Attention-based Graph Neural Network for Semi-supervised Learning

Recently popularized graph neural networks achieve the state-of-the-art accuracy on a number of standard benchmark datasets for graph-based semi-supervised learning, improving significantly over existing approaches. These architectures alternate between a propagation layer that aggregates the hidden states of the local neighborhood and a fully-connected layer. Perhaps surprisingly, we show that a linear model, that removes all the intermediate fully-connected layers, is still able to achieve a performance comparable to the state-of-the-art models. This significantly reduces the number of parameters, which is critical for semi-supervised learning where number of labeled examples are small. This in turn allows a room for designing more innovative propagation layers. Based on this insight, we propose a novel graph neural network that removes all the intermediate fully-connected layers, and replaces the propagation layers with attention mechanisms that respect the structure of the graph. The attention mechanism allows us to learn a dynamic and adaptive local summary of the neighborhood to achieve more accurate predictions. In a number of experiments on benchmark citation networks datasets, we demonstrate that our approach outperforms competing methods. By examining the attention weights among neighbors, we show that our model provides some interesting insights on how neighbors influence each other

Kernel-Induced Label Propagation by Mapping for Semi-Supervised Classification

Kernel methods have been successfully applied to the areas of pattern recognition and data mining. In this paper, we mainly discuss the issue of propagating labels in kernel space. A Kernel-Induced Label Propagation (Kernel-LP) framework by mapping is proposed for high-dimensional data classification using the most informative patterns of data in kernel space. The essence of Kernel-LP is to perform joint label propagation and adaptive weight learning in a transformed kernel space. That is, our Kernel-LP changes the task of label propagation from the commonly-used Euclidean space in most existing work to kernel space. The motivation of our Kernel-LP to propagate labels and learn the adaptive weights jointly by the assumption of an inner product space of inputs, i.e., the original linearly inseparable inputs may be mapped to be separable in kernel space. Kernel-LP is based on existing positive and negative LP model, i.e., the effects of negative label information are integrated to improve the label prediction power. Also, Kernel-LP performs adaptive weight construction over the same kernel space, so it can avoid the tricky process of choosing the optimal neighborhood size suffered in traditional criteria. Two novel and efficient out-of-sample approaches for our Kernel-LP to involve new test data are also presented, i.e., (1) direct kernel mapping and (2) kernel mapping-induced label reconstruction, both of which purely depend on the kernel matrix between training set and testing set. Owing to the kernel trick, our algorithms will be applicable to handle the high-dimensional real data. Extensive results on real datasets demonstrate the effectiveness of our approach.Comment: Accepted by IEEE TB

Low-rank Label Propagation for Semi-supervised Learning with 100 Millions Samples

The success of semi-supervised learning crucially relies on the scalability to a huge amount of unlabelled data that are needed to capture the underlying manifold structure for better classification. Since computing the pairwise similarity between the training data is prohibitively expensive in most kinds of input data, currently, there is no general ready-to-use semi-supervised learning method/tool available for learning with tens of millions or more data points. In this paper, we adopted the idea of two low-rank label propagation algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nystr\"om Approximation, and implemented the parallelized version of the two algorithms accelerated with Nesterov's accelerated projected gradient descent for Big-data Label Propagation (BigLP). The parallel algorithms are tested on five real datasets ranging from 7000 to 10,000,000 in size and a simulation dataset of 100,000,000 samples. In the experiments, the implementation can scale up to datasets with 100,000,000 samples and hundreds of features and the algorithms also significantly improved the prediction accuracy when only a very small percentage of the data is labeled. The results demonstrate that the BigLP implementation is highly scalable to big data and effective in utilizing the unlabeled data for semi-supervised learning

Fusion Graph Convolutional Networks

Semi-supervised node classification in attributed graphs, i.e., graphs with node features, involves learning to classify unlabeled nodes given a partially labeled graph. Label predictions are made by jointly modeling the node and its' neighborhood features. State-of-the-art models for node classification on such attributed graphs use differentiable recursive functions that enable aggregation and filtering of neighborhood information from multiple hops. In this work, we analyze the representation capacity of these models to regulate information from multiple hops independently. From our analysis, we conclude that these models despite being powerful, have limited representation capacity to capture multi-hop neighborhood information effectively. Further, we also propose a mathematically motivated, yet simple extension to existing graph convolutional networks (GCNs) which has improved representation capacity. We extensively evaluate the proposed model, F-GCN on eight popular datasets from different domains. F-GCN outperforms the state-of-the-art models for semi-supervised learning on six datasets while being extremely competitive on the other two

Pairwise Constraint Propagation on Multi-View Data

This paper presents a graph-based learning approach to pairwise constraint propagation on multi-view data. Although pairwise constraint propagation has been studied extensively, pairwise constraints are usually defined over pairs of data points from a single view, i.e., only intra-view constraint propagation is considered for multi-view tasks. In fact, very little attention has been paid to inter-view constraint propagation, which is more challenging since pairwise constraints are now defined over pairs of data points from different views. In this paper, we propose to decompose the challenging inter-view constraint propagation problem into semi-supervised learning subproblems so that they can be efficiently solved based on graph-based label propagation. To the best of our knowledge, this is the first attempt to give an efficient solution to inter-view constraint propagation from a semi-supervised learning viewpoint. Moreover, since graph-based label propagation has been adopted for basic optimization, we develop two constrained graph construction methods for interview constraint propagation, which only differ in how the intra-view pairwise constraints are exploited. The experimental results in cross-view retrieval have shown the promising performance of our inter-view constraint propagation

