A large-scale dynamic network (LDN) is a source of data in many big
data-related applications due to their large number of entities and large-scale
dynamic interactions. They can be modeled as a high-dimensional incomplete
(HDI) tensor that contains a wealth of knowledge about time patterns. A Latent
factorization of tensors (LFT) model efficiently extracts this time pattern,
which can be established using stochastic gradient descent (SGD) solvers.
However, LFT models based on SGD are often limited by training schemes and have
poor tail convergence. To solve this problem, this paper proposes a novel
nonlinear LFT model (MNNL) based on momentum-incorporated SGD, which extracts
non-negative latent factors from HDI tensors to make training unconstrained and
compatible with general training schemes, while improving convergence accuracy
and speed. Empirical studies on two LDN datasets show that compared to existing
models, the MNNL model has higher prediction accuracy and convergence speed.

本文提出了一种基于动量梯度下降的非线性潜在张量因子分解模型 (MNNL)，可从高维不完整张量 (HDI) 中提取非负潜在因子，改善了传统 LFT 模型的训练问题，提高了预测准确性和收敛速度。

动态网络表示的动量非负张量因式分解模型

A Momentum-Incorporated Non-Negative Latent Factorization of Tensors  Model for Dynamic Network Representation

Large-scale Dynamic Networks (LDNs) are becoming increasingly important in
the Internet age, yet the dynamic nature of these networks captures the
evolution of the network structure and how edge weights change over time,
posing unique challenges for data analysis and modeling. A Latent Factorization
of Tensors (LFT) model facilitates efficient representation learning for a LDN.
But the existing LFT models are almost based on Canonical Polyadic
Factorization (CPF). Therefore, this work proposes a model based on Tensor Ring
(TR) decomposition for efficient representation learning for a LDN.
Specifically, we incorporate the principle of single latent factor-dependent,
non-negative, and multiplicative update (SLF-NMU) into the TR decomposition
model, and analyze the particular bias form of TR decomposition. Experimental
studies on two real LDNs demonstrate that the propose method achieves higher
accuracy than existing models.

本文提出一种基于张量环分解的模型，将单个潜在因子相关的、非负的、乘性的更新方法融入到张量分解模型中，分析了张量环分解的特定偏差形式。在两个真实的大规模动态网络上的实验研究表明，该提出的方法比现有模型的准确性更高。