半监督学习得到了研究人员的关注，因为它允许其中利用未标记数据的结构来实现比监督方法更少的标签来实现竞争分类结果。本地和全局一致性（LGC）算法是最着名的基于图形的半监督（GSSL）分类器之一。值得注意的是，其解决方案可以写成已知标签的线性组合。这种线性组合的系数取决于参数$ \ alpha $，在随机步行中达到标记的顶点时，确定随时间的衰减。在这项工作中，我们讨论如何删除标记实例的自我影响可能是有益的，以及它如何与休留次误差。此外，我们建议尽量减少自动分化的休假。在此框架内，我们提出了估计标签可靠性和扩散速率的方法。优化扩散速率以频谱表示更有效地完成。结果表明，标签可靠性方法与强大的L1-NORM方法竞争，删除对角线条目会降低过度的风险，并导致参数选择的合适标准。

An approach to semi-supervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning problem is then formulated in terms of a Gaussian random field on this graph, where the mean of the field is characterized in terms of harmonic functions, and is efficiently obtained using matrix methods or belief propagation. The resulting learning algorithms have intimate connections with random walks, electric networks, and spectral graph theory. We discuss methods to incorporate class priors and the predictions of classifiers obtained by supervised learning. We also propose a method of parameter learning by entropy minimization, and show the algorithm's ability to perform feature selection. Promising experimental results are presented for synthetic data, digit classification, and text classification tasks.

We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.

近几十年来，科学和工程的可用数据数量的重大增长彻底改变了。然而，尽管现在收集和存储数据的空前很容易，但通过补充每个功能的标签来标记数据仍然是具有挑战性的。标签过程需要专家知识或乏味且耗时的说明任务包括用诊断X射线标记X射线，具有蛋白质类型的蛋白质序列，其主题的文本，通过其情感推文或视频通过其类型的视频。在这些和许多其他示例中，由于成本和时间限制，只能手动标记一些功能。我们如何才能最好地将标签信息从少数昂贵的标签功能到大量未标记的标签信息传播？这是半监督学习（SSL）提出的问题。本文概述了基于图的贝叶斯SSL的最新基础发展，这是一种使用功能之间的相似性的标签传播概率框架。 SSL是一个活跃的研究领域，对现有文献的彻底回顾超出了本文的范围。我们的重点将放在我们自己的研究中得出的主题，这些主题说明了对基于图的贝叶斯SSL的统计准确性和计算效率进行严格研究的广泛数学工具和思想。

本文介绍了HyperGraph神经网络方法的新颖版本。该方法用于解决嘈杂的标签学习问题。首先，我们将PCA尺寸还原技术应用于图像数据集的特征矩阵，以减少图像数据集的特征矩阵中的“噪声”和冗余功能方法。然后，基于经典的半监督学习方法，经典的基于超毛图的半手法学习方法，图形神经网络，HyperGraph神经网络和我们提出的HyperGraph神经网络用于解决嘈杂的标签学习问题。评估和比较这五种方法的精度。实验结果表明，当噪声水平提高时，超图神经网络方法达到了最佳性能。此外，高图神经网络方法至少与图神经网络一样好。

Semi-supervised learning is becoming increasingly important because it can combine data carefully labeled by humans with abundant unlabeled data to train deep neural networks. Classic methods on semi-supervised learning that have focused on transductive learning have not been fully exploited in the inductive framework followed by modern deep learning. The same holds for the manifold assumption-that similar examples should get the same prediction. In this work, we employ a transductive label propagation method that is based on the manifold assumption to make predictions on the entire dataset and use these predictions to generate pseudo-labels for the unlabeled data and train a deep neural network. At the core of the transductive method lies a nearest neighbor graph of the dataset that we create based on the embeddings of the same network. Therefore our learning process iterates between these two steps. We improve performance on several datasets especially in the few labels regime and show that our work is complementary to current state of the art.

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.

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.

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

子空间聚类是将大约位于几个低维子空间的数据样本集合集合的经典问题。此问题的当前最新方法基于自我表达模型，该模型表示样品是其他样品的线性组合。但是，这些方法需要足够广泛的样品才能准确表示，这在许多应用中可能不一定是可以访问的。在本文中，我们阐明了这个常见的问题，并认为每个子空间中的数据分布在自我表达模型的成功中起着至关重要的作用。我们提出的解决此问题的解决方案是由数据扩展在深神经网络的概括力中的核心作用引起的。我们为无监督和半监督的设置提出了两个子空间聚类框架，这些框架使用增强样品作为扩大词典来提高自我表达表示的质量。我们提出了一种使用一些标记的样品进行半监督问题的自动增强策略，该问题取决于数据样本位于多个线性子空间的联合以下事实。实验结果证实了数据增强的有效性，因为它显着提高了一般自我表达模型的性能。

Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely instrumental to design deep network building blocks with spectral graph characteristics. For instance, such a network allows the design of optimal graphs for certain tasks or obtaining a canonical orthogonal low-dimensional embedding of the data. Recent attempts to solve this problem were based on minimizing Rayleigh-quotient type losses. We propose a different approach of directly learning the eigensapce. A severe problem of the direct approach, applied in batch-learning, is the inconsistent mapping of features to eigenspace coordinates in different batches. We analyze the degrees of freedom of learning this task using batches and propose a stable alignment mechanism that can work both with batch changes and with graph-metric changes. We show that our learnt spectral embedding is better in terms of NMI, ACC, Grassman distance, orthogonality and classification accuracy, compared to SOTA. In addition, the learning is more stable.

