Learning Structural Node Embeddings via Diffusion Wavelets

Donnat, Claire; Žitnik, Marinka; Hallac, David; Leskovec, Jure

doi:10.1145/3219819.3220025

Cited by 303 publications

(305 citation statements)

References 24 publications

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“…DeepWalk [6], Node2vec [8] and LINE [7] are state-of-the-art random walk based models that use uniform, BFS/DFS like random walks and first/second order distance for this purpose, respectively. Examples of other static node embedding methods are proposed in [18], [19].…”

Section: Related Workmentioning

confidence: 99%

Dynamic Graph Embedding via LSTM History Tracking

Khoshraftar

Mahdavi

et al. 2019

2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA)

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Many real world networks are very large and constantly change over time. These dynamic networks exist in various domains such as social networks, traffic networks and biological interactions. To handle large dynamic networks in downstream applications such as link prediction and anomaly detection, it is essential for such networks to be transferred into a low dimensional space. Recently, network embedding, a technique that converts a large graph into a low-dimensional representation, has become increasingly popular due to its strength in preserving the structure of a network. Efficient dynamic network embedding, however, has not yet been fully explored. In this paper, we present a dynamic network embedding method that integrates the history of nodes over time into the current state of nodes. The key contribution of our work is 1) generating dynamic network embedding by combining both dynamic and static node information 2) tracking history of neighbors of nodes using LSTM 3) significantly decreasing the time and memory by training an autoencoder LSTM model using temporal walks rather than adjacency matrices of graphs which are the common practice. We evaluate our method in multiple applications such as anomaly detection, link prediction and node classification in datasets from various domains.

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Section: Related Workmentioning

confidence: 99%

Dynamic Graph Embedding via LSTM History Tracking

Khoshraftar

Mahdavi

et al. 2019

2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA)

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“…Several approaches [14], [15] have been proposed to fill this gap in recent years. Despite their success, these methods do not make full use of existing network embedding approaches, making them either rely heavily on heuristic feature engineering or suffer from high computation and space cost, thus hard to generalize across graphs and scale to massive networks.…”

Section: Introductionmentioning

confidence: 99%

“…We compare our proposed methods with state-of-the-art baselines [11], [14], [15] on several real-world datasets. Firstly, we illustratively demonstrate the difference between typical network embededing and structural embedding on an expressway network.…”

Section: Introductionmentioning

confidence: 99%

RiWalk: Fast Structural Node Embedding via Role Identification

Qin

Qiu

et al. 2019

2019 IEEE International Conference on Data Mining (ICDM)

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Nodes performing different functions in a network have different roles, and these roles can be gleaned from the structure of the network. Learning latent representations for the roles of nodes helps to understand the network and to transfer knowledge across networks. However, most existing structural embedding approaches suffer from high computation and space cost or rely on heuristic feature engineering.Here we propose RiWalk, a flexible paradigm for learning structural node representations. It decouples the structural embedding problem into a role identification procedure and a network embedding procedure. Through role identification, rooted kernels with structural dependencies kept are built to better integrate network embedding methods. To demonstrate the effectiveness of RiWalk, we develop two different role identification methods named RiWalk-SP and RiWalk-WL respectively and employ random walk based network embedding methods.Experiments on within-network classification tasks show that our proposed algorithms achieve comparable performance with other baselines while being an order of magnitude more efficient. Besides, we also conduct across-network role classification tasks. The results show potential of structural embeddings in transfer learning. RiWalk is also scalable, making it capable of capturing structural roles in massive networks.

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“…In this paper, motivated by the diffusion wavelet transform [14]- [18] and convolutional neural networks [19] on graphs that all use Chebyshev polynomials, we propose a new spectral method to solve the heat diffusion by approximating the heat kernel by orthogonal polynomials. The previous works did the spectral decomposition on mostly graph Laplacian exclusively using Chebyshev polynomials.…”

mentioning

confidence: 99%

“…The proposed method is faster than the LB-eigenfunction approach and FEM based diffusion solvers [9]. We further applied the fast polynomial approximation method to iterative convolution to obtain multiscale features, which is shown to be as good as the diffusion wavelet in detecting localized surface signals [14]- [18].…”

mentioning

confidence: 99%

Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis

Huang

Lyu

Qiu

et al. 2020

IEEE Trans. Med. Imaging

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Heat diffusion has been widely used in brain imaging for surface fairing, mesh regularization and cortical data smoothing. Motivated by diffusion wavelets and convolutional neural networks on graphs, we present a new fast and accurate numerical scheme to solve heat diffusion on surface meshes. This is achieved by approximating the heat kernel convolution using high degree orthogonal polynomials in the spectral domain. We also derive the closed-form expression of the spectral decomposition of the Laplace-Beltrami operator and use it to solve heat diffusion on a manifold for the first time. The proposed fast polynomial approximation scheme avoids solving for the eigenfunctions of the Laplace-Beltrami operator, which is computationally costly for large mesh size, and the numerical instability associated with the finite element method based diffusion solvers. The proposed method is applied in localizing the male and female differences in cortical sulcal and gyral graph patterns obtained from MRI in an innovative way. The MATLAB code is available at http://www.stat.wisc.edu/ ∼ mchung/chebyshev.

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Learning Structural Node Embeddings via Diffusion Wavelets

Cited by 303 publications

References 24 publications

Dynamic Graph Embedding via LSTM History Tracking

Dynamic Graph Embedding via LSTM History Tracking

RiWalk: Fast Structural Node Embedding via Role Identification

Fast Polynomial Approximation of Heat Kernel Convolution on Manifolds and Its Application to Brain Sulcal and Gyral Graph Pattern Analysis

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