Community detection was a hot topic on network analysis, where the main aim is to perform unsupervised learning or clustering in networks. Recently, semi-supervised learning has received increasing attention among researchers. In this paper, we propose a new algorithm, called weighted inverse Laplacian (WIL), for predicting labels in partially labeled networks. The idea comes from the first hitting time in random walk, and it also has nice explanations both in information propagation and the regularization framework. We propose a partially labeled degree-corrected block model (pDCBM) to describe the generation of partially labeled networks. We show that WIL ensures the misclassification rate is of order @math for the pDCBM with average degree @math and that it can handle situations with greater unbalanced than traditional Laplacian methods. WIL outperforms other state-of-the-art methods in most of our simulations and real datasets, especially in unbalanced networks and heterogeneous networks.
Graph-based semi-supervised learning (GSSL) is a well-studied topic in computer science and engineering. @cite_8 first used min-cuts in a graph to perform clustering and @cite_25 introduced normalized min-cuts to deal with the issue of unbalanced networks. Other spectral-based methods were later proposed, including @cite_26 @cite_18 . A Gaussian kernel was used to construct the graph in @cite_0 . A random walk based method called Adsorption was proposed in @cite_21 and was modified in @cite_30 into something called MAD. TACO, which was proposed in @cite_20 , introduced an additional quantity of confidence in labeling. We recommend @cite_22 for a good review of GSSL. While many methods on GSSL were developed in the last decade, few considered the consistency theoretically. @cite_35 is the only paper we found that discussed the consistency of the basic GSSL method theoretically.
@cite_30 @cite_35 @cite_18 @cite_26 @cite_22 @cite_8 @cite_21 @cite_0 @cite_25 @cite_20
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Graph-based semisupervised learning (GSSL) provides a promising paradigm for modeling the manifold structures that may exist in massive data sources in high-dimensional spaces. It has been shown effective in propagating a limited amount of initial labels to a large amount of unlabeled data, matching the needs of many emerging applications such as image annotation and information retrieval. In this paper, we provide reviews of several classical GSSL methods and a few promising methods in handling challenging issues often encountered in web-scale applications. First, to successfully incorporate the contaminated noisy labels associated with web data, label diagnosis and tuning techniques applied to GSSL are surveyed. Second, to support scalability to the gigantic scale (millions or billions of samples), recent solutions based on anchor graphs are reviewed. To help researchers pursue new ideas in this area, we also summarize a few popular data sets and software tools publicly available. Important open issues are discussed at the end to stimulate future research. 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. Graph-based semi-supervised learning is one of the most popular methods in machine learning. Some of its theoretical properties such as bounds for the generalization error and the convergence of the graph Laplacian regularizer have been studied in computer science and statistics literatures. However, a fundamental statistical property, the consistency of the estimator from this method has not been proved. In this article, we study the consistency problem under a non-parametric framework. We prove the consistency of graph-based learning in the case that the estimated scores are enforced to be equal to the observed responses for the labeled data. The sample sizes of both labeled and unlabeled data are allowed to grow in this result. When the estimated scores are not required to be equal to the observed responses, a tuning parameter is used to balance the loss function and the graph Laplacian regularizer. We give a counterexample demonstrating that the estimator for this case can be inconsistent. The theoretical findings are supported by numerical studies. In the literature, most existing graph-based semi-supervised learning methods only use the label information of observed samples in the label propagation stage, while ignoring such valuable information when learning the graph. In this paper, we argue that it is beneficial to consider the label information in the graph learning stage. Specifically, by enforcing the weight of edges between labeled samples of different classes to be zero, we explicitly incorporate the label information into the state-of-the-art graph learning methods, such as the low-rank representation (LRR), and propose a novel semi-supervised graph learning method called semi-supervised low-rank representation. This results in a convex optimization problem with linear constraints, which can be solved by the linearized alternating direction method. Though we take LRR as an example, our proposed method is in fact very general and can be applied to any self-representation graph learning methods. Experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data, and therefore is more effective for semi-supervised learning tasks. Graph based semi-supervised learning (SSL) methods play an increasingly important role in practical machine learning systems. A crucial step in graph based SSL methods is the conversion of data into a weighted graph. However, most of the SSL literature focuses on developing label inference algorithms without extensively studying the graph building method and its effect on performance. This article provides an empirical study of leading semi-supervised methods under a wide range of graph construction algorithms. These SSL inference algorithms include the Local and Global Consistency (LGC) method, the Gaussian Random Field (GRF) method, the Graph Transduction via Alternating Minimization (GTAM) method as well as other techniques. Several approaches for graph construction, sparsification and weighting are explored including the popular k-nearest neighbors method (kNN) and the b-matching method. As opposed to the greedily constructed kNN graph, the b-matched graph ensures each node in the graph has the same number of edges and produces a balanced or regular graph. Experimental results on both artificial data and real benchmark datasets indicate that b-matching produces more robust graphs and therefore provides significantly better prediction accuracy without