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

Sawyer Jack Robertson, Chester Holtz, Zhengchao Wan, Gal Mishne, Alex Cloninger

Keywords: semi-supervised learning, node classification, graph Laplacians, minimum cuts

TL;DR: We propose a graph-based semi-supervised learning method using a $p$-Laplacian-inspired objective and an affine relaxation of label constraints called $p$-conductance learning to optimize for sparse edge removal and accurate label separation.

Abstract: We study the problem of semi-supervised learning in the regime where data labels are scarce or possibly corrupted. We propose a graph-based 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). 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.

Submission Type: Extended abstract (max 4 main pages).

Submission Number: 84