针对潜在低秩表示学习的投影矩阵不能解释提取特征重要程度和保持数据的局部几何结构的问题,提出了一种基于双邻域和特征选择的潜在低秩稀疏投影算法(LLRSP:Latent Low-Rank And Sparse Projection)。该算法首先融合低秩约束和正交重构...针对潜在低秩表示学习的投影矩阵不能解释提取特征重要程度和保持数据的局部几何结构的问题,提出了一种基于双邻域和特征选择的潜在低秩稀疏投影算法(LLRSP:Latent Low-Rank And Sparse Projection)。该算法首先融合低秩约束和正交重构保持数据的主要能量,然后对投影矩阵施加行稀疏约束进行特征选择,使特征更加紧凑和具有可解释性。此外引入l_(2,1)范数对误差分量进行正则化使模型对噪声更具健壮性。最后在低维数据和低秩表示系数矩阵上施加邻域保持正则化以保留数据的局部几何结构。公开数据集上的大量实验结果表明,所提方法与其他先进算法相比具有更好的性能。展开更多
The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be ...The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.展开更多
文摘针对潜在低秩表示学习的投影矩阵不能解释提取特征重要程度和保持数据的局部几何结构的问题,提出了一种基于双邻域和特征选择的潜在低秩稀疏投影算法(LLRSP:Latent Low-Rank And Sparse Projection)。该算法首先融合低秩约束和正交重构保持数据的主要能量,然后对投影矩阵施加行稀疏约束进行特征选择,使特征更加紧凑和具有可解释性。此外引入l_(2,1)范数对误差分量进行正则化使模型对噪声更具健壮性。最后在低维数据和低秩表示系数矩阵上施加邻域保持正则化以保留数据的局部几何结构。公开数据集上的大量实验结果表明,所提方法与其他先进算法相比具有更好的性能。
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,11871381)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146)。
文摘The task of dividing corrupted-data into their respective subspaces can be well illustrated,both theoretically and numerically,by recovering low-rank and sparse-column components of a given matrix.Generally,it can be characterized as a matrix and a 2,1-norm involved convex minimization problem.However,solving the resulting problem is full of challenges due to the non-smoothness of the objective function.One of the earliest solvers is an 3-block alternating direction method of multipliers(ADMM)which updates each variable in a Gauss-Seidel manner.In this paper,we present three variants of ADMM for the 3-block separable minimization problem.More preciously,whenever one variable is derived,the resulting problems can be regarded as a convex minimization with 2 blocks,and can be solved immediately using the standard ADMM.If the inner iteration loops only once,the iterative scheme reduces to the ADMM with updates in a Gauss-Seidel manner.If the solution from the inner iteration is assumed to be exact,the convergence can be deduced easily in the literature.The performance comparisons with a couple of recently designed solvers illustrate that the proposed methods are effective and competitive.
