Graph Auto-Encoders (GAEs) are powerful tools for graph representation
learning. In this paper, we develop a novel Hierarchical Cluster-based GAE
(HC-GAE), that can learn effective structural characteristics for graph data
analysis. To this end, during the encoding process, we commence by utilizing
the hard node assignment to decompose a sample graph into a family of separated
subgraphs. We compress each subgraph into a coarsened node, transforming the
original graph into a coarsened graph. On the other hand, during the decoding
process, we adopt the soft node assignment to reconstruct the original graph
structure by expanding the coarsened nodes. By hierarchically performing the
above compressing procedure during the decoding process as well as the
expanding procedure during the decoding process, the proposed HC-GAE can
effectively extract bidirectionally hierarchical structural features of the
original sample graph. Furthermore, we re-design the loss function that can
integrate the information from either the encoder or the decoder. Since the
associated graph convolution operation of the proposed HC-GAE is restricted in
each individual separated subgraph and cannot propagate the node information
between different subgraphs, the proposed HC-GAE can significantly reduce the
over-smoothing problem arising in the classical convolution-based GAEs. The
proposed HC-GAE can generate effective representations for either node
classification or graph classification, and the experiments demonstrate the
effectiveness on real-world datasets.

通过使用硬节点分配将样本图分解为分离子图的系列，并利用软节点分配重新构建原始图结构，该研究提出的层次聚类 GAE（HC-GAE）能够有效提取原始样本图的双向分层结构特征，解决了经典基于卷积的 GAE 中的过度平滑问题。

HC-GAE: 基于层次聚类的图自编码器用于图表示学习

HC-GAE: The Hierarchical Cluster-based Graph Auto-Encoder for Graph  Representation Learning

Graph Anomaly Detection (GAD) is a technique used to identify abnormal nodes
within graphs, finding applications in network security, fraud detection,
social media spam detection, and various other domains. A common method for GAD
is Graph Auto-Encoders (GAEs), which encode graph data into node
representations and identify anomalies by assessing the reconstruction quality
of the graphs based on these representations. However, existing GAE models are
primarily optimized for direct link reconstruction, resulting in nodes
connected in the graph being clustered in the latent space. As a result, they
excel at detecting cluster-type structural anomalies but struggle with more
complex structural anomalies that do not conform to clusters. To address this
limitation, we propose a novel solution called GAD-NR, a new variant of GAE
that incorporates neighborhood reconstruction for graph anomaly detection.
GAD-NR aims to reconstruct the entire neighborhood of a node, encompassing the
local structure, self-attributes, and neighbor attributes, based on the
corresponding node representation. By comparing the neighborhood reconstruction
loss between anomalous nodes and normal nodes, GAD-NR can effectively detect
any anomalies. Extensive experimentation conducted on six real-world datasets
validates the effectiveness of GAD-NR, showcasing significant improvements (by
up to 30% in AUC) over state-of-the-art competitors. The source code for GAD-NR
is openly available. Importantly, the comparative analysis reveals that the
existing methods perform well only in detecting one or two types of anomalies
out of the three types studied. In contrast, GAD-NR excels at detecting all
three types of anomalies across the datasets, demonstrating its comprehensive
anomaly detection capabilities.

本文提出了一种新颖的图自编码器方法 GAD-NR，它通过邻域重构来检测图的异常节点，相较于现有方法在克服聚类型结构异常检测的同时还能检测其他类型的异常，实验结果显示 GAD-NR 较现有竞争方法在真实世界数据集中的性能提升了多达 30%。

邻域重构图异常检测

GAD-NR: Graph Anomaly Detection via Neighborhood Reconstruction

Most recent graph clustering methods have resorted to Graph Auto-Encoders
(GAEs) to perform joint clustering and embedding learning. However, two
critical issues have been overlooked. First, the accumulative error, inflicted
by learning with noisy clustering assignments, degrades the effectiveness and
robustness of the clustering model. This problem is called Feature Randomness.
Second, reconstructing the adjacency matrix sets the model to learn irrelevant
similarities for the clustering task. This problem is called Feature Drift.
Interestingly, the theoretical relation between the aforementioned problems has
not yet been investigated. We study these issues from two aspects: (1) there is
a trade-off between Feature Randomness and Feature Drift when clustering and
reconstruction are performed at the same level, and (2) the problem of Feature
Drift is more pronounced for GAE models, compared with vanilla auto-encoder
models, due to the graph convolutional operation and the graph decoding design.
Motivated by these findings, we reformulate the GAE-based clustering
methodology. Our solution is two-fold. First, we propose a sampling operator
$\Xi$ that triggers a protection mechanism against the noisy clustering
assignments. Second, we propose an operator $\Upsilon$ that triggers a
correction mechanism against Feature Drift by gradually transforming the
reconstructed graph into a clustering-oriented one. As principal advantages,
our solution grants a considerable improvement in clustering effectiveness and
robustness and can be easily tailored to existing GAE models.

为了解决图聚类中的关键问题：特性随机性和特性漂移，本文提出了一种 GAE 聚类方法，并提出采样和操作符，以提高聚类效果和鲁棒性。

重新思考基于图自编码器的属性图聚类模型

Rethinking Graph Auto-Encoder Models for Attributed Graph Clustering

In this paper, we propose a novel approach to predict group activities given
the beginning frames with incomplete activity executions. Existing action
prediction approaches learn to enhance the representation power of the partial
observation. However, for group activity prediction, the relation evolution of
people's activity and their positions over time is an important cue for
predicting group activity. To this end, we propose a sequential relational
anticipation model (SRAM) that summarizes the relational dynamics in the
partial observation and progressively anticipates the group representations
with rich discriminative information. Our model explicitly anticipates both
activity features and positions by two graph auto-encoders, aiming to learn a
discriminative group representation for group activity prediction. Experimental
results on two popularly used datasets demonstrate that our approach
significantly outperforms the state-of-the-art activity prediction methods.

本研究提出一种基于序列关系预测模型的组活动预测方法，该模型可以总结部分观测数据中的关系动态并逐步预测具有区分性信息的群体表示，通过两种图形自编码器预测活动特征和位置，并在实验中取得了显著的预测效果。