Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates

TL;DR

Poisson learning introduces a graph-based semi-supervised learning framework that replaces label assignment with source-sink placement, solving a Poisson equation to achieve more stable and accurate results at very low label rates.

Contribution

The paper presents a novel Poisson learning method that addresses Laplacian degeneracy in low-label regimes, offering a simple, efficient, and more stable alternative for semi-supervised learning.

Findings

Outperforms recent methods on MNIST, FashionMNIST, and Cifar-10.

Proposes Poisson MBO, a graph-cut enhancement with higher accuracy.

Demonstrates stability and effectiveness at very low label rates.

Abstract

We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.