Matrix factorization (MF) and Autoencoder (AE) are among the most successful approaches of unsupervised learning. While MF based models have been extensively exploited in the graph modeling and link prediction literature, the AE family has not gained much attention. In this paper we investigate both MF and AE's application to the link prediction problem in sparse graphs. We show the connection between AE and MF from the perspective of multiview learning, and further propose MF+AE: a model training MF and AE jointly with shared parameters. We apply dropout to training both the MF and AE parts, and show that it can significantly prevent overfitting by acting as an adaptive regularization. We conduct experiments on six real world sparse graph datasets, and show that MF+AE consistently outperforms the competing methods, especially on datasets that demonstrate strong non-cohesive structures.
This work is also related to graph representation learning. Recently, @cite_22 propose to learn node embeddings by predicting the path of a random walk, and they show that the learned representation can boost the performance of the classification task on graph data. It would also be interesting to evaluate the effectiveness of MF+AE in the same setting.
@cite_22
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Celebrated and its fruitful variants are powerful models to achieve excellent performance on the tasks that map sequences to sequences. However, these are many machine learning tasks with inputs naturally represented in a form of graphs, which imposes significant challenges to existing Seq2Seq models for lossless conversion from its graph form to the sequence. In this work, we present a general end-to-end approach to map the input graph to a sequence of vectors, and then another attention-based LSTM to decode the target sequence from these vectors. Specifically, to address inevitable information loss for data conversion, we introduce a novel graph-to-sequence neural network model that follows the encoder-decoder architecture. Our method first uses an improved graph-based neural network to generate the node and graph embeddings by a novel aggregation strategy to incorporate the edge direction information into the node embeddings. We also propose an attention based mechanism that aligns node embeddings and decoding sequence to better cope with large graphs. Experimental results on bAbI task, Shortest Path Task, and Natural Language Generation Task demonstrate that our model achieves the state-of-the-art performance and significantly outperforms other baselines. We also show that with the proposed aggregation strategy, our proposed model is able to quickly converge to good performance. Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10 accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark datasets. We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the graph likelihood, which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76 and 55 , on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller. Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10 accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.