鲁棒自适应对称非负矩阵分解聚类算法

对称非负矩阵分解SNMF作为一种基于图的聚类算法，能够更自然地捕获图表示中嵌入的聚类结构，并且在线性和非线性流形上获得更好的聚类结果，但对变量的初始化比较敏感。另外，标准的SNMF算法利用误差平方和来衡量分解的质量，对噪声和异常值敏感。为了解决这些问题，在集成学习视角下，提出一种鲁棒自适应对称非负矩阵分解聚类算法RS³NMF(robust self-adaptived symmetric nonnegative matrix factorization)。基于L_2,1范数的RS³NMF模型缓解了噪声和异常值的影响，保持了特征旋转不变性，提高了模型的鲁棒性。同时，在不借助任何附加信息的前提下，利用SNMF对初始化特征的敏感性来逐步增强聚类性能。采用交替迭代方法优化，并保证目标函数值的收敛性。大量实验结果表明，所提RS³NMF算法优于其他先进的算法，具有较强的鲁棒性。

Robust self-adaptived symmetric nonnegative matrix factorization clustering algorithm

As a graph-based clustering method, SNMF can more naturally capture the clustering structure embedded in the graph representation and obtain better clustering results on linear and nonlinear manifolds, but it is sensitive to the initialization of variables. In addition, standard SNMF algorithm uses the sum of error squares to measure the quality of decomposition, which is sensitive to noise and outliers. In order to solve these problems, this paper proposed a novel robust self-adaptived symmetric nonnegative matrix factorization for clustering(RS3NMF) from the perspective of ensemble learning. The L2, 1 norm-based RS3NMF model alleviated the noise and outliers influence, and keeped the rotation invariance property to improve the model robustness. Meanwhile, using the sensitivity of SNMF to initialization features, it gradually enhanced the clustering performance, without relying on any additional information. It adopted alternating iteration method to optimize, and ensured the convergence of the objective function value. Extensive experimental results show that the proposed RS3NMF outperforms other state-of-the-art algorithms in terms of both clustering performance and robustness.