Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.

翻译：非负张量分解（NTF）已成为从非负高阶数据中提取特征并保持固有结构信息进行基于部分表示的重要工具。然而，原始NTF方法采用欧几里得散度或库尔贝克-莱布勒散度作为损失函数，平等对待每个特征，导致特征侧信息被忽略。为利用特征的相关性信息和样本的流形信息，我们引入Wasserstein流形非负张量分解（WMNTF），该方法最小化输入张量数据分布与重构数据分布之间的Wasserstein距离。尽管已有研究将Wasserstein距离引入非负矩阵分解（NMF），但这些方法忽略了高阶数据的空间结构信息。我们采用Wasserstein距离（又称地球移动距离或最优传输距离）作为度量，并在潜在因子上添加图正则化项。实验结果表明，与其它NMF和NTF方法相比，所提方法具有有效性。