基于相关熵和流形正则化的图像聚类

Image clustering based on correntropy and manifold regularization

近年来,聚类作为机器学习、数据挖掘等领域的基本问题受到广泛的关注及研究,然而数据中普遍存在的噪声和异常值严重影响聚类结果.提出一个基于相关熵和流形正则化的聚类框架CRNMF(Correntropy and Manifold Regularization Non-Negative Matrix Factorization).首先,采用基于相关熵的非负矩阵分解(Non-Negative Matrix Factorization,NMF)作为损失函数来抑制非高斯噪声和异常值的影响;其次,充分考虑数据的结构信息,采用流形正则化学习数据的局部结构,并通过l2,1-范数对非负矩阵进行稀疏约束;最后,利用半二次优化技术(Half-Quadratic Optimization Technique,HQ)进行优化,并分析了收敛性和计算复杂度.在五个图像数据集上进行测试,实验结果表明,提出的框架在图像聚类任务中具有较好的有效性和鲁棒性.

As a basic problem in machine learning,data mining and other fields,clustering has received extensive attention and research in recent years. However,the widespread noise and outliers of data affect the clustering results seriously.Therefore,a clustering framework based on correntropy and manifold regularization(CRNMF) is proposed. First,the NonNegative Matrix Factorization(NMF) based on correntropy is used as the loss function to suppress the effects of non-Gaussian noise and outliers. Second,the structure information of the data is fully considered,the manifold regularization is used to learn the local structure of the data,and the sparse constraint is applied to the non-negative matrix by l2,1-norm.Finally,the Half-Quadratic Optimization Technique(HQ) is used to optimize the algorithm,and the convergence and computational complexity are analyzed. Experimental results show that the proposed CRNMF is effective and robust on five image datasets.