融合块对角约束的鲁棒低秩多核聚类

Low-rank robust multiple kernel clustering with block diagonal constraints

针对现有的多核学习(multiple kernel learning,MKL)子空间聚类方法忽略噪声和特征空间中数据的低秩结构问题,提出一种新的鲁棒多核子空间聚类方法(low-rank robust multiple kernel clustering,LRMKC),该方法结合块对角表示(block diagonal representation,BDR)与低秩共识核(low-rank consensus kernel,LRCK)学习,可以更好地挖掘数据的潜在结构.为了学习最优共识核,设计一种基于混合相关熵度量(mixture correntropy induced metric,MCIM)的自动加权策略,其不仅为每个核设置最优权重,而且通过抑制噪声提高模型的鲁棒性;为了探索特征空间数据的低秩结构,提出一种非凸低秩共识核学习方法;考虑到亲和度矩阵的块对角性质,对系数矩阵应用块对角约束.LRMKC将MKL、LRCK与BDR巧妙融合,以迭代提高各种方法的效率,最终形成一个处理非线性结构数据的全局优化方法.与最先进的MKL子空间聚类方法相比,通过在图像和文本数据集上的大量实验验证了LRMKC的优越性.

Existing(multiple kernel learning,MKL)subspace clustering algorithms ignore the noise and the low-rank structure of the data in the feature space,therefore,we propose a new low-rank robust multiple kernel clustering algorithm(LRMKC)with block diagonal representation(BDR)and low-rank consensus kernel(LRCK),which is better for mining the underlying structure of the data.In particular,1)to learn the optimal consensus kernel,we design an automatic weighting strategy using the mixture correntropy induced metric(MCIM),which not only sets the optimal weight for each kernel but also improves the robustness of the LRMKC by suppressing noise;2)to explore the low-rank structure of input data in feature space,we learn the low-rank consensus kernel by the Schatten p-norm constraint on the optimal consensus kernel;3)considering the block diagonal property of the affinity matrix,we apply block diagonal constraint to the coefficient matrix.The LRMKC combines MKL,LRCK,and BDR to solve these problems at the same time.Through the interaction of three technologies,the results of other technologies are used in the overall optimal solution to iteratively improve the efficiency of each technology,and finally form an overall optimal algorithm for processing nonlinear structural data.Compared with the most advanced MKL subspace clustering algorithms,extensive experiments on image and text datasets verify the competitiveness of the LRMKC.