A wide range of data science problems can be modeled in terms of a graph (or network), e.g., social, sensor, communication, infrastructure, and biological networks. The nodes in a graph/network represent the entities of interest, and the edges reflect relations between these entities, such as geographic proximity (e.g., wireless networks), social relations (e.g., Facebook), biological mechanisms (e.g., brain networks), similarity (e.g., texts by identical authors), and statistical dependencies (e.g., gene expression data). Graph signal processing (GSP) advocates the use of graphs as combined data and computation models and has become a groundbreaking and powerful paradigm for solving diverse learning and inference tasks in the area of data science. GSP uses tools from linear algebra, (spectral) graph theory, computational harmonic analysis, and optimization theory to extend conventional signal processing concepts to data located on irregular domains that are characterized by graphs (networks). For entry-level expositions of GSP fundamentals and the relevant state of the art, we refer to [1]-[4] and the May 2018 Proceedings of the IEEE.

中文翻译：

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有符号图上的信号处理：基本原理和潜力

可以根据图（或网络）对广泛的数据科学问题进行建模，例如社会、传感器、通信、基础设施和生物网络。图/网络中的节点代表感兴趣的实体，边反映这些实体之间的关系，例如地理邻近性（例如，无线网络）、社会关系（例如，Facebook）、生物机制（例如，大脑网络）、相似性（例如，相同作者的文本）和统计相关性（例如，基因表达数据）。图信号处理 (GSP) 提倡使用图作为组合数据和计算模型，并已成为解决数据科学领域各种学习和推理任务的开创性和强大范式。GSP 使用来自线性代数、（谱）图论、计算调和分析的工具，和优化理论将传统的信号处理概念扩展到位于以图（网络）为特征的不规则域上的数据。对于 GSP 基础知识和相关最新技术的入门级阐述，我们参考 [1]-[4] 和 2018 年 5 月的 IEEE 会议录。