基于核技巧和超图正则的稀疏非负矩阵分解

针对传统的非负矩阵分解（NMF）应用于聚类时，没有同时考虑到鲁棒性和稀疏性，导致聚类性能较低的问题，提出了基于核技巧和超图正则的稀疏非负矩阵分解算法（KHGNMF）。首先，在继承核技巧的良好性能的基础上，用L_2，1范数改进标准非负矩阵分解中的F范数，并添加超图正则项以尽可能多地保留原始数据间的内在几何结构信息；其次，引入L_2，1/2伪范数和L_1/2正则项作为稀疏约束合并到NMF模型中；最后，提出新算法并将新算法应用于图像聚类。在6个标准的数据集上进行验证，实验结果表明，相对于非线性正交图正则非负矩阵分解方法，KHGNMF使聚类性能（精度和归一化互信息）成功地提升了39%~54%，有效地改善和提高了算法的稀疏性和鲁棒性，聚类效果更好。

Sparse non-negative matrix factorization based on kernel and hypergraph regularization

Focused on the problem that when traditional Non-negative Matrix Factorization (NMF) is applied to clustering, robustness and sparsity are not considered at the same time, which leads to low clustering performance, a sparse Non-negative Matrix Factorization algorithm based on Kernel technique and HyperGraph regularization (KHGNMF) was proposed. Firstly, on the basis of inheriting good performance of kernel technique, L_2,1 norm was used to improve F-norm of standard NMF, and hyper-graph regularization terms were added to preserve inherent geometric structure information among the original data as much as possible. Secondly, L_2,1/2 pseudo norm and L_1/2 regularization terms were merged into NMF model as sparse constraints. Finally, a new algorithm was proposed and applied to image clustering. The experimental results on six standard datasets show that KHGNMF can improve clustering performance (accuracy and normalized mutual information) by 39% to 54% compared with nonlinear orthogonal graph regularized non-negative matrix factorization, and the sparsity and robustness of the proposed algorithm are increased and the clustering effect is improved.