多分辨率矩阵分解(MMF)是不寻常之中的,因为它不会使一个低等级的假设快速矩阵分解算法。这使得MMF尤其适合于模拟某些类型的复杂的多尺度或等级strucutre图形。虽然MMF承诺收益率的有益波基,找到分解本身是硬的,和现有的贪婪方法往往易碎。在本文中,我们提出了MMF的可学习版本carfully优化通过backpropagating错误的强化学习和施蒂费尔歧管优化组合的分解。我们发现,所产生的小波基远远优于之前MMF算法,并提供这种类型的分解的,可以有力部署标准的学习任务的第一个版本。
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图表表示学习有许多现实世界应用,从超级分辨率的成像,3D计算机视觉到药物重新扫描,蛋白质分类,社会网络分析。图表数据的足够表示对于图形结构数据的统计或机器学习模型的学习性能至关重要。在本文中,我们提出了一种用于图形数据的新型多尺度表示系统,称为抽取帧的图形数据,其在图表上形成了本地化的紧密框架。抽取的帧系统允许在粗粒链上存储图形数据表示,并在每个比例的多个尺度处处理图形数据,数据存储在子图中。基于此,我们通过建设性数据驱动滤波器组建立用于在多分辨率下分解和重建图数据的抽取G-Framewelet变换。图形帧构建基于基于链的正交基础,支持快速图傅里叶变换。由此,我们为抽取的G-Frameword变换或FGT提供了一种快速算法,该算法具有线性计算复杂度O(n),用于尺寸N的图表。用数值示例验证抽取的帧谱和FGT的理论,用于随机图形。现实世界应用的效果是展示的,包括用于交通网络的多分辨率分析,以及图形分类任务的图形神经网络。
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Pre-publication draft of a book to be published byMorgan & Claypool publishers. Unedited version released with permission. All relevant copyrights held by the author and publisher extend to this pre-publication draft.
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Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with the pace of new research, proper experimental design, fair evaluation, and independent benchmarks are essential. Design of strong baselines is an indispensable element of such works. In this thesis, we explore multiple approaches to graph classification. We focus on Graph Neural Networks (GNNs), which emerged as a de facto standard deep learning technique for graph representation learning. Classical approaches, such as graph descriptors and molecular fingerprints, are also addressed. We design fair evaluation experimental protocol and choose proper datasets collection. This allows us to perform numerous experiments and rigorously analyze modern approaches. We arrive to many conclusions, which shed new light on performance and quality of novel algorithms. We investigate application of Jumping Knowledge GNN architecture to graph classification, which proves to be an efficient tool for improving base graph neural network architectures. Multiple improvements to baseline models are also proposed and experimentally verified, which constitutes an important contribution to the field of fair model comparison.
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基于光谱的图形神经网络(SGNNS)在图表表示学习中一直吸引了不断的关注。然而,现有的SGNN是限于实现具有刚性变换的曲线滤波器(例如,曲线图傅立叶或预定义的曲线波小波变换)的限制,并且不能适应驻留在手中的图形和任务上的信号。在本文中,我们提出了一种新颖的图形神经网络,实现了具有自适应图小波的曲线图滤波器。具体地,自适应图表小波通过神经网络参数化提升结构学习,其中开发了基于结构感知的提升操作(即,预测和更新操作)以共同考虑图形结构和节点特征。我们建议基于扩散小波提升以缓解通过分区非二分类图引起的结构信息损失。通过设计,得到了所得小波变换的局部和稀疏性以及提升结构的可扩展性。我们进一步通过在学习的小波中学习稀疏图表表示来引导软阈值滤波操作,从而产生局部,高效和可伸缩的基于小波的图形滤波器。为了确保学习的图形表示不变于节点排列,在网络的输入中采用层以根据其本地拓扑信息重新排序节点。我们在基准引用和生物信息图形数据集中评估节点级和图形级别表示学习任务的所提出的网络。大量实验在准确性,效率和可扩展性方面展示了在现有的SGNN上的所提出的网络的优越性。
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Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.
