Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering

TL;DR

This paper introduces FLGC, a fully linear graph convolutional network that uses a closed-form solution for training, improving efficiency and performance in semi-supervised and unsupervised learning on graph and regular data.

Contribution

The paper proposes FLGC, a novel linear GCN framework trained via closed-form solutions, simplifying implementation and enhancing efficiency for semi-supervised and unsupervised tasks.

Findings

FLGC effectively handles both graph-structured and regular data.

Closed-form training improves computational efficiency without performance loss.

FLGC outperforms state-of-the-art methods in accuracy and robustness.

Abstract

This paper presents FLGC, a simple yet effective fully linear graph convolutional network for semi-supervised and unsupervised learning. Instead of using gradient descent, we train FLGC based on computing a global optimal closed-form solution with a decoupled procedure, resulting in a generalized linear framework and making it easier to implement, train, and apply. We show that (1) FLGC is powerful to deal with both graph-structured data and regular data, (2) training graph convolutional models with closed-form solutions improve computational efficiency without degrading performance, and (3) FLGC acts as a natural generalization of classic linear models in the non-Euclidean domain, e.g., ridge regression and subspace clustering. Furthermore, we implement a semi-supervised FLGC and an unsupervised FLGC by introducing an initial residual strategy, enabling FLGC to aggregate long-range neighborhoods and alleviate over-smoothing. We compare our semi-supervised and unsupervised FLGCs against many state-of-the-art methods on a variety of classification and clustering benchmarks, demonstrating that the proposed FLGC models consistently outperform previous methods in terms of accuracy, robustness, and learning efficiency. The core code of our FLGC is released at https://github.com/AngryCai/FLGC.