Abstract:

Most of the existing multi-view clustering algorithms assume that there is a linear relationship between multi-view data points， and fail to maintain the locality of original feature space during the learning process. At the same time， merging subspace in Euclidean space is too rigid to align learned subspace representations. To solve the above problems， a multi-view clustering algorithm via subspaces merging on Grassmann manifold was proposed. Firstly， the kernel trick and the learning of local manifold structure were combined to obtain the subspace representations of different views. Then， the subspace representations were merged on the Grassmann manifold to obtain the consensus affinity matrix. Finally， spectral clustering was performed on the consensus affinity matrix to obtain the final clustering result. And Alternating Direction Method of Multipliers （ADMM） was used to optimize the proposed model. Compared with Kernel Multi-view Low-Rank Sparse Subspace Clustering （KMLRSSC） algorithm， the proposed algorithm has the clustering accuracy improved by 20.83 percentage points， 9.47 percentage points and 7.33 percentage points on MSRCV1， Prokaryotic and Not-Hill datasets. Experimental results verify the effectiveness and good performance of the multi-view clustering algorithm via subspace merging on Grassmann manifold.

Key words: subspace merging, multi-view clustering, kernel trick, local manifold structure, Grassmann manifold

摘要：

现有的多视图聚类算法大多假设多视图数据点之间为线性关系，且在学习过程中无法保留原始特征空间的局部性；而在欧氏空间中进行子空间融合又过于单调，无法将学习到的子空间表示对齐。针对以上问题，提出了基于格拉斯曼流形融合子空间的多视图聚类算法。首先，将核技巧和局部流形结构学习结合以得到不同视图的子空间表示；然后，在格拉斯曼流形上融合这些子空间表示以得到一致性亲和矩阵；最后，对一致性亲和矩阵执行谱聚类来得到最终的聚类结果，并利用交替方向乘子法（ADMM）来优化所提模型。与核多视图低秩稀疏子空间聚类（KMLRSSC）算法相比，所提算法的聚类精度在MSRCV1、Prokaryotic、Not-Hill数据集上分别提高了20.83个百分点、9.47个百分点和7.33个百分点。实验结果验证了基于格拉斯曼流形融合子空间的多视图聚类算法的有效性和良好性能。

关键词: 子空间融合, 多视图聚类, 核技巧, 局部流形结构, 格拉斯曼流形