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Hoang Nt
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some family of graphs (e.g. paths or non-isomorphic trees). We show that graph homomorphism numbers provide a natural invariant (isomorphism invariant and $mathcal{F}$-invariant) embedding maps which can be used for graph classification. Viewing the expressive power of a graph classifier by the $mathcal{F}$-indistinguishable concept, we prove the universality property of graph homomorphism vectors in approximating $mathcal{F}$-invariant functions. In practice, by choosing $mathcal{F}$ whose elements have bounded tree-width, we show that the homomorphism method is efficient compared with other methods.
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Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical properties and ability to take into account inductive bias. For this, we propose a high-performance implementation of a simple sampling algorithm which computes additive approximations of homomorphism densities. In the context of graph machine learning, we demonstrate in experiments that simple linear models trained on sample homomorphism densities can achieve performance comparable to graph neural networks on standard graph classification datasets. Finally, we show in experiments on synthetic data that this algorithm scales to very large graphs when implemented with Bloom filters.
Real-world recommender system needs to be regularly retrained to keep with the new data. In this work, we consider how to efficiently retrain graph convolution network (GCN) based recommender models, which are state-of-the-art techniques for collaborative recommendation. To pursue high efficiency, we set the target as using only new data for model updating, meanwhile not sacrificing the recommendation accuracy compared with full model retraining. This is non-trivial to achieve, since the interaction data participates in both the graph structure for model construction and the loss function for model learning, whereas the old graph structure is not allowed to use in model updating. Towards the goal, we propose a textit{Causal Incremental Graph Convolution} approach, which consists of two new operators named textit{Incremental Graph Convolution} (IGC) and textit{Colliding Effect Distillation} (CED) to estimate the output of full graph convolution. In particular, we devise simple and effective modules for IGC to ingeniously combine the old representations and the incremental graph and effectively fuse the long-term and short-term preference signals. CED aims to avoid the out-of-date issue of inactive nodes that are not in the incremental graph, which connects the new data with inactive nodes through causal inference. In particular, CED estimates the causal effect of new data on the representation of inactive nodes through the control of their collider. Extensive experiments on three real-world datasets demonstrate both accuracy gains and significant speed-ups over the existing retraining mechanism.
The Blood-Oxygen-Level-Dependent (BOLD) signal of resting-state fMRI (rs-fMRI) records the temporal dynamics of intrinsic functional networks in the brain. However, existing deep learning methods applied to rs-fMRI either neglect the functional dependency between different brain regions in a network or discard the information in the temporal dynamics of brain activity. To overcome those shortcomings, we propose to formulate functional connectivity networks within the context of spatio-temporal graphs. We train a spatio-temporal graph convolutional network (ST-GCN) on short sub-sequences of the BOLD time series to model the non-stationary nature of functional connectivity. Simultaneously, the model learns the importance of graph edges within ST-GCN to gain insight into the functional connectivities contributing to the prediction. In analyzing the rs-fMRI of the Human Connectome Project (HCP, N=1,091) and the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA, N=773), ST-GCN is significantly more accurate than common approaches in predicting gender and age based on BOLD signals. Furthermore, the brain regions and functional connections significantly contributing to the predictions of our model are important markers according to the neuroscience literature.
Graph Convolutional Network (GCN) has been widely applied in transportation demand prediction due to its excellent ability to capture non-Euclidean spatial dependence among station-level or regional transportation demands. However, in most of the existing research, the graph convolution was implemented on a heuristically generated adjacency matrix, which could neither reflect the real spatial relationships of stations accurately, nor capture the multi-level spatial dependence of demands adaptively. To cope with the above problems, this paper provides a novel graph convolutional network for transportation demand prediction. Firstly, a novel graph convolution architecture is proposed, which has different adjacency matrices in different layers and all the adjacency matrices are self-learned during the training process. Secondly, a layer-wise coupling mechanism is provided, which associates the upper-level adjacency matrix with the lower-level one. It also reduces the scale of parameters in our model. Lastly, a unitary network is constructed to give the final prediction result by integrating the hidden spatial states with gated recurrent unit, which could capture the multi-level spatial dependence and temporal dynamics simultaneously. Experiments have been conducted on two real-world datasets, NYC Citi Bike and NYC Taxi, and the results demonstrate the superiority of our model over the state-of-the-art ones.
Heterogeneous graphs are pervasive in practical scenarios, where each graph consists of multiple types of nodes and edges. Representation learning on heterogeneous graphs aims to obtain low-dimensional node representations that could preserve both node attributes and relation information. However, most of the existing graph convolution approaches were designed for homogeneous graphs, and therefore cannot handle heterogeneous graphs. Some recent methods designed for heterogeneous graphs are also faced with several issues, including the insufficient utilization of heterogeneous properties, structural information loss, and lack of interpretability. In this paper, we propose HGConv, a novel Heterogeneous Graph Convolution approach, to learn comprehensive node representations on heterogeneous graphs with a hybrid micro/macro level convolutional operation. Different from existing methods, HGConv could perform convolutions on the intrinsic structure of heterogeneous graphs directly at both micro and macro levels: A micro-level convolution to learn the importance of nodes within the same relation, and a macro-level convolution to distinguish the subtle difference across different relations. The hybrid strategy enables HGConv to fully leverage heterogeneous information with proper interpretability. Moreover, a weighted residual connection is designed to aggregate both inherent attributes and neighbor information of the focal node adaptively. Extensive experiments on various tasks demonstrate not only the superiority of HGConv over existing methods, but also the intuitive interpretability of our approach for graph analysis.
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