|
| 摘要: |
| 非负矩阵分解已经被广泛应用于数据挖掘和机器学习等领域. 然而，极大多数原始数据都包含了许多噪音值和异常值点，这给处理原始数据和提高算法的性能带来了极大的挑战. 因此，为了快速的处理数据并更好地提高算法的性能，本文提出了基于核技巧的$L_{2,1}$范数非负矩阵分解，该方法便于数据处理和改善算法的稀疏性和鲁棒性，并给出了更新迭代规则和算法的收敛性证明. 数值实验表明，和已有的非负矩阵分解方法相比，本文提出的方法是很有效的. |
| 关键词: 非负矩阵分解 核技巧 $L_{2,1}$范数 稀疏性 鲁棒性. |
| DOI： |
| 分类号:029 |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目）,广西密码学与信息安全重点实验室研究课题和宁夏自然科学基金，获桂林电子科技大学研究生优秀学位论文培育项目资助. |
|
| Kernel-based $L_{2,1}$ norm Non-negative Matrix Factorization in Image Clustering |
|
Jianglan Yu,Xiangli Li
|
| Abstract: |
| Non-negative matrix factorization has been widely used in fields such as data mining and machine learning. However, most of the original data contains many noise values and outliers, which brings many difficulties of processing to the original data and improving the performance of the algorithm. In order to process quickly data and improve better the performance of the algorithm, the kernel-based $L_{2,1}$ norm non-negative matrix factorization is proposed, which facilitate the data processing and improve the sparsity and robustness of the algorithm. In addition, the update iteration rules and the convergence of the algorithm are given. Numerical experiments illustrate that our method is superior to existing method. |
| Key words: Non-negative matrix factorization kernel trick $L_{2,1}$norm Sparsity Robustness. |
