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Improved Image Classification with Manifold Neural Networks

Caio F. Deberaldini Netto, Zhiyang Wang, Luana Ruiz

TL;DR

Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, GNNs’ potential in this context is explored, and experiments demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.

Abstract

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting from GNNs' message-passing framework. However, the potential of GNNs in more general data representations, especially in the image domain, remains underexplored. Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, we explore GNNs' potential in this context. We construct an image manifold using variational autoencoders, then sample the manifold to generate graphs where each node is an image. This approach reduces data dimensionality while preserving geometric information. We then train a GNN to predict node labels corresponding to the image labels in the classification task, and leverage convergence of GNNs to manifold neural networks to analyze GNN generalization. Experiments on MNIST and CIFAR10 datasets demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.

Improved Image Classification with Manifold Neural Networks

TL;DR

Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, GNNs’ potential in this context is explored, and experiments demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.

Abstract

Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting from GNNs' message-passing framework. However, the potential of GNNs in more general data representations, especially in the image domain, remains underexplored. Leveraging the manifold hypothesis, which posits that high-dimensional data lies in a low-dimensional manifold, we explore GNNs' potential in this context. We construct an image manifold using variational autoencoders, then sample the manifold to generate graphs where each node is an image. This approach reduces data dimensionality while preserving geometric information. We then train a GNN to predict node labels corresponding to the image labels in the classification task, and leverage convergence of GNNs to manifold neural networks to analyze GNN generalization. Experiments on MNIST and CIFAR10 datasets demonstrate that GNNs generalize effectively to unseen graphs, achieving competitive accuracy in classification tasks.
Paper Structure (10 sections, 27 equations, 2 figures, 1 table)

This paper contains 10 sections, 27 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Graph Signals, Graph Convolutions, Graph Neural Networks
  4. Manifold Signals, Manifold Convolutions, Manifold Neural Networks
  5. Exploiting Image Manifolds and Generalization of GNNs via MNNs
  6. Image manifolds
  7. GNNs for image classification
  8. Generalization of GNNs
  9. Experimental Results
  10. Conclusions

Figures (2)

  • Figure 1: Accuracy difference between train and test set for an increasing number of sampled nodes for MNIST dataset. The generalization gap (GA) decreases as the number of nodes increases.
  • Figure 2: Accuracy difference between train and test set for an increasing number of sampled nodes for CIFAR10 dataset. The generalization gap (GA) decreases as the number of nodes increases.