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→工程技术和计算机科学中的粗粒化
=== 工程技术和计算机科学中的粗粒化 ===
=== 工程技术和计算机科学中的粗粒化 ===
开发互联网及其他通信与交通网络的缩尺工程模型方法，一直是通信技术领域研究的长期目标<ref name="Papadopoulos_Topological_downscaling">{{cite journal|author1=Papadopoulos F|author2=Psounis K|author3=Govindan R.|title=Performance preserving topological downscaling of internet-like networks|journal=IEEE J. Sel. Areas Commun.|year=2006|volume=24|url=}}</ref><ref name="Papadopoulos_Uncongested_links">{{cite journal|author1=Papadopoulos F|author2=Psounis K.|title=Efficient identification of uncongested internet links for topology downscaling|journal=SIGCOMM Comput. Commun. Rev.|year=2007|volume=37|url=}}</ref><ref name="Di_Similitude_theory_traffic">{{cite journal|author1=Di X|author2=Zhao Y|author3=Huang S|author4=Liu H. X.|title=A similitude theory for modeling traffic flow dynamics|journal=IEEE Trans. Intell. Transp. Syst.|year=2019|volume=20|url=}}</ref>。近年来，如何在保持图结构关键属性基本不变的前提下缩减其规模，也成为机器学习领域的重要课题——图嵌入技术和图神经网络等深度学习工具正日益广泛应用于图结构数据分析。粗粒化方案旨在通过压缩图结构降低实际应用中的计算成本与复杂度<ref name="Chen_HARP">{{cite journal|author1=Chen H|author2=Perozzi B|author3=Hu Y|author4=Skiena S.|title=HARP: hierarchical representation learning for networks|journal=Proc. 32nd AAAI Conference on Artificial Intelligence|year=2018|pages=2127–2134|url=}}</ref><ref name="Loukas_Graph_reduction">{{cite journal|author1=Loukas A.|title=Graph reduction with spectral and cut guarantees|journal=J. Mach. Learn. Res.|year=2019|volume=20|url=}}</ref><ref name="Jin_Graph_coarsening">{{cite journal|author1=Jin Y|author2=Loukas A|author3=JaJa J.|title=Graph coarsening with preserved spectral properties|journal=Proc. International Conference on Artificial Intelligence and Statistics|year=2020|pages=4452–4462|url=}}</ref><ref name="Fahrbach_Faster_graph_embeddings">{{cite journal|author1=Fahrbach M|author2=Goranci G|author3=Peng R|author4=Sachdeva S|author5=Wang C.|title=Faster graph embeddings via coarsening|journal=Proc. International Conference on Machine Learning|year=2020|pages=2953–2963|url=}}</ref><ref name="Liang_MILE">{{cite journal|author1=Liang J|author2=Gurukar S|author3=Parthasarathy S.|title=MILE: A multi-level framework for scalable graph embedding|journal=Proc. International AAAI Conference on Web and Social Media|year=2021|volume=15|pages=361–372|url=}}</ref><ref name="Huang_Scaling_up_GNNs">{{cite journal|author1=Huang Z|author2=Zhang S|author3=Xi C|author4=Liu T|author5=Zhou M.|title=Scaling up graph neural networks via graph coarsening|journal=Proc. 27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining|year=2021|pages=675–684|url=}}</ref><ref name="Zhang_Coarse_graining_network_flow">{{cite journal|author1=Zhang Z|author2=Ghavasieh A|author3=Zhang J|author4=De Domenico M.|title=Coarse-graining network flow through statistical physics and machine learning|journal=Nat. Commun.|year=2025|volume=16|url=}}</ref>，其在设计高效通信与数据存储纠错编码方面具有重要价值。研究者已运用重整化群方法生成小型网络编码，可有效计算树状网络中置信传播的性能<ref name="Yedidia_RG_error_correction">{{cite journal|author1=Yedidia J. S.|author2=Bouchaud J.-P.|title=Renormalization group approach to error-correcting codes|journal=J. Phys. A|year=2003|volume=36|url=}}</ref>。尽管这些方法受网络重整化思想驱动，但其通常聚焦于特定过程，对图结构数据与复杂系统多尺度本质的底层原理揭示有限。
=== 信息论方法 ===
=== 信息论方法 ===