中文说明：非负矩阵分解 （NMF） 已成为最广泛使用的聚类技术的探索性数据之一分析。但是，由于每个数据点进入平方的残留错误的目标函数与大了一些局外人错误很容易地主宰的目标函数。在本文中，我们提出了鲁棒流形的非负矩阵分解使用 ℓ2、 1-范数和整合 NMF 和相同的聚类框架下的谱聚类 （RMNMF） 方法。我们还指出，对于现有的非负矩阵分解方法，解唯一性问题，并建议额外正交约束为解决这一问题。新的约束，与常规的辅助函数的方法不再有效。我们解决这一困难的优化问题通过增广拉格朗日方法 （ALM） 算法，并将转换的小说原始的约束的优化问题，对一个变量的多元到约束问题。新的目标函数然后可以分解成若干子问题，每有一个封闭形式解。更重要的是，我们揭示了我们的方法具有鲁棒性的 K-均值和光谱的连接聚类，并证明其理论意义。所有的实证结果表明的有效性和广泛的实验，在九个基准数据集上我们的方法。
English Description：
Nonnegative matrix factorization (NMF) has become one of the most widely used clustering techniques for exploratory data analysis. However, because each data point into the square of the residual error objective function and some outsider error is easy to dominate the objective function. In this paper, we propose a nonnegative matrix factorization of robust manifolds using ℓ 2,1-norm and integrating NMF and spectral clustering (rmnmf) under the same clustering framework. We also point out that for the existing nonnegative matrix factorization methods, the uniqueness problem is solved, and propose additional orthogonal constraints to solve this problem. The new constraint is no longer valid compared with the conventional auxiliary function method. We solve this difficult optimization problem through the augmented Lagrangian method (ALM) algorithm, and transform the novel original constrained optimization problem to a multivariate constrained problem. The new objective function can then be decomposed into several subproblems, each of which has a closed form solution. More importantly, we reveal the robust K-means and spectral join clustering of our method, and prove its theoretical significance. All empirical results show the effectiveness and extensive experiments of our method on nine benchmark datasets.