Semi-Supervised Representation Learning based on Probabilistic Labeling

In this paper, we present a new algorithm for semi-supervised representation learning. In this algorithm, we first find a vector representation for the labels of the data points based on their local positions in the space. Then, we map the data to lower-dimensional space using a linear transformation such that the dependency between the transformed data and the assigned labels is maximized. In fact, we try to find a mapping that is as discriminative as possible. The approach will use Hilber-Schmidt Independence Criterion (HSIC) as the dependence measure. We also present a kernelized version of the algorithm, which allows non-linear transformations and provides more flexibility in finding the appropriate mapping. Use of unlabeled data for learning new representation is not always beneficial and there is no algorithm that can deterministically guarantee the improvement of the performance by exploiting unlabeled data. Therefore, we also propose a bound on the performance of the algorithm, which can be used to determine the effectiveness of using the unlabeled data in the algorithm. We demonstrate the ability of the algorithm in finding the transformation using both toy examples and real-world datasets.Comment: 8 pages, 7 figure

Deep graph learning for semi-supervised classification

Graph learning (GL) can dynamically capture the distribution structure (graph structure) of data based on graph convolutional networks (GCN), and the learning quality of the graph structure directly influences GCN for semi-supervised classification. Existing methods mostly combine the computational layer and the related losses into GCN for exploring the global graph(measuring graph structure from all data samples) or local graph (measuring graph structure from local data samples). Global graph emphasises on the whole structure description of the inter-class data, while local graph trend to the neighborhood structure representation of intra-class data. However, it is difficult to simultaneously balance these graphs of the learning process for semi-supervised classification because of the interdependence of these graphs. To simulate the interdependence, deep graph learning(DGL) is proposed to find the better graph representation for semi-supervised classification. DGL can not only learn the global structure by the previous layer metric computation updating, but also mine the local structure by next layer local weight reassignment. Furthermore, DGL can fuse the different structures by dynamically encoding the interdependence of these structures, and deeply mine the relationship of the different structures by the hierarchical progressive learning for improving the performance of semi-supervised classification. Experiments demonstrate the DGL outperforms state-of-the-art methods on three benchmark datasets (Citeseer,Cora, and Pubmed) for citation networks and two benchmark datasets (MNIST and Cifar10) for images

Machine Learning on Graphs: A Model and Comprehensive Taxonomy

There has been a surge of recent interest in learning representations for graph-structured data. Graph representation learning methods have generally fallen into three main categories, based on the availability of labeled data. The first, network embedding (such as shallow graph embedding or graph auto-encoders), focuses on learning unsupervised representations of relational structure. The second, graph regularized neural networks, leverages graphs to augment neural network losses with a regularization objective for semi-supervised learning. The third, graph neural networks, aims to learn differentiable functions over discrete topologies with arbitrary structure. However, despite the popularity of these areas there has been surprisingly little work on unifying the three paradigms. Here, we aim to bridge the gap between graph neural networks, network embedding and graph regularization models. We propose a comprehensive taxonomy of representation learning methods for graph-structured data, aiming to unify several disparate bodies of work. Specifically, we propose a Graph Encoder Decoder Model (GRAPHEDM), which generalizes popular algorithms for semi-supervised learning on graphs (e.g. GraphSage, Graph Convolutional Networks, Graph Attention Networks), and unsupervised learning of graph representations (e.g. DeepWalk, node2vec, etc) into a single consistent approach. To illustrate the generality of this approach, we fit over thirty existing methods into this framework. We believe that this unifying view both provides a solid foundation for understanding the intuition behind these methods, and enables future research in the area

Semi-Supervised Learning on Graphs Based on Local Label Distributions

Most approaches that tackle the problem of node classification consider nodes to be similar, if they have shared neighbors or are close to each other in the graph. Recent methods for attributed graphs additionally take attributes of neighboring nodes into account. We argue that the class labels of the neighbors bear important information and considering them helps to improve classification quality. Two nodes which are similar based on class labels in their neighborhood do not need to be close-by in the graph and may even belong to different connected components. In this work, we propose a novel approach for the semi-supervised node classification. Precisely, we propose a new node embedding which is based on the class labels in the local neighborhood of a node. We show that this is a different setting from attribute-based embeddings and thus, we propose a new method to learn label-based node embeddings which can mirror a variety of relations between the class labels of neighboring nodes. Our experimental evaluation demonstrates that our new methods can significantly improve the prediction quality on real world data sets

Inductive Representation Learning on Large Graphs

Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings for previously unseen data. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions.Comment: Published in NIPS 2017; version with full appendix and minor correction