Graph is a ubiquitous representation of data in various research fields, and
graph embedding is a prevalent machine learning technique for capturing key
features and generating fixed-sized attributes. However, most state-of-the-art
graph embedding methods are computationally and spatially expensive. Recently,
the Graph Encoder Embedding (GEE) has been shown as the fastest graph embedding
technique and is suitable for a variety of network data applications. As
real-world data often involves large and sparse graphs, the huge sparsity
usually results in redundant computations and storage. To address this issue,
we propose an improved version of GEE, sparse GEE, which optimizes the
calculation and storage of zero entries in sparse matrices to enhance the
running time further. Our experiments demonstrate that the sparse version
achieves significant speedup compared to the original GEE with Python
implementation for large sparse graphs, and sparse GEE is capable of processing
millions of edges within minutes on a standard laptop.

图编码嵌入（GEE）的稀疏版本在计算和存储零元素方面进行了优化，与原始 GEE 相比，这种改进后的方法在处理大规模稀疏图时实现了显著的加速，可以在标准笔记本上几分钟内处理数百万条边。

Python 大规模稀疏图的高效图编码嵌入

Efficient Graph Encoder Embedding for Large Sparse Graphs in Python

Graph encoder embedding, a recent technique for graph data, offers speed and
scalability in producing vertex-level representations from binary graphs. In
this paper, we extend the applicability of this method to a general graph
model, which includes weighted graphs, distance matrices, and kernel matrices.
We prove that the encoder embedding satisfies the law of large numbers and the
central limit theorem on a per-observation basis. Under certain condition, it
achieves asymptotic normality on a per-class basis, enabling optimal
classification through discriminant analysis. These theoretical findings are
validated through a series of experiments involving weighted graphs, as well as
text and image data transformed into general graph representations using
appropriate distance metrics.

将图编码嵌入方法扩展到包括加权图、距离矩阵和核矩阵等一般图模型，证明该方法满足大数定律和中心极限定理，能够在一定条件下实现渐近正态性，并通过一系列实验证实了这些理论发现。