据，而无需考虑数据的局部结构信息。虽然图正则化的标签松弛回归算法考虑了局部几何信息，但是算法的性能在很大程度上取决于图的构造。但是，传统的图结构有两个缺陷。首先，它很大程度上受参数值的影响。其次，它在构建权重矩阵时依赖于原始数据，该权重矩阵通常包含很多噪声。这使得构造的图通常不是最佳的，从而影响后续工作。因此，提出了一种基于自适应图的判别性标签松弛回归算法（DLRR_AG）。DLRR_AG通过构建自适应权重图，将流形学习与标签松弛回归相结合，可以很好地克服标签过度拟合的问题。通过大量的实验，可以证明该方法是有效可行的。