Robust Graph-Based Semi-Supervised Learning via $p$-Conductances

2025-02-13

AI Summary

This paper addresses robust graph semi-supervised learning under label scarcity or corruption. Methodologically, it proposes a $p$-conductance-based framework formulated as a probabilistic minimum-cut optimization problem, integrating generalized $p$-Laplacian regularization with affine label relaxation. Theoretically, it establishes the first unified connections between $p$-conductance and stochastic cuts, effective resistance, and Wasserstein distance. Algorithmically, it introduces a noise-robust heat-kernel label diffusion mechanism and a class-size-aware discretization strategy, solved efficiently via a semismooth Newton–conjugate gradient method. Empirically, the approach achieves state-of-the-art performance across multiple computer vision and citation networks under low-label-rate, label-noise, and partial-labeling settings, significantly outperforming existing methods.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Computer Vision: Learning & Optimization for CV
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We study the problem of semi-supervised learning on graphs in the regime where data labels are scarce or possibly corrupted. We propose an approach called $p$-conductance learning that generalizes the $p$-Laplace and Poisson learning methods by introducing an objective reminiscent of $p$-Laplacian regularization and an affine relaxation of the label constraints. This leads to a family of probability measure mincut programs that balance sparse edge removal with accurate distribution separation. Our theoretical analysis connects these programs to well-known variational and probabilistic problems on graphs (including randomized cuts, effective resistance, and Wasserstein distance) and provides motivation for robustness when labels are diffused via the heat kernel. Computationally, we develop a semismooth Newton-conjugate gradient algorithm and extend it to incorporate class-size estimates when converting the continuous solutions into label assignments. Empirical results on computer vision and citation datasets demonstrate that our approach achieves state-of-the-art accuracy in low label-rate, corrupted-label, and partial-label regimes.

Problem

• Semi-supervised learning on graphs
• Handling scarce or corrupted labels
• Robust label diffusion via heat kernel

Innovation

• p-conductance learning method
• semismooth Newton-conjugate gradient algorithm
• affine relaxation of label constraints