We propose Embedding Propagation (EP), an unsupervised learning framework for graph-structured data. EP learns vector representations of graphs by passing two types of messages between neighboring nodes. Forward messages consist of label representations such as representations of words and other attributes associated with the nodes. Backward messages consist of gradients that result from aggregating the label representations and applying a reconstruction loss. Node representations are finally computed from the representation of their labels. With significantly fewer parameters and hyperparameters an instance of EP is competitive with and often outperforms state of the art unsupervised and semi-supervised learning methods on a range of benchmark data sets.
We propose EP, Embedding Propagation, an unsupervised learning framework for graph-structured data. EP learns vector representations of graphs by passing two types of messages between neighboring nodes. Forward messages consist of label representations such as representations of words and other attributes associated with the nodes. Backward messages consist of gradients that result from aggregating the label representations and applying a reconstruction loss. Node representations are finally computed from the representation of their labels.
The graph convolution network (GCN) is a widely-used facility to realize graph-based semi-supervised learning, which usually integrates node features and graph topologic information to build learning models. However, as for multi-label learning tasks, the supervision part of GCN simply minimizes the cross-entropy loss between the last layer outputs and the ground-truth label distribution, which tends to lose some useful information such as label correlations, so that prevents from obtaining high performance. In this paper, we pro-pose a novel GCN-based semi-supervised learning approach for multi-label classification, namely ML-GCN. ML-GCN first uses a GCN to embed the node features and graph topologic information. Then, it randomly generates a label matrix, where each row (i.e., label vector) represents a kind of labels. The dimension of the label vector is the same as that of the node vector before the last convolution operation of GCN. That is, all labels and nodes are embedded in a uniform vector space. Finally, during the ML-GCN model training, label vectors and node vectors are concatenated to serve as the inputs of the relaxed skip-gram model to detect the node-label correlation as well as the label-label correlation. Experimental results on several graph classification datasets show that the proposed ML-GCN outperforms four state-of-the-art methods.
Graph neural networks aggregate features in vertex neighborhoods to learn vector representations of all vertices, using supervision from some labeled vertices during training. The predictor is then a function of the vector representation, and predictions are made independently on unlabeled nodes. This widely-adopted approach implicitly assumes that vertex labels are independent after conditioning on their neighborhoods. We show that this strong assumption is far from true on many real-world graph datasets and severely limits predictive power on a number of regression tasks. Given that traditional graph-based semi-supervised learning methods operate in the opposite manner by explicitly modeling the correlation in predicted outcomes, this limitation may not be all that surprising. Here, we address this issue with a simple and interpretable framework that can improve any graph neural network architecture by modeling correlation structure in regression outcome residuals. Specifically, we model the joint distribution of outcome residuals on vertices with a parameterized multivariate Gaussian, where the parameters are estimated by maximizing the marginal likelihood of the observed labels. Our model achieves substantially boosts the performance of graph neural networks, and the learned parameters can also be interpreted as the strength of correlation among connected vertices. To allow us to scale to large networks, we design linear time algorithms for low-variance, unbiased model parameter estimates based on stochastic trace estimation. We also provide a simplified version of our method that makes stronger assumptions on correlation structure but is extremely easy to implement and provides great practical performance in several cases.
Recently graph based dimensionality reduction has received a lot of interests in many fields of information processing. Central to it is a graph structure which models the geometrical and discriminant structure of the data manifold. When label information is available, it is usually incorporated into the graph structure by modifying the weights between data points. In this paper, we propose a novel dimensionality reduction algorithm, called Constrained Graph Embedding, which considers the label information as additional constraints. Specifically, we constrain the space of the solutions that we explore only to contain embedding results that are consistent with the labels. Experimental results on two real life data sets illustrate the effectiveness of our proposed method.