Datasets in Multi View Clustering with Adaptive Similarity Graph Joint Optimization

Compared to single view learning, multi view learning can often obtain more comprehensive information about the learning object. Therefore, in the field of unsupervised learning, multi view clustering has received great attention from researchers. Among them, graph based multi view clustering has made great research progress in recent years. Graph based multi view clustering generally first learns similar graphs from the original data of each view, and then fuses similar graphs between views to obtain the final clustering result. Therefore, the effectiveness of multi view clustering is determined by the quality of similar graphs and the fusion method of similar graphs. However, existing graph based multi view clustering methods almost focus on the fusion method of similar graphs between views, and lack attention to the quality of similar graphs themselves. Most of these methods are... Learning similar graphs from the original data of each view in isolation and keeping them unchanged during the subsequent graph fusion process. This inevitably results in similar graphs containing noise and redundant information, which in turn affects subsequent graph fusion and clustering. However, a small amount of research that considers the quality of similar graphs, either the construction of similar graphs and the process of graph fusion are directly iterative, Either rank constraints are used in advance during the predefined similarity graph process to further initialize, or some underlying structures of the similarity graph are used to obtain the fusion graph. These methods have little improvement on the similarity graph itself, and the final clustering performance improvement is also very limited. At the same time, existing graph based multi view clustering processes also lack comprehensive consideration of consistency and inconsistency between views, which will seriously affect the final multi view clustering performance. In order to avoid the adverse effects of low-quality predefined similarity graphs on clustering results and comprehensively consider consistency and inconsistency between views to improve the final clustering effect, this paper proposes an adaptive multi view clustering method for joint optimization of similarity graphs. Firstly, the Hadamard product is used to obtain high-quality consistency between views. Partial information is then compared with each predefined similar graph to reconstruct the preset similar graphs for each view. This process strengthens the consistency between views and weakens the inconsistency. Secondly, a joint iterative optimization framework for similar graph reconstruction and graph fusion is designed to achieve adaptive improvement of similar graphs, The ultimate goal is to achieve the combined improvement of similar graphs and clustering results. This method combines the process of improving similar graphs with the process of graph fusion for adaptive iterative optimization, and continuously strengthens the consistency between views and weakens the inconsistency between views during iterative optimization. In addition, this method also integrates some advantages of existing multi view clustering methods, such as self weighting and no additional clustering steps. The effectiveness and superiority of this method have been verified through experiments on nine benchmark datasets and eight comparison methods

与单视图学习（single view learning）相比，多视图学习（multi view learning）通常能获取更全面的学习对象信息。因此，在无监督学习领域，多视图聚类（multi view clustering）受到了研究者的广泛关注。其中，基于图的多视图聚类（graph-based multi view clustering）近年来取得了显著的研究进展。基于图的多视图聚类通常首先从各视图的原始数据中学习相似图（similar graphs），然后融合视图间的相似图以得到最终聚类结果。因此，多视图聚类的有效性取决于相似图的质量和相似图的融合方法。然而，现有基于图的多视图聚类方法几乎都聚焦于视图间相似图的融合方法，而对相似图自身的质量缺乏关注。这些方法大多孤立地从各视图原始数据中学习相似图，并在后续图融合过程中保持其不变。这不可避免地导致相似图包含噪声和冗余信息，进而影响后续的图融合与聚类。然而，少数考虑相似图质量的研究，要么将相似图的构建与图融合过程直接迭代，要么在预定义相似图过程中预先使用秩约束（rank constraints）进行进一步初始化，要么利用相似图的某些潜在结构获取融合图。这些方法对相似图本身的改进有限，最终聚类性能的提升也非常有限。同时，现有基于图的多视图聚类过程也缺乏对视图间一致性与不一致性的全面考量，这将严重影响最终的多视图聚类性能。为避免低质量预定义相似图对聚类结果的不利影响，并全面考量视图间的一致性与不一致性以提升最终聚类效果，本文提出一种相似图联合优化的自适应多视图聚类方法。首先，利用哈达玛积（Hadamard product）获取视图间的高质量一致性信息。随后，将该部分信息与各预定义相似图进行比对，以重构各视图的预设相似图。此过程增强了视图间的一致性，同时弱化了不一致性。其次，设计了相似图重构与图融合的联合迭代优化框架，以实现相似图的自适应改进，最终目标是达成相似图与聚类结果的协同提升。该方法将相似图改进过程与图融合过程相结合，进行自适应迭代优化，并在迭代优化中持续增强视图间的一致性、弱化视图间的不一致性。此外，该方法还融合了现有多视图聚类方法的若干优势，如自加权（self-weighting）和无需额外聚类步骤。通过在9个基准数据集（benchmark datasets）上与8种对比方法的实验，验证了该方法的有效性与优越性。