分区与编码：学习如何压缩图
Partition and Code: learning how to compress graphs
AI总结：
本文提出可学习的无损图压缩框架“Partition and Code”，通过分区、字典映射与熵编码三阶段以梯度下降联合训练，在理论上证明其压缩增益随顶点数线性或二次增长，并在真实网络数据上取得显著改进。
摘要：
我们能否使用机器学习来压缩图数据？图中缺乏顺序性对传统压缩算法构成了重大挑战，限制了它们可获得的增益以及发现相关模式的能力。另一方面，大多数图压缩方法依赖于领域相关的手工设计表示，无法适应不同的底层图分布。本工作旨在建立无损图压缩方法应遵循的必要原则，以接近熵存储下界。我们不对图分布做出刚性假设，而是将压缩器表述为一个概率模型，该模型可以从数据中学习并泛化到未见实例。我们的“Partition and Code”框架包含三个步骤：首先，一个分区算法将图分解为子图；然后，将这些子图映射到一个小编码字典的元素上，并在该字典上学习一个概率分布；最后，一个熵编码器将表示转换为比特。所有组件（分区、字典和分布）都是参数化的，并且可以通过梯度下降进行训练。我们从理论上比较了几种图编码的压缩质量，并在温和条件下证明，PnC 实现的压缩增益随顶点数量呈线性或二次增长。在实验上，PnC 在多种真实世界网络上取得了显著的压缩改进。
英文摘要：
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant patterns. On the other hand, most graph compression approaches rely on domain-dependent handcrafted representations and cannot adapt to different underlying graph distributions. This work aims to establish the necessary principles a lossless graph compression method should follow to approach the entropy storage lower bound. Instead of making rigid assumptions about the graph distribution, we formulate the compressor as a probabilistic model that can be learned from data and generalise to unseen instances. Our "Partition and Code" framework entails three steps: first, a partitioning algorithm decomposes the graph into subgraphs, then these are mapped to the elements of a small dictionary on which we learn a probability distribution, and finally, an entropy encoder translates the representation into bits. All the components (partitioning, dictionary and distribution) are parametric and can be trained with gradient descent. We theoretically compare the compression quality of several graph encodings and prove, under mild conditions, that PnC achieves compression gains that grow either linearly or quadratically with the number of vertices. Empirically, PnC yields significant compression improvements on diverse real-world networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