扩散是分子从较高浓度的区域的运动到较低浓度的区域。它可用于描述数据点之间的交互。在许多机器学习问题包括转导半监督学习和少量学习的问题，标记和未标记的数据点之间的关系是高分类精度的关键组件。在本文中，由对流扩散颂歌的启发，我们提出了一种新颖的扩散剩余网络（Diff-Reset），将扩散机制引入内部的神经网络中。在结构化数据假设下，证明扩散机构可以提高距离直径比，从而提高了阶级间点间的可分离性，并减少了局部分类点之间的距离。该特性可以通过用于构建可分离超平面的剩余网络来轻松采用。各种数据集中的半监控图节点分类和几次拍摄图像分类的广泛实验验证了所提出的扩散机制的有效性。

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。

The accuracy of k-nearest neighbor (kNN) classification depends significantly on the metric used to compute distances between different examples. In this paper, we show how to learn a Mahalanobis distance metric for kNN classification from labeled examples. The Mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes kNN classification using Euclidean distances. In our approach, the metric is trained with the goal that the k-nearest neighbors always belong to the same class while examples from different classes are separated by a large margin. As in support vector machines (SVMs), the margin criterion leads to a convex optimization based on the hinge loss. Unlike learning in SVMs, however, our approach requires no modification or extension for problems in multiway (as opposed to binary) classification. In our framework, the Mahalanobis distance metric is obtained as the solution to a semidefinite program. On several data sets of varying size and difficulty, we find that metrics trained in this way lead to significant improvements in kNN classification. Sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster. We show how to learn and combine these local metrics in a globally integrated manner.

考虑到不完美的预测器，我们在测试时间下利用其他功能来改善所做的预测，而不会再培训并且没有知识的预测功能。如果培训标签或数据是专有的，限制或不再可用的话，则出现这种情况，或者如果培训本身非常昂贵。我们假设额外的功能如果他们对潜在的完美预测器表现出强烈的统计依赖性，则很有用。然后，我们经验估计和加强初始嘈杂预测因子与通过歧管去噪的附加特征之间的统计依赖性。作为一个例子，我们表明这种方法导致现实世界的视觉属性排名的改进。项目网页：http：//www.jamespkin.com/tupi

Many interesting problems in machine learning are being revisited with new deep learning tools. For graph-based semisupervised learning, a recent important development is graph convolutional networks (GCNs), which nicely integrate local vertex features and graph topology in the convolutional layers. Although the GCN model compares favorably with other state-of-the-art methods, its mechanisms are not clear and it still requires considerable amount of labeled data for validation and model selection. In this paper, we develop deeper insights into the GCN model and address its fundamental limits. First, we show that the graph convolution of the GCN model is actually a special form of Laplacian smoothing, which is the key reason why GCNs work, but it also brings potential concerns of oversmoothing with many convolutional layers. Second, to overcome the limits of the GCN model with shallow architectures, we propose both co-training and self-training approaches to train GCNs. Our approaches significantly improve GCNs in learning with very few labels, and exempt them from requiring additional labels for validation. Extensive experiments on benchmarks have verified our theory and proposals.

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.

深度学习的最新进展依赖于大型标签的数据集来培训大容量模型。但是，以时间和成本效益的方式收集大型数据集通常会导致标签噪声。我们提出了一种从嘈杂的标签中学习的方法，该方法利用特征空间中的训练示例之间的相似性，鼓励每个示例的预测与其最近的邻居相似。与使用多个模型或不同阶段的训练算法相比，我们的方法采用了简单，附加的正规化项的形式。它可以被解释为经典的，偏置标签传播算法的归纳版本。我们在数据集上彻底评估我们的方法评估合成（CIFAR-10，CIFAR-100）和现实（迷你网络，网络vision，Clotsing1m，Mini-Imagenet-Red）噪声，并实现竞争性或最先进的精度，在所有人之间。

We present a semi-supervised learning framework based on graph embeddings. Given a graph between instances, we train an embedding for each instance to jointly predict the class label and the neighborhood context in the graph. We develop both transductive and inductive variants of our method. In the transductive variant of our method, the class labels are determined by both the learned embeddings and input feature vectors, while in the inductive variant, the embeddings are defined as a parametric function of the feature vectors, so predictions can be made on instances not seen during training. On a large and diverse set of benchmark tasks, including text classification, distantly supervised entity extraction, and entity classification, we show improved performance over many of the existing models.

这篇综述的目的是将读者介绍到图表内，以将其应用于化学信息学中的分类问题。图内核是使我们能够推断分子的化学特性的功能，可以帮助您完成诸如寻找适合药物设计的化合物等任务。内核方法的使用只是一种特殊的两种方式量化了图之间的相似性。我们将讨论限制在这种方法上，尽管近年来已经出现了流行的替代方法，但最著名的是图形神经网络。