在本文中，我们提出了一种设计用于图形域的域适配算法。给定具有许多标记节点的源图和具有少数或没有标记节点的目标图，我们的目标是通过利用两个图表上标签函数的变化的特征之间的相似性来估计目标标签。我们对源和目标域的假设是标签函数的本地行为，例如图表上的速度和变化的变化速度，在两个图形之间存在相似之处。我们通过求解标签信息基于之前的标签函数的投影在源图和目标图之间类似地将标签信息从源图传输到目标图来求解从源图到目标图的优化问题来估计未知的目标标签。为了有效地捕获图形上标签函数的局部变化，光谱图小波用作图形基础。与参考域适配方法相比，各种数据集的实验表明，该方法产生了相当令人满意的分类精度。

In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogues to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting, and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

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.

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.

域适应性是现代机器学习中的一种流行范式，旨在解决培训或验证数据集之间具有用于学习和测试分类器（源域）和潜在的大型未标记数据集的培训或验证数据集之间的分歧问题，其中利用了模型（目标域）（目标域）（目标域） 。任务是找到源数据集的源和目标数据集的这种常见表示，其中源数据集提供了培训的信息，因此可以最大程度地减少来源和目标之间的差异。目前，最流行的领域适应性解决方案是基于训练神经网络，这些神经网络结合了分类和对抗性学习模块，这些模块是饥饿的，通常很难训练。我们提出了一种称为域适应性主成分分析（DAPCA）的方法，该方法发现线性减少的数据表示有助于解决域适应任务。 DAPCA基于数据点对之间引入正权重，并概括了主成分分析的监督扩展。 DAPCA代表一种迭代算法，因此在每次迭代中都解决了一个简单的二次优化问题。保证算法的收敛性，并且在实践中的迭代次数很少。我们验证了先前提出的用于解决域适应任务的基准的建议算法，还显示了在生物医学应用中对单细胞法数据集进行分析中使用DAPCA的好处。总体而言，考虑到源域和目标域之间可能的差异，DAPCA可以作为许多机器学习应用程序中有用的预处理步骤。

Transfer learning aims at improving the performance of target learners on target domains by transferring the knowledge contained in different but related source domains. In this way, the dependence on a large number of target domain data can be reduced for constructing target learners. Due to the wide application prospects, transfer learning has become a popular and promising area in machine learning. Although there are already some valuable and impressive surveys on transfer learning, these surveys introduce approaches in a relatively isolated way and lack the recent advances in transfer learning. Due to the rapid expansion of the transfer learning area, it is both necessary and challenging to comprehensively review the relevant studies. This survey attempts to connect and systematize the existing transfer learning researches, as well as to summarize and interpret the mechanisms and the strategies of transfer learning in a comprehensive way, which may help readers have a better understanding of the current research status and ideas. Unlike previous surveys, this survey paper reviews more than forty representative transfer learning approaches, especially homogeneous transfer learning approaches, from the perspectives of data and model. The applications of transfer learning are also briefly introduced. In order to show the performance of different transfer learning models, over twenty representative transfer learning models are used for experiments. The models are performed on three different datasets, i.e., Amazon Reviews, Reuters-21578, and Office-31. And the experimental results demonstrate the importance of selecting appropriate transfer learning models for different applications in practice.

无监督的域适应（UDA）显示出近年来工作条件下的轴承故障诊断的显着结果。但是，大多数UDA方法都不考虑数据的几何结构。此外，通常应用全局域适应技术，这忽略了子域之间的关系。本文通过呈现新的深亚域适应图卷积神经网络（DSAGCN）来解决提到的挑战，具有两个关键特性：首先，采用图形卷积神经网络（GCNN）来模拟数据结构。二，对抗域适应和局部最大平均差异（LMMD）方法同时应用，以对准子域的分布并降低相关子域和全局域之间的结构差异。 CWRU和Paderborn轴承数据集用于验证DSAGCN方法的比较模型之间的效率和优越性。实验结果表明，将结构化子域与域适应方法对准，以获得无监督故障诊断的准确数据驱动模型。

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。

Domain adaptation is an important emerging topic in computer vision. In this paper, we present one of the first studies of domain shift in the context of object recognition. We introduce a method that adapts object models acquired in a particular visual domain to new imaging conditions by learning a transformation that minimizes the effect of domain-induced changes in the feature distribution. The transformation is learned in a supervised manner and can be applied to categories for which there are no labeled examples in the new domain. While we focus our evaluation on object recognition tasks, the transform-based adaptation technique we develop is general and could be applied to non-image data. Another contribution is a new multi-domain object database, freely available for download. We experimentally demonstrate the ability of our method to improve recognition on categories with few or no target domain labels and moderate to large changes in the imaging conditions.

We propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution. We focus on a semi-supervised framework that incorporates labeled and unlabeled data in a general-purpose learner. Some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases. We use properties of reproducing kernel Hilbert spaces to prove new Representer theorems that provide theoretical basis for the algorithms. As a result (in contrast to purely graph-based approaches) we obtain a natural out-of-sample extension to novel examples and so are able to handle both transductive and truly semi-supervised settings. We present experimental evidence suggesting that our semi-supervised algorithms are able to use unlabeled data effectively. Finally we have a brief discussion of unsupervised and fully supervised learning within our general framework.

我们介绍了一种新颖的谐波分析，用于在函数上定义的函数，随机步行操作员是基石。作为第一步，我们将随机步行操作员的一组特征向量作为非正交傅里叶类型的功能，用于通过定向图。我们通过将从其Dirichlet能量获得的随机步行操作员的特征向量的变化与其相关的特征值的真实部分连接来发现频率解释。从这个傅立叶基础，我们可以进一步继续，并在有向图中建立多尺度分析。通过将Coifman和MagGioni扩展到定向图，我们提出了一种冗余小波变换和抽取的小波变换。因此，我们对导向图的谐波分析的发展导致我们考虑应用于突出了我们框架效率的指示图的图形上的半监督学习问题和信号建模问题。

最近有一项激烈的活动在嵌入非常高维和非线性数据结构的嵌入中，其中大部分在数据科学和机器学习文献中。我们分四部分调查这项活动。在第一部分中，我们涵盖了非线性方法，例如主曲线，多维缩放，局部线性方法，ISOMAP，基于图形的方法和扩散映射，基于内核的方法和随机投影。第二部分与拓扑嵌入方法有关，特别是将拓扑特性映射到持久图和映射器算法中。具有巨大增长的另一种类型的数据集是非常高维网络数据。第三部分中考虑的任务是如何将此类数据嵌入中等维度的向量空间中，以使数据适合传统技术，例如群集和分类技术。可以说，这是算法机器学习方法与统计建模（所谓的随机块建模）之间的对比度。在论文中，我们讨论了两种方法的利弊。调查的最后一部分涉及嵌入$ \ mathbb {r}^ 2 $，即可视化中。提出了三种方法：基于第一部分，第二和第三部分中的方法，$ t $ -sne，UMAP和大节。在两个模拟数据集上进行了说明和比较。一个由嘈杂的ranunculoid曲线组成的三胞胎，另一个由随机块模型和两种类型的节点产生的复杂性的网络组成。

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.

We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired by the theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on features that cannot discriminate between the training (source) and test (target) domains.The approach implements this idea in the context of neural network architectures that are trained on labeled data from the source domain and unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of features that are (i) discriminative for the main learning task on the source domain and (ii) indiscriminate with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation and stochastic gradient descent, and can thus be implemented with little effort using any of the deep learning packages.We demonstrate the success of our approach for two distinct classification problems (document sentiment analysis and image classification), where state-of-the-art domain adaptation performance on standard benchmarks is achieved. We also validate the approach for descriptor learning task in the context of person re-identification application.

