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Register a new userPINE: Universal Deep Embedding for Graph Nodes via Partial Permutation Invariant Set Functions
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Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph node embedding lies in how to define the dependence to neighbors. Existing approaches specify (either explicitly or implicitly) certain dependencies on neighbors, which may lead to loss of subtle but important structural information within the graph and other dependencies among neighbors. This intrigues us to ask the question: can we design a model to give the maximal flexibility of dependencies to each nodes neighborhood. In this paper, we propose a novel graph node embedding (named PINE) via a novel notion of partial permutation invariant set function, to capture any possible dependence. Our method 1) can learn an arbitrary form of the representation function from the neighborhood, withour losing any potential dependence structures, and 2) is applicable to both homogeneous and heterogeneous graph embedding, the latter of which is challenged by the diversity of node types. Furthermore, we provide theoretical guarantee for the representation capability of our method for general homogeneous and heterogeneous graphs. Empirical evaluation results on benchmark data sets show that our proposed PINE method outperforms the state-of-the-art approaches on producing node vectors for various learning tasks of both homogeneous and heterogeneous graphs.
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Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.
Scoring functions (SFs), which measure the plausibility of triplets in knowledge graph (KG), have become the crux of KG embedding. Lots of SFs, which target at capturing different kinds of relations in KGs, have been designed by humans in recent years. However, as relations can exhibit complex patterns that are hard to infer before training, none of them can consistently perform better than others on existing benchmark data sets. In this paper, inspired by the recent success of automated machine learning (AutoML), we propose to automatically design SFs (AutoSF) for distinct KGs by the AutoML techniques. However, it is non-trivial to explore domain-specific information here to make AutoSF efficient and effective. We firstly identify a unified representation over popularly used SFs, which helps to set up a search space for AutoSF. Then, we propose a greedy algorithm to search in such a space efficiently. The algorithm is further sped up by a filter and a predictor, which can avoid repeatedly training SFs with same expressive ability and help removing bad candidates during the search before model training. Finally, we perform extensive experiments on benchmark data sets. Results on link prediction and triplets classification show that the searched SFs by AutoSF, are KG dependent, new to the literature, and outperform the state-of-the-art SFs designed by humans.
We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.
The creation of social ties is largely determined by the entangled effects of peoples similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose emph{AN2VEC}, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared feature-network information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.
Representation learning of static and more recently dynamically evolving graphs has gained noticeable attention. Existing approaches for modelling graph dynamics focus extensively on the evolution of individual nodes independently of the evolution of mesoscale community structures. As a result, current methods do not provide useful tools to study and cannot explicitly capture temporal community dynamics. To address this challenge, we propose GRADE - a probabilistic model that learns to generate evolving node and community representations by imposing a random walk prior over their trajectories. Our model also learns node community membership which is updated between time steps via a transition matrix. At each time step link generation is performed by first assigning node membership from a distribution over the communities, and then sampling a neighbor from a distribution over the nodes for the assigned community. We parametrize the node and community distributions with neural networks and learn their parameters via variational inference. Experiments demonstrate GRADE outperforms baselines in dynamic link prediction, shows favourable performance on dynamic community detection, and identifies coherent and interpretable evolving communities.
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