The rapid growth of the number of data brings great challenges to clustering, especially the introduction of multi-view data, which collected from multiple sources or represented by multiple features, makes these challenges more arduous. How to clustering large-scale data efficiently has become the hottest topic of current large-scale clustering tasks. Although several accelerated multi-view methods have been proposed to improve the efficiency of clustering large-scale data, they still cannot be applied to some scenarios that require high efficiency because of the high computational complexity. To cope with the issue of high computational complexity of existing multi-view methods when dealing with large-scale data, a fast multi-view clustering model via nonnegative and orthogonal factorization (FMCNOF) is proposed in this paper. Instead of constraining the factor matrices to be nonnegative as traditional nonnegative and orthogonal factorization (NOF), we constrain a factor matrix of this model to be cluster indicator matrix which can assign cluster labels to data directly without extra post-processing step to extract cluster structures from the factor matrix. Meanwhile, the F-norm instead of the L2-norm is utilized on the FMCNOF model, which makes the model very easy to optimize. Furthermore, an efficient optimization algorithm is proposed to solve the FMCNOF model. Different from the traditional NOF optimization algorithm requiring dense matrix multiplications, our algorithm can divide the optimization problem into three decoupled small size subproblems that can be solved by much less matrix multiplications. Combined with the FMCNOF model and the corresponding fast optimization method, the efficiency of the clustering process can be significantly improved, and the computational complexity is nearly $O(n)$ . Extensive experiments on various benchmark data sets validate our approach can greatly improve the efficiency when achieve acceptable performance.

中文翻译：

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通过非负和正交分解实现快速的多视图聚类

数据数量的快速增长给聚类带来了巨大的挑战，尤其是引入多视图数据（这些数据是从多个来源收集或由多种功能表示）的，这些挑战更加艰巨。如何有效地对大型数据进行聚类已经成为当前大规模聚类任务中最热门的话题。尽管已经提出了几种加速的多视图方法来提高对大规模数据进行聚类的效率，但是由于计算复杂性高，它们仍然无法应用于需要高效率的某些场景。为了解决现有的多视图方法在处理大规模数据时计算量大的问题，提出了一种基于非负和正交分解的快速多视图聚类模型（FMCNOF）。代替将因子矩阵约束为传统的非负和正交因式分解（NOF）来约束非负矩阵，我们将此模型的因子矩阵约束为聚类指标矩阵，该矩阵可以直接将聚类标签分配给数据，而无需额外的后处理步骤即可提取聚类结构从因子矩阵。同时，FMCNOF模型使用F范数而不是L2范数，这使得模型易于优化。此外，提出了一种有效的优化算法来求解FMCNOF模型。与需要密集矩阵乘法的传统NOF优化算法不同，我们的算法可以将优化问题分为三个解耦的小子问题，这些问题可以用更少的矩阵乘法来解决。 $ O（n）$ 。在各种基准数据集上进行的大量实验证明，当达到可接受的性能时，我们的方法可以大大提高效率。