基于统一标签矩阵的快速多视图聚类

Fast Multi-View Clustering Based on Uniform Label Matrix

在多视图聚类领域,众多方法直接从原始数据中学习相似矩阵,但是这忽视了原始数据中的噪声所产生的影响;此外,还有一些方法必须对图拉普拉斯矩阵进行特征分解,这导致可解释性的降低且需要k-means等后处理。为解决以上问题,文中提出一种基于统一标签矩阵的快速多视图聚类。首先,从松弛的归一化切割和比率切割的统一观点出发对目标函数增加非负约束;然后,通过指示矩阵对相似矩阵进行结构化图重构,确保获得的图具有强簇内连接和弱簇间连接;此外,通过设置统一的标签矩阵降低迭代次数,从而进一步提升该方法的运行速度;最后,基于交替方向乘子法的策略对问题进行优化求解。算法通过随机选择锚点地址的方法对多视图数据集进行对齐,对齐视图能够大幅提升聚类的精度。在迭代过程中通过使用奇异值分解来替代特征分解,有效地解决了传统谱聚类算法计算复杂度高的问题;通过按行索引指示矩阵的最大元素的列标直接获得标签。在4个真实数据集上的实验结果证明了该算法的有效性,表明其聚类性能优于现有的9种基准算法。

In the field of multi-view clustering,many methods learn the similarity matrix directly from the original data,but this ignores the effect of noise in the original data.In addition,some methods must perform a feature de⁃composition on the graph Laplacian matrix,which leads to reduced interpretability and requires post-processing such as k-means.To address these issues,this paper proposed a fast multi-view clustering based on a unified label matrix.Firstly,a non-negative constraint was added to the objective function from the unified viewpoint of the nor⁃malized cut of the relaxation and the ratio cut.Then,a structured graph reconstruction was performed on the simi⁃larity matrix by the indicator matrix to ensure that the obtained graph has strong intra-cluster connections and weak inter-cluster connections.In addition,the number of iterations was reduced by setting a unified label matrix,thus further improving the speed of the method.Finally,the problem was solved optimally based on an alternating direc⁃tion multiplication strategy.The algorithm aligns the multi-view dataset by randomly selecting the anchor ad⁃dresses,and aligning the views can significantly improve the accuracy of clustering.The problem of the high com⁃putational complexity of traditional spectral clustering algorithms was effectively solved by using singular value de⁃composition instead of feature decomposition in the iterative process.Labels were obtained directly by indicating the column labels of the largest element of the matrix by row index.Experimental results on four real datasets demonstrate the effectiveness of the algorithm,and show that its clustering performance outperformed the nine existing benchmark algorithms.