鲁棒结构正则化非负矩阵分解

现有的非负矩阵分解方法既忽略数据的非局部结构，又难以有效应对噪声和野值点。为了解决上述问题，提出一种新的用于聚类的鲁棒结构正则化非负矩阵分解算法。所提出的算法分别构建一个近邻图和一个最大熵图描述数据的局部结构和非局部结构，并使用L_2,1范数代价函数尝试解决噪声问题，从而学习到鲁棒具有判别力的表征。给出一个最优的迭代算法求解两个非负因子，该优化算法的收敛性已被理论和实验证明。在七个图像数据集上的聚类实验结果表明，所提出的算法在无噪声和有噪声情况下聚类均优于其他主流方法。

Robust structure regularized nonnegative matrix factorization

Most existing NMF methods not only ignore the non-local structure of data, but also are difficult to deal with noise and outliers effectively. To address these issues, this paper proposed a novel robust structure regularized nonnegative matrix factorization(RSNMF) algorithm for clustering. The proposed RSNMF constructed a nearest neighbor graph and a maximum entropy graph to respect local and non-local structures of the data, respectively. Moreover, the L2, 1-norm-based cost function tries to address noise and outliers. Therefore, RSNMF could learn robust compact and discriminative representations. This paper presented an optimal iterative algorithm to solve two nonnegative factors. The convergence of such an optimization scheme has been proved theoretically and empirically. Experimental clustering results on seven image datasets show that the proposed algorithm is superior to the state-of-the-art methods in both noiseless and noisy situations.