这是本文的第二部分，为异质变化检测（HCD）问题提供了新的策略，即从图形信号处理（GSP）的角度解决HCD。我们构造一个图表以表示每个图像的结构，并将每个图像视为图表上定义的图形信号。这样，我们可以将HCD问题转换为图表上定义的系统的信号响应的比较。在第一部分中，通过比较顶点域的图之间的结构差来衡量变化。在本第二部分中，我们分析了来自光谱域的HCD的GSP。我们首先分析同一图上不同图像的光谱特性，并表明它们的光谱表现出共同点和差异。特别是，正是变化导致了光谱的差异。然后，我们提出了HCD的回归模型，该模型将源信号分解为回归信号并更改信号，并且需要回归的信号具有与同一图上的目标信号相同的光谱属性。借助图光谱分析，提出的回归模型是灵活且可扩展的。对七个真实数据集进行的实验显示了该方法的有效性。

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation of CNNs in the context of spectral graph theory, which provides the necessary mathematical background and efficient numerical schemes to design fast localized convolutional filters on graphs. Importantly, the proposed technique offers the same linear computational complexity and constant learning complexity as classical CNNs, while being universal to any graph structure. Experiments on MNIST and 20NEWS demonstrate the ability of this novel deep learning system to learn local, stationary, and compositional features on graphs.

虽然在许多域内生成并提供了大量的未标记数据，但对视觉数据的自动理解的需求高于以往任何时候。大多数现有机器学习模型通常依赖于大量标记的训练数据来实现高性能。不幸的是，在现实世界的应用中，不能满足这种要求。标签的数量有限，手动注释数据昂贵且耗时。通常需要将知识从现有标记域传输到新域。但是，模型性能因域之间的差异（域移位或数据集偏差）而劣化。为了克服注释的负担，域适应（DA）旨在在将知识从一个域转移到另一个类似但不同的域中时减轻域移位问题。无监督的DA（UDA）处理标记的源域和未标记的目标域。 UDA的主要目标是减少标记的源数据和未标记的目标数据之间的域差异，并在培训期间在两个域中学习域不变的表示。在本文中，我们首先定义UDA问题。其次，我们从传统方法和基于深度学习的方法中概述了不同类别的UDA的最先进的方法。最后，我们收集常用的基准数据集和UDA最先进方法的报告结果对视觉识别问题。

Recent work reported the label alignment property in a supervised learning setting: the vector of all labels in the dataset is mostly in the span of the top few singular vectors of the data matrix. Inspired by this observation, we derive a regularization method for unsupervised domain adaptation. Instead of regularizing representation learning as done by popular domain adaptation methods, we regularize the classifier so that the target domain predictions can to some extent ``align" with the top singular vectors of the unsupervised data matrix from the target domain. In a linear regression setting, we theoretically justify the label alignment property and characterize the optimality of the solution of our regularization by bounding its distance to the optimal solution. We conduct experiments to show that our method can work well on the label shift problems, where classic domain adaptation methods are known to fail. We also report mild improvement over domain adaptation baselines on a set of commonly seen MNIST-USPS domain adaptation tasks and on cross-lingual sentiment analysis tasks.

Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and $\epsilon$-neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of parameters associated with these methods, such as k and $\epsilon$, is still ad hoc. We make two main contributions in this paper. First, we present an alternative view of neighborhood selection, where we show that neighborhood construction is equivalent to a sparse signal approximation problem. Second, we propose an algorithm, non-negative kernel regression~(NNK), for obtaining neighborhoods that lead to better sparse representation. NNK draws similarities to the orthogonal matching pursuit approach to signal representation and possesses desirable geometric and theoretical properties. Experiments demonstrate (i) the robustness of the NNK algorithm for neighborhood and graph construction, (ii) its ability to adapt the number of neighbors to the data properties, and (iii) its superior performance in local neighborhood and graph-based machine learning tasks.

所有著名的机器学习算法构成了受监督和半监督的学习工作，只有在一个共同的假设下：培训和测试数据遵循相同的分布。当分布变化时，大多数统计模型必须从新收集的数据中重建，对于某些应用程序，这些数据可能是昂贵或无法获得的。因此，有必要开发方法，以减少在相关领域中可用的数据并在相似领域中进一步使用这些数据，从而减少需求和努力获得新的标签样品。这引起了一个新的机器学习框架，称为转移学习：一种受人类在跨任务中推断知识以更有效学习的知识能力的学习环境。尽管有大量不同的转移学习方案，但本调查的主要目的是在特定的，可以说是最受欢迎的转移学习中最受欢迎的次级领域，概述最先进的理论结果，称为域适应。在此子场中，假定数据分布在整个培训和测试数据中发生变化，而学习任务保持不变。我们提供了与域适应性问题有关的现有结果的首次最新描述，该结果涵盖了基于不同统计学习框架的学习界限。