Beyond Spectral Clustering: Probabilistic Cuts for Differentiable Graph Partitioning

Ayoub Ghriss

TL;DR: probabilistic formulation of graph cuts that avoid spectral decomposition of spectral clustering offering a scalable alternative

Abstract: Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and principled gradients. We present a unified probabilistic framework that covers a wide class of cuts, including Normalized Cut. Our framework provides tight analytic upper bounds on expected discrete cuts via integral representations and Gauss hypergeometric functions with closed-form forward and backward. Together, these results deliver a rigorous, numerically stable foundation for scalable, differentiable graph partitioning covering a wide range of clustering and contrastive learning objectives.

Code Dataset Promise: Yes

Code Dataset Url: https://github.com/ayghri/pgcuts

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Submission Number: 1726