Spectral Networks and Locally Connected Networks on Graphs

Abstract

Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.

14 pages

References in corpus (2)

• A Tutorial on Spectral Clustering
• Emergence of Complex-Like Cells in a Temporal Product Network with Local Receptive Fields

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• Learning Chebyshev Basis in Graph Convolutional Networks for Skeleton-based Action Recognition
• Accelerating Metropolis-Hastings with Lightweight Inference Compilation
• On the Global Self-attention Mechanism for Graph Convolutional Networks
• RaWaNet: Enriching Graph Neural Network Input via Random Walks on Graphs
• Deep Learning for Predicting Dynamic Uncertain Opinions in Network Data
• Cascading: Association Augmented Sequential Recommendation
• Constrained Shortest Path Search with Graph Convolutional Neural Networks
• STR-GODEs: Spatial-Temporal-Ridership Graph ODEs for Metro Ridership Prediction
• Learning-based Real-time Detection of Intrinsic Reflectional Symmetry
• Dense Graph Convolutional Neural Networks on 3D Meshes for 3D Object Segmentation and Classification
• Community-preserving Graph Convolutions for Structural and Functional Joint Embedding of Brain Networks
• Timestamping Documents and Beliefs
• Using Laplacian Spectrum as Graph Feature Representation
• Interferometric Graph Transform for Community Labeling
• Parameter-Efficient Neural Question Answering Models via Graph-Enriched Document Representations
• Estimating Early Fundraising Performance of Innovations via Graph-based Market Environment Model
• Contributions to Representation Learning with Graph Autoencoders and Applications to Music Recommendation
• A de Finetti-type representation of joint hierarchically exchangeable arrays on directed acyclic graphs
• Placement Optimization with Deep Reinforcement Learning
• Intrinsic Geometric Information Transfer Learning on Multiple Graph-Structured Datasets
• Wall Stress Estimation of Cerebral Aneurysm based on Zernike Convolutional Neural Networks
• Meta-Path-Free Representation Learning on Heterogeneous Networks
• Spectral Transform Forms Scalable Transformer
• Diversified Multiscale Graph Learning with Graph Self-Correction
• Dynamic Virtual Graph Significance Networks for Predicting Influenza
• Combining exogenous and endogenous signals with a semi-supervised co-attention network for early detection of COVID-19 fake tweets
• DeepWORD: A GCN-based Approach for Owner-Member Relationship Detection in Autonomous Driving
• Action Recognition with Kernel-based Graph Convolutional Networks
• Predicting Station-Level Bike-Sharing Demands Using Graph Convolutional Neural Network
• Relevant Region Prediction for Crowd Counting
• Joint Forecasting and Interpolation of Graph Signals Using Deep Learning