any significant change in computation time. Graph-based approaches have been successful in unsupervised and semi-supervised learning. In this paper, we focus on the real-world applications where the same instance can be represented by multiple heterogeneous features. The key point of utilizing the graph-based knowledge to deal with this kind of data is to reasonably integrate the different representations and obtain the most consistent manifold with the real data distributions. In this paper, we propose a novel framework via the reformulation of the standard spectral learning model, which can be used for multiview clustering and semisupervised tasks. Unlike other methods in the literature, the proposed methods can learn an optimal weight for each graph automatically without introducing an additive parameter as previous methods do. Furthermore, our objective under semisupervised learning is convex and the global optimal result will be obtained. Extensive empirical results on different real-world data sets demonstrate that the proposed methods achieve comparable performance with the state-of-the-art approaches and can be used more practically. The recently proposed self-ensembling methods have achieved promising results in deep semi-supervised learning, which penalize inconsistent predictions of unlabeled data under different perturbations. However, they only consider adding perturbations to each single data point, while ignoring the connections between data samples. In this paper, we propose a novel method, called Smooth Neighbors on Teacher Graphs (SNTG). In SNTG, a graph is constructed based on the predictions of the teacher model, i.e., the implicit self-ensemble of models. Then the graph serves as a similarity measure with respect to which the representations of "similar" neighboring points are learned to be smooth on the low-dimensional manifold. We achieve state-of-the-art results on semi-supervised learning benchmarks. The error rates are 9.89 , 3.99 for CIFAR-10 with 4000 labels, SVHN with 500 labels, respectively. In particular, the improvements are significant when the labels are fewer. For the non-augmented MNIST with only 20 labels, the error rate is reduced from previous 4.81 to 1.36 . Our method also shows robustness to noisy labels. This work addresses graph-based semi-supervised classification and betweenness computation in large, sparse, networks (several millions of nodes). The objective of semi-supervised classification is to assign a label to unlabeled nodes using the whole topology of the graph and the labeling at our disposal. Two approaches are developed to avoid explicit computation of pairwise proximity between the nodes of the graph, which would be impractical for graphs containing millions of nodes. The first approach directly computes, for each class, the sum of the similarities between the nodes to classify and the labeled nodes of the class, as suggested initially in [1,2]. Along this approach, two algorithms exploiting different state-of-the-art kernels on a graph are developed. The same strategy can also be used in order to compute a betweenness measure. The second approach works on a trellis structure built from biased random walks on the graph, extending an idea introduced in [3]. These random walks allow to define a biased bounded betweenness for the nodes of interest, defined separately for each class. All the proposed algorithms have a linear computing time in the number of edges while providing good results, and hence are applicable to large sparse networks. They are empirically validated on medium-size standard data sets and are shown to be competitive with state-of-the-art techniques. Finally, we processed a novel data set, which is made available for benchmarking, for multi-class classification in a large network: the U.S. patents citation network containing 3M nodes (of six different classes) and 38M edges. The three proposed algorithms achieve competitive results (around 85 classification rate) on this large network-they classify the unlabeled nodes within a few minutes on a standard workstation. This paper presents a semi-supervised graph-based method for the classification of hyperspectral images. The method is designed to handle the special characteristics of hyperspectral images, namely, high-input dimension of pixels, low number of labeled samples, and spatial variability of the spectral signature. To alleviate these problems, the method incorporates three ingredients, respectively. First, being a kernel-based method, it combats the curse of dimensionality efficiently. Second, following a semi-supervised approach, it exploits the wealth of unlabeled samples in the image, and naturally gives relative importance to the labeled ones through a graph-based methodology. Finally, it incorporates contextual information through a full family of composite kernels. Noting that the graph method relies on inverting a huge kernel matrix formed by both labeled and unlabeled samples, we originally introduce the Nystro umlm method in the formulation to speed up the classification process. The presented semi-supervised-graph-based method is compared to state-of-the-art support vector machines in the classification of hyperspectral data. The proposed method produces better classification maps, which capture the intrinsic structure collectively revealed by labeled and unlabeled points. Good and stable accuracy is produced in ill-posed classification problems (high dimensional spaces and low number of labeled samples). In addition, the introduction of the composite-kernel framework drastically improves results, and the new fast formulation ranks almost linearly in the computational cost, rather than cubic as in the original method, thus allowing the use of this method in remote-sensing applications. Graph-based semi-supervised learning (SSL) algorithms have been successfully used to extract class-instance pairs from large unstructured and structured text collections. However, a careful comparison of different graph-based SSL algorithms on that task has been lacking. We compare three graph-based SSL algorithms for class-instance acquisition on a variety of graphs constructed from different domains. We find that the recently proposed MAD algorithm is the most effective. We also show that class-instance extraction can be significantly improved by adding semantic information in the form of instance-attribute edges derived from an independently developed knowledge base. All of our code and data will be made publicly available to encourage reproducible research in this area.