国家自然科学基金(62072293, U21A20473); 山西省自然科学基金(202203021222048)
多视图聚类在图像处理、数据挖掘和机器学习等领域引起了越来越多的关注. 现有的多视图聚类算法存在两个不足, 一是在图构造过程中只考虑每个视图数据之间的成对关系生成亲和矩阵, 而缺乏邻域关系的刻画; 二是现有的方法将多视图信息融合和聚类的过程相分离, 从而降低了算法的聚类性能. 为此, 提出一种更为准确和鲁棒的基于二部图的联合谱嵌入多视图聚类算法. 首先, 基于多视图子空间聚类的思想构造二部图进而产生相似图, 接着利用相似图的谱嵌入矩阵进行图融合, 其次, 在融合过程中考虑每个视图的重要性进行权重约束, 进而引入聚类指示矩阵得到最终的聚类结果. 提出的模型将二部图、嵌入矩阵与聚类指示矩阵约束在一个框架下进行优化. 此外, 提供一种求解该模型的快速优化策略, 该策略将优化问题分解成小规模子问题, 并通过迭代步骤高效解决. 提出算法和已有的多视图聚类算法在真实数据集上进行实验分析. 实验结果表明, 相比已有方法, 提出算法在处理多视图聚类问题上是更加有效和鲁棒的.
Multi-view clustering has attracted more and more attention in the fields of image processing, data mining, and machine learning. Existing multi-view clustering algorithms have two shortcomings. One is that in the process of graph construction, only the pairwise relationship between each view data is considered to generate an affinity matrix, which lacks the characterization of neighborhood relationships; the second is that existing methods separate the process of multi-view information fusion and clustering, thereby reducing the clustering performance of the algorithm. Therefore, this study proposes a more accurate and robust joint spectral embedding multi-view clustering algorithm based on bipartite graphs. Firstly, based on the multi-view subspace clustering idea,bipartite graphs are constructed, and similar graphs are generated.Then the spectral embedding matrix of similar graphs is used to perform graph fusion. Secondly, by considering the importance of each view during the fusion process, weight constraints are applied, and an indicator matrix is introduced to obtain the final clustering result. A model is proposed to optimize the bipartite graph, embedding matrix, and clustering indicator matrix within a single framework. In addition, a fast optimization strategy for solving the model is provided, which decomposes the optimization problem into small module subproblems and efficiently solves them through iterative steps. The proposed algorithm and existing multi-view clustering algorithms have been experimentally analyzed on real data sets. Experimental results show that the proposed algorithm is more effective and robust in dealing with multi-view clustering problems compared with existing methods.