基于邻域图的低秩投影学习

特征提取算法通常只单独用到了数据的局部结构或者整体结构，这样将得不到全局最优投影矩阵，且投影矩阵不具备很好的可解释性。为此，提出了一种基于邻域图的低秩投影学习算法。该算法通过在数据的重构残差上施加图约束来保持数据的局部结构，同时引入低秩项来保持整体结构；算法利用L2，1范数行稀疏的性质对投影矩阵进行约束，这样可以剔除冗余特征，提高投影矩阵的可解释性；并且算法引入噪声稀疏项来减弱样本本身存在噪声的干扰。模型采用交替迭代方法求解，在多个数据集上的实验结果表明该算法能有效地提高分类精度。

Low-Rank Projection Learning Based on Neighbor Graph

The feature extraction algorithms only use the local structure or the global structure of data, so they will not get the global optimal projection matrix, and projection matrix does not have good interpretability. In this paper, a low-rank projection learning algorithm based on neighborhood graph is proposed. The algorithm imposes the graph constraint on the reconstruction error of data to maintain the local structure of data , and introduces a low-rank term to preserve the global structure; the property of L2，1 norm row sparsity is used to constrain the projection matrix. In this way, redundant features can be eliminated, and the interpretability of projection matrix can be improved. Meanwhile, a noise sparse term is introduced to weaken the interference of noise from samples. The model is solved by alternating iteration method, and the experimental results on multiple datasets show that the algorithm can effectively improve the classification accuracies.