Temporal networks are an important type of network whose topological
structure changes over time. Compared with methods on static networks, temporal
network embedding (TNE) methods are facing three challenges: 1) it cannot
describe the temporal dependence across network snapshots; 2) the node
embedding in the latent space fails to indicate changes in the network
topology; and 3) it cannot avoid a lot of redundant computation via parameter
inheritance on a series of snapshots. To this end, we propose a novel temporal
network embedding method named Dynamic Cluster Structure Constraint model
(DyCSC), whose core idea is to capture the evolution of temporal networks by
imposing a temporal constraint on the tendency of the nodes in the network to a
given number of clusters. It not only generates low-dimensional embedding
vectors for nodes but also preserves the dynamic nonlinear features of temporal
networks. Experimental results on multiple realworld datasets have demonstrated
the superiority of DyCSC for temporal graph embedding, as it consistently
outperforms competing methods by significant margins in multiple temporal link
prediction tasks. Moreover, the ablation study further validates the
effectiveness of the proposed temporal constraint.

本文提出了一种名为动态集群结构约束模型（DyCSC）的新型时间网络嵌入方法，旨在通过对节点在网络中朝给定数量的簇的趋势施加时间约束来捕捉时间网络的演变。实验结果表明，DyCSC 在多个实际数据集上表现出优越性，它在多个时间链接预测任务中始终大幅优于竞争方法。此外，消融研究进一步验证了所提出的时间约束的有效性。

基于簇结构的动态网络演化过程建模

DyCSC: Modeling the Evolutionary Process of Dynamic Networks Based on Cluster Structure

We study the problem of learning a mixture of multiple linear dynamical
systems (LDSs) from unlabeled short sample trajectories, each generated by one
of the LDS models. Despite the wide applicability of mixture models for
time-series data, learning algorithms that come with end-to-end performance
guarantees are largely absent from existing literature. There are multiple
sources of technical challenges, including but not limited to (1) the presence
of latent variables (i.e. the unknown labels of trajectories); (2) the
possibility that the sample trajectories might have lengths much smaller than
the dimension $d$ of the LDS models; and (3) the complicated temporal
dependence inherent to time-series data. To tackle these challenges, we develop
a two-stage meta-algorithm, which is guaranteed to efficiently recover each
ground-truth LDS model up to error $\tilde{O}(\sqrt{d/T})$, where $T$ is the
total sample size. We validate our theoretical studies with numerical
experiments, confirming the efficacy of the proposed algorithm.

研究了从未标记的短样本轨迹中学习多个线性动态系统（LDS）混合模型的问题，并开发了二阶段元算法，其执行效果得到了验证。

学习线性动力系统混合模型

Learning Mixtures of Linear Dynamical Systems

Time series data introduces two key challenges for explainability methods:
firstly, observations of the same feature over subsequent time steps are not
independent, and secondly, the same feature can have varying importance to
model predictions over time. In this paper, we propose Windowed Feature
Importance in Time (WinIT), a feature removal based explainability approach to
address these issues. Unlike existing feature removal explanation methods,
WinIT explicitly accounts for the temporal dependence between different
observations of the same feature in the construction of its importance score.
Furthermore, WinIT captures the varying importance of a feature over time, by
summarizing its importance over a window of past time steps. We conduct an
extensive empirical study on synthetic and real-world data, compare against a
wide range of leading explainability methods, and explore the impact of various
evaluation strategies. Our results show that WinIT achieves significant gains
over existing methods, with more consistent performance across different
evaluation metrics. The code for our work is publicly available at
https://github.com/layer6ai-labs/WinIT.

本研究提出双重解释方法，旨在解决时间序列数据中不同观测对同一特征的相关性以及特征重要性的变化，经过对合成和实际数据的实证研究，与目前领先的解释方法相比，具有更高的一致性和更好的性能表现