Nonnegative matrix factorization (NMF) plays a significant role of finding parts-based representations of nonnegative data that is widely used in data analysis applications. However, sequential data (e.g., video scene, human action) with ordered structures usually share obvious similar features between neighboring data points unless a sudden change occurs, it is important to exploit temporal information for sequential data representation. However, this remains a challenging problem for NMF-based methods, which are unsuitable for the analysis of such data. In this work, we propose structural constraint deep matrix factorization (SC-MF), which captures the ordered structure information into the deep matrix factorization process to improve data representation. With a novel neighbor penalty term in each layer process, SC-MF enforces the similarity of neighboring data in the final layer. The appropriate iterative updating algorithm is derived to solve SC-MF’s objective function. The proofs of the convergence and complexity of the SC-MF are also presented. Experimental results on several real sequential datasets for face clustering, video scene segmentation, and action segmentation tasks demonstrate the effectiveness of our approach.

中文翻译：

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用于顺序数据聚类的结构约束深度矩阵分解

非负矩阵分解（NMF）在寻找基于零件的非负数据表示中起着重要作用，该数据在数据分析应用程序中得到了广泛使用。但是，具有顺序结构的顺序数据（例如，视频场景，人类动作）通常会在相邻数据点之间共享明显的相似特征，除非发生突然的变化，利用时间信息进行顺序数据表示很重要。但是，这对于基于NMF的方法仍然是一个具有挑战性的问题，不适用于此类数据的分析。在这项工作中，我们提出了结构约束深度矩阵分解（SC-MF），它将有序结构信息捕获到深度矩阵分解过程中以改善数据表示。在每一层流程中都有一个新颖的邻居惩罚项，SC-MF在最后一层强制执行相邻数据的相似性。推导了适当的迭代更新算法来求解SC-MF的目标函数。还介绍了SC-MF收敛性和复杂性的证明。针对面部聚类，视频场景分割和动作分割任务的几个真实序列数据集的实验结果证明了我们方法的有效性。