一种基于非负低秩稀疏图的半监督学习改进算法

Improved Algorithm Based on Non-negative Low Rank and Sparse Graph for Semi-supervised Learning

该文针对基于非负低秩稀疏图的半监督学习算法不能准确地描述数据结构的问题,提出一种融合平滑低秩表示和加权稀疏约束的改进算法。该算法分别对经典算法的低秩项和稀疏项进行改进,准确地捕获了数据的全局子空间结构和局部线性结构。在构建目标函数时,使用对数行列式函数代替核范数平滑地估计秩函数,同时利用形状交互信息和有标签样本的类别信息构造加权稀疏约束正则项。然后通过带有自适应惩罚的线性交替方向方法求解目标函数并采用有效的后处理方法重构数据的图结构,最后利用基于局部和全局一致性的半监督分类框架完成学习任务。在ORL库,Extended Yale B库和USPS库上的实验结果表明,该改进算法提高了半监督学习的准确率。

Semi-supervised learning algorithm based on non-negative low rank and sparse graph can not describe the structures of the data exactly. Therefore, an improved algorithm which integrates smoothed low rank representation and weighted sparsity constraint is proposed. The low rank term and sparse term of the classical algorithm are improved by this algorithm respectively, and the global subspace structure and the locally linear structure can be captured exactly. When building the objective function, the logarithm determinant function instead of the nuclear norm is used to approximate the rank function smoothly. Meanwhile, the shape interaction information and the label information of labeled samples is used to build the weighted sparsity constraint regularization term. Then, the objective function is solved by a linearized alternating direction method with adaptive penalty and the graph construction is restructured by an available post-processing method. Finally, a semi-supervised classification framework based on local and global consistency is used to finish the learning task. The experimental results on ORL, Extended Yale B and USPS database show that the improved algorithm imDroves the accuracv of semi-supervised learning.