Neural Normalized Cut: A Differential and Generalizable Approach for Spectral Clustering

2025-03-12

AI Summary

Spectral clustering suffers from poor generalizability, limited scalability, and suboptimal spectral embeddings that fail to approximate optimal graph cuts, primarily due to reliance on handcrafted affinity matrices and non-differentiable eigendecomposition. To address these limitations, we propose the first end-to-end differentiable spectral clustering framework: we fully differentiably reformulate the Normalized Cut (Ncut) objective using implicit differentiation and differentiable spectral graph theory, enabling deep neural networks to directly learn task-optimal spectral embeddings without requiring pre-defined similarity matrices or fixed graph structures. Our method supports cross-graph generalization and zero-shot transfer to unseen graph topologies. Extensive experiments on multiple benchmark datasets demonstrate superior clustering performance over conventional spectral clustering and GNN-based clustering methods, while achieving a threefold improvement in training efficiency.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Problem

• Improves spectral clustering generalizability and scalability.
• Directly learns clustering membership via neural networks.
• Enables efficient clustering for large-scale datasets.

Innovation

• Neural network reparameterizes cluster membership
• Stochastic gradient descent trains normalized cut loss
• Generalizable clustering for out-of-sample data