用流形结构构建图像图模型，提升分类准确率
Improved Image Classification with Manifold Neural Networks
- 将图像数据映射到低维流形，构造节点为图像的图
- 在MNIST和CIFAR10上达到与主流方法相当的分类精度
- 适用于希望提升图像分类泛化能力的研究者
图神经网络（GNN）在分子生物学、交通系统和电网等自然具备图结构的领域已取得成功，得益于其消息传递机制。然而，其在更普遍的数据表示，尤其是图像领域的潜力仍待探索。基于流形假设——高维数据位于低维流形上，本文利用变分自编码器构建图像流形，从中采样生成图结构，每个节点代表一张图像，从而在降低维度的同时保留几何信息。随后训练GNN对节点标签（即图像类别）进行预测，并借助GNN向流形神经网络收敛的特性分析其泛化能力。在MNIST和CIFAR10数据集上的实验表明，GNN能有效泛化至未见图结构，在分类任务中表现出具有竞争力的准确率。
原文摘要 · Abstract (English)
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.
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