# Graph Laplacian Regularized Graph Convolutional Networks for Semi-supervised Learning

arXiv: https://arxiv.org/abs/1809.09839 · HTML: https://mlsanity.com/paper/1809.09839/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2018.

## Built on by (most cited first, 2 of 2)

- [Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification](https://mlsanity.com/paper/2305.16239/) (2023)
- [Spectral Gap Regularization of Neural Networks](https://mlsanity.com/paper/2304.03096/) (2023)

## Abstract (arXiv)

Recently, graph convolutional network (GCN) has been widely used for semi-supervised classification and deep feature representation on graph-structured data. However, existing GCN generally fails to consider the local invariance constraint in learning and representation process. That is, if two data points Xi and Xj are close in the intrinsic geometry of the data distribution, then their labels/representations should also be close to each other. This is known as local invariance assumption which plays an essential role in the development of various kinds of traditional algorithms, such as dimensionality reduction and semi-supervised learning, in machine learning area. To overcome this limitation, we introduce a graph Laplacian GCN (gLGCN) approach for graph data representation and semi-supervised classification. The proposed gLGCN model is capable of encoding both graph structure and node features together while maintains the local invariance constraint naturally for robust data representation and semi-supervised classification. Experiments show the benefit of the benefits the proposed gLGCN network.