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雷达卡
摘要翻译：
几乎每一个科学学科都使用图形来表示一组对象之间的关系。因此，比较图并输出贴近度得分或节点间对应关系的算法是极其重要的。尽管做了大量的工作，许多用于比较图的可伸缩算法并不能产生满足度量直观特性的贴近度分数。这是有问题的，因为已知非度量会降低算法的性能，如基于距离的图聚类（Stratis和Bento2018)。另一方面，度量的使用提高了几个机器学习任务的性能（Indyk et al.1999，Clarkson et al.1999，Angiulli et al.2002，Ackermann et al.2010)。在本文中，我们引入了一个新的多距离族（两个以上元素之间的距离），它满足度量的性质对多元素的推广。在比较图的上下文中，我们第一个证明了多距离的存在，它同时包含了有用的对准一致性性质（Nguyen et al.2011)，以及一个广义的度量性质。进一步，我们证明了这些多距离可以松弛到凸优化问题，而不损失广义度量性质。
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英文标题：
《Tractable $n$-Metrics for Multiple Graphs》
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作者：
Sam Safavi and Jos\'e Bento
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最新提交年份：
2020
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Discrete Mathematics 离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Machine Learning 机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Electrical Engineering and Systems Science 电气工程与系统科学
二级分类：Signal Processing 信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Mathematics 数学
二级分类：Combinatorics 组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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一级分类：Mathematics 数学
二级分类：Optimization and Control 优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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英文摘要：
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite the large amount of work done, many of the scalable algorithms to compare graphs do not produce closeness scores that satisfy the intuitive properties of metrics. This is problematic since non-metrics are known to degrade the performance of algorithms such as distance-based clustering of graphs (Stratis and Bento 2018). On the other hand, the use of metrics increases the performance of several machine learning tasks (Indyk et al. 1999, Clarkson et al. 1999, Angiulli et al. 2002, Ackermann et al. 2010). In this paper, we introduce a new family of multi-distances (a distance between more than two elements) that satisfies a generalization of the properties of metrics to multiple elements. In the context of comparing graphs, we are the first to show the existence of multi-distances that simultaneously incorporate the useful property of alignment consistency (Nguyen et al. 2011), and a generalized metric property. Furthermore, we show that these multi-distances can be relaxed to convex optimization problems, without losing the generalized metric property.
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PDF链接：
https://arxiv.org/pdf/1807.03368
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