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多模式数据通过将来自来自各个域的数据与具有非常不同的统计特性的数据集成来提供自然现象的互补信息。捕获多模式数据的模态和跨换体信息是多模式学习方法的基本能力。几何感知数据分析方法通过基于其几何底层结构隐式表示各种方式的数据来提供这些能力。此外,在许多应用中,在固有的几何结构上明确地定义数据。对非欧几里德域的深度学习方法是一个新兴的研究领域,最近在许多研究中被调查。大多数流行方法都是为单峰数据开发的。本文提出了一种多模式多缩放图小波卷积网络(M-GWCN)作为端到端网络。 M-GWCN同时通过应用多尺度图小波变换来找到模态表示,以在每个模态的图形域中提供有用的本地化属性,以及通过学习各种方式之间的相关性的学习置换的跨模式表示。 M-GWCN不限于具有相同数量的数据的均匀模式,或任何指示模式之间的对应关系的现有知识。已经在三个流行的单峰显式图形数据集和五个多模式隐式界面进行了几个半监督节点分类实验。实验结果表明,与光谱图域卷积神经网络和最先进的多模式方法相比,所提出的方法的优越性和有效性。
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Deep learning has been shown to be successful in a number of domains, ranging from acoustics, images, to natural language processing. However, applying deep learning to the ubiquitous graph data is non-trivial because of the unique characteristics of graphs. Recently, substantial research efforts have been devoted to applying deep learning methods to graphs, resulting in beneficial advances in graph analysis techniques. In this survey, we comprehensively review the different types of deep learning methods on graphs. We divide the existing methods into five categories based on their model architectures and training strategies: graph recurrent neural networks, graph convolutional networks, graph autoencoders, graph reinforcement learning, and graph adversarial methods. We then provide a comprehensive overview of these methods in a systematic manner mainly by following their development history. We also analyze the differences and compositions of different methods. Finally, we briefly outline the applications in which they have been used and discuss potential future research directions.
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近年来,基于Weisfeiler-Leman算法的算法和神经架构,是一个众所周知的Graph同构问题的启发式问题,它成为具有图形和关系数据的机器学习的强大工具。在这里,我们全面概述了机器学习设置中的算法的使用,专注于监督的制度。我们讨论了理论背景,展示了如何将其用于监督的图形和节点表示学习,讨论最近的扩展,并概述算法的连接(置换 - )方面的神经结构。此外,我们概述了当前的应用和未来方向,以刺激进一步的研究。
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组合优化是运营研究和计算机科学领域的一个公认领域。直到最近,它的方法一直集中在孤立地解决问题实例,而忽略了它们通常源于实践中的相关数据分布。但是,近年来,人们对使用机器学习,尤其是图形神经网络(GNN)的兴趣激增,作为组合任务的关键构件,直接作为求解器或通过增强确切的求解器。GNN的电感偏差有效地编码了组合和关系输入,因为它们对排列和对输入稀疏性的意识的不变性。本文介绍了对这个新兴领域的最新主要进步的概念回顾,旨在优化和机器学习研究人员。
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在过去十年中,图形内核引起了很多关注,并在结构化数据上发展成为一种快速发展的学习分支。在过去的20年中,该领域发生的相当大的研究活动导致开发数十个图形内核,每个图形内核都对焦于图形的特定结构性质。图形内核已成功地成功地在广泛的域中,从社交网络到生物信息学。本调查的目标是提供图形内核的文献的统一视图。特别是,我们概述了各种图形内核。此外,我们对公共数据集的几个内核进行了实验评估,并提供了比较研究。最后,我们讨论图形内核的关键应用,并概述了一些仍有待解决的挑战。
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最新提出的基于变压器的图形模型的作品证明了香草变压器用于图形表示学习的不足。要了解这种不足,需要研究变压器的光谱分析是否会揭示其对其表现力的见解。类似的研究已经确定,图神经网络(GNN)的光谱分析为其表现力提供了额外的观点。在这项工作中,我们系统地研究并建立了变压器领域中的空间和光谱域之间的联系。我们进一步提供了理论分析,并证明了变压器中的空间注意机制无法有效捕获所需的频率响应,因此,固有地限制了其在光谱空间中的表现力。因此,我们提出了feta,该框架旨在在整个图形频谱(即图形的实际频率成分)上进行注意力类似于空间空间中的注意力。经验结果表明,FETA在标准基准的所有任务中为香草变压器提供均匀的性能增益,并且可以轻松地扩展到具有低通特性的基于GNN的模型(例如GAT)。
