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.

利用 Wasserstein 距离作为度量，并将图形正则化器添加到潜在因子中，我们引入了 Wasserstein 流形非负张量分解（WMNTF），以利用特征的相关信息和样本的流形信息。实验证明，与其他 NMF 和 NTF 方法相比，所提方法的有效性。

具峰值非负张量分解的 Wasserstein 流形正则化

Wasserstein Nonnegative Tensor Factorization with Manifold  Regularization

The technology of traffic flow forecasting plays an important role in
intelligent transportation systems. Based on graph neural networks and
attention mechanisms, most previous works utilize the transformer architecture
to discover spatiotemporal dependencies and dynamic relationships. However,
they have not considered correlation information among spatiotemporal sequences
thoroughly. In this paper, based on the maximal information coefficient, we
present two elaborate spatiotemporal representations, spatial correlation
information (SCorr) and temporal correlation information (TCorr). Using SCorr,
we propose a correlation information-based spatiotemporal network (CorrSTN)
that includes a dynamic graph neural network component for integrating
correlation information into spatial structure effectively and a multi-head
attention component for modeling dynamic temporal dependencies accurately.
Utilizing TCorr, we explore the correlation pattern among different periodic
data to identify the most relevant data, and then design an efficient data
selection scheme to further enhance model performance. The experimental results
on the highway traffic flow (PEMS07 and PEMS08) and metro crowd flow (HZME
inflow and outflow) datasets demonstrate that CorrSTN outperforms the
state-of-the-art methods in terms of predictive performance. In particular, on
the HZME (outflow) dataset, our model makes significant improvements compared
with the ASTGNN model by 12.7%, 14.4% and 27.4% in the metrics of MAE, RMSE and
MAPE, respectively.

本文提出了基于最大信息系数的空间 / 时间相关性表示方法，利用该方法构建了一个基于相关信息的时空网络（CorrSTN），包括动态图神经网络和多头注意力，并使用这个网络在公路和地铁数据集上进行道路和人群的流量预测，结果表明 CorrSTN 在所有度量标准下均优于当前最先进的方法。