# Connecting Graph Convolutional Networks and Graph-Regularized PCA

arXiv: https://arxiv.org/abs/2006.12294 · HTML: https://mlsanity.com/paper/2006.12294/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [On the Detection of Reviewer-Author Collusion Rings From Paper Bidding](https://mlsanity.com/paper/2402.07860/) (2024)
- [Beyond Graph Convolutional Network: An Interpretable Regularizer-centered Optimization Framework](https://mlsanity.com/paper/2301.04318/) (2023)
- [Semi-Supervised Graph Learning Meets Dimensionality Reduction](https://mlsanity.com/paper/2203.12522/) (2022)

## Abstract (arXiv)

Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a textitmathematical connection between graph convolution and graph-regularized PCA (GPCA). Based on this connection, GCN architecture, shaped by stacking graph convolution layers, shares a close relationship with stacking GPCA. We empirically demonstrate that the textitunsupervised embeddings by GPCA paired with a 1- or 2-layer MLP achieves similar or even better performance than GCN on semi-supervised node classification tasks across five datasets including Open Graph Benchmark footnoteurlhttps://ogb.stanford.edu/. This suggests that the prowess of GCN is driven by graph based regularization. In addition, we extend GPCA to the (semi-)supervised setting and show that it is equivalent to GPCA on a graph extended with "ghost" edges between nodes of the same label. Finally, we capitalize on the discovered relationship to design an effective initialization strategy based on stacking GPCA, enabling GCN to converge faster and achieve robust performance at large number of layers. Notably, the proposed initialization is general-purpose and applies to other GNNs.