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Register a new userGraph Embedding via Diffusion-Wavelets-Based Node Feature Distribution Characterization
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Added by
Soroush Vosoughi Dr
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Recent years have seen a rise in the development of representational learning methods for graph data. Most of these methods, however, focus on node-level representation learning at various scales (e.g., microscopic, mesoscopic, and macroscopic node embedding). In comparison, methods for representation learning on whole graphs are currently relatively sparse. In this paper, we propose a novel unsupervised whole graph embedding method. Our method uses spectral graph wavelets to capture topological similarities on each k-hop sub-graph between nodes and uses them to learn embeddings for the whole graph. We evaluate our method against 12 well-known baselines on 4 real-world datasets and show that our method achieves the best performance across all experiments, outperforming the current state-of-the-art by a considerable margin.
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We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem that involves a fidelity term to the layers of a given multilayer graph, and a regularization on the (single-layer) graph induced by the embedding. The fidelity term uses the contrastive loss to properly aggregate the observed layers into a representative embedding. The regularization pushes for a sparse and community-aware graph, and it is based on a measure of graph sparsification called effective resistance, coupled with a penalization of the first few eigenvalues of the representative graph Laplacian matrix to favor the formation of communities. The proposed optimization problem is nonconvex but fully differentiable, and thus can be solved via the descent gradient method. Experiments show that our method leads to a significant improvement w.r.t. state-of-the-art multilayer graph clustering algorithms.
Nodes residing in different parts of a graph can have similar structural roles within their local network topology. The identification of such roles provides key insight into the organization of networks and can be used for a variety of machine learning tasks. However, learning structural representations of nodes is a challenging problem, and it has typically involved manually specifying and tailoring topological features for each node. In this paper, we develop GraphWave, a method that represents each nodes network neighborhood via a low-dimensional embedding by leveraging heat wavelet diffusion patterns. Instead of training on hand-selected features, GraphWave learns these embeddings in an unsupervised way. We mathematically prove that nodes with similar network neighborhoods will have similar GraphWave embeddings even though these nodes may reside in very different parts of the network, and our method scales linearly with the number of edges. Experiments in a variety of different settings demonstrate GraphWaves real-world potential for capturing structural roles in networks, and our approach outperforms existing state-of-the-art baselines in every experiment, by as much as 137%.
Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural networks. In this paper, we introuduce graph feature to feature (Fea2Fea) prediction pipelines in a low dimensional space to explore some preliminary results on structural feature correlation, which is based on graph neural network. The results show that there exists high correlation between some of the structural features. An irredundant feature combination with initial node features, which is filtered by graph neural network has improved its classification accuracy in some graph-based tasks. We compare differences between concatenation methods on connecting embeddings between features and show that the simplest is the best. We generalize on the synthetic geometric graphs and certify the results on prediction difficulty between structural features.
Graph representation learning has achieved great success in many areas, including e-commerce, chemistry, biology, etc. However, the fundamental problem of choosing the appropriate dimension of node embedding for a given graph still remains unsolved. The commonly used strategies for Node Embedding Dimension Selection (NEDS) based on grid search or empirical knowledge suffer from heavy computation and poor model performance. In this paper, we revisit NEDS from the perspective of minimum entropy principle. Subsequently, we propose a novel Minimum Graph Entropy (MinGE) algorithm for NEDS with graph data. To be specific, MinGE considers both feature entropy and structure entropy on graphs, which are carefully designed according to the characteristics of the rich information in them. The feature entropy, which assumes the embeddings of adjacent nodes to be more similar, connects node features and link topology on graphs. The structure entropy takes the normalized degree as basic unit to further measure the higher-order structure of graphs. Based on them, we design MinGE to directly calculate the ideal node embedding dimension for any graph. Finally, comprehensive experiments with popular Graph Neural Networks (GNNs) on benchmark datasets demonstrate the effectiveness and generalizability of our proposed MinGE.
Spectral graph convolutional networks (SGCNs) have been attracting increasing attention in graph representation learning partly due to their interpretability through the prism of the established graph signal processing framework. However, existing SGCNs are limited in implementing graph convolutions with rigid transforms that could not adapt to signals residing on graphs and tasks at hand. In this paper, we propose a novel class of spectral graph convolutional networks that implement graph convolutions with adaptive graph wavelets. Specifically, the adaptive graph wavelets are learned with neural network-parameterized lifting structures, where structure-aware attention-based lifting operations are developed to jointly consider graph structures and node features. We propose to lift based on diffusion wavelets to alleviate the structural information loss induced by partitioning non-bipartite graphs. By design, the locality and sparsity of the resulting wavelet transform as well as the scalability of the lifting structure for large and varying-size graphs are guaranteed. We further derive a soft-thresholding filtering operation by learning sparse graph representations in terms of the learned wavelets, which improves the scalability and interpretablity, and yield a localized, efficient and scalable spectral graph convolution. To ensure that the learned graph representations are invariant to node permutations, a layer is employed at the input of the networks to reorder the nodes according to their local topology information. We evaluate the proposed networks in both node-level and graph-level representation learning tasks on benchmark citation and bioinformatics graph datasets. Extensive experiments demonstrate the superiority of the proposed networks over existing SGCNs in terms of accuracy, efficiency and scalability.
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