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图表是一个宇宙数据结构,广泛用于组织现实世界中的数据。像交通网络,社交和学术网络这样的各种实际网络网络可以由图表代表。近年来,目睹了在网络中代表顶点的快速发展,进入低维矢量空间,称为网络表示学习。表示学习可以促进图形数据上的新算法的设计。在本调查中,我们对网络代表学习的当前文献进行了全面审查。现有算法可以分为三组:浅埋模型,异构网络嵌入模型,图形神经网络的模型。我们为每个类别审查最先进的算法,并讨论这些算法之间的基本差异。调查的一个优点是,我们系统地研究了不同类别的算法底层的理论基础,这提供了深入的见解,以更好地了解网络表示学习领域的发展。
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Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them.Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
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随着从现实世界所收集的图形数据仅仅是无噪声,图形的实际表示应该是强大的噪声。现有的研究通常侧重于特征平滑,但留下几何结构不受影响。此外,大多数工作需要L2-Norm,追求全局平滑度,这限制了图形神经网络的表现。本文根据特征和结构噪声裁定图表数据的常规程序,其中目标函数用乘法器(ADMM)的交替方向方法有效地解决。该方案允许采用多个层,而无需过平滑的关注,并且保证对最佳解决方案的收敛性。实证研究证明,即使在重大污染的情况下,我们的模型也与流行的图表卷积相比具有明显更好的性能。
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图表神经网络(GNNS)在各种机器学习任务中获得了表示学习的提高。然而,应用邻域聚合的大多数现有GNN通常在图中的图表上执行不良,其中相邻的节点属于不同的类。在本文中,我们示出了在典型的异界图中,边缘可以被引导,以及是否像是处理边缘,也可以使它们过度地影响到GNN模型的性能。此外,由于异常的限制,节点对来自本地邻域之外的类似节点的消息非常有益。这些激励我们开发一个自适应地学习图表的方向性的模型,并利用潜在的长距离相关性节点之间。我们首先将图拉普拉斯概括为基于所提出的特征感知PageRank算法向数字化,该算法同时考虑节点之间的图形方向性和长距离特征相似性。然后,Digraph Laplacian定义了一个图形传播矩阵,导致一个名为{\ em diglaciangcn}的模型。基于此,我们进一步利用节点之间的通勤时间测量的节点接近度,以便在拓扑级别上保留节点的远距离相关性。具有不同级别的10个数据集的广泛实验,同意级别展示了我们在节点分类任务任务中对现有解决方案的有效性。
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在本文中,我们提出了多分辨率的等级图变分性Autiachoders(MGVAE),第一层级生成模型以多分辨率和等分的方式学习和生成图。在每个分辨率级别,MGVAE采用更高的顺序消息,以便在学习中对图进行编码,同时学习将其分配到互斥的集群中并赋予最终产生潜在分布的层次结构的较低分辨率。然后,MGVAE构造分层生成模型以改变地解码成粗糙的图形的层次。重要的是,我们提出的框架是关于节点排序的端到端排列等级。MGVAE通过多种生成任务实现竞争结果,包括一般图生成,分子产生,无监督的分子表示学习,以预测分子特性,引用图的链路预测,以及基于图的图像生成。
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Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing, along with a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas. We then summarize recent advances in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning.
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We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral decomposition of the discrete graph Laplacian L. Given a wavelet generating kernel g and a scale parameter t, we define the scaled wavelet operator T t g = g(tL). The spectral graph wavelets are then formed by localizing this operator by applying it to an indicator function. Subject to an admissibility condition on g, this procedure defines an invertible transform. We explore the localization properties of the wavelets in the limit of fine scales. Additionally, we present a fast Chebyshev polynomial approximation algorithm for computing the transform that avoids the need for diagonalizing L. We highlight potential applications of the transform through examples of wavelets on graphs corresponding to a variety of different problem domains.
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本文旨在为多尺度帧卷积提供一种新颖的光谱图神经网络设计。在光谱范例中,光谱GNN通过提出频谱域中的各种光谱滤波器来提高图形学习任务性能,以捕获全局和本地图形结构信息。虽然现有的光谱方法在某些图表中显示出卓越的性能,但是当图表信息不完整或扰乱时,它们患有缺乏灵活性并脆弱。我们的新帧卷曲卷积包括直接在光谱域中设计的过滤功能,以克服这些限制。所提出的卷积在切断光谱信息中表现出具有很大的灵活性,并有效地减轻了噪声曲线图信号的负效应。此外,为了利用现实世界图数据中的异质性,具有我们新的帧卷积的异构图形神经网络提供了一种用于将元路径的内在拓扑信息与多级图分析嵌入的解决方案。进行了扩展实验实现了具有嘈杂节点特征和卓越性能结果的设置下的现实异构图和均匀图。
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