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

arXiv: https://arxiv.org/abs/2503.09260 · HTML: https://mlsanity.com/paper/2503.09260/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [SCAN: Learning to Classify Images without Labels](https://mlsanity.com/paper/2005.12320/) (2020)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reduction](https://mlsanity.com/paper/2006.08558/) (2020)
- [Deep Clustering via Joint Convolutional Autoencoder Embedding and Relative Entropy Minimization](https://mlsanity.com/paper/1704.06327/) (2017)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering](https://mlsanity.com/paper/1605.02633/) (2016)
- [Learning a Self-Expressive Network for Subspace Clustering](https://mlsanity.com/paper/2110.04318/) (2021)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)
- [SpecNet2: Orthogonalization-free spectral embedding by neural networks](https://mlsanity.com/paper/2206.06644/) (2022)
- [BASiS: Batch Aligned Spectral Embedding Space](https://mlsanity.com/paper/2211.16960/) (2022)
- [Generalized Clustering by Learning to Optimize Expected Normalized Cuts](https://mlsanity.com/paper/1910.07623/) (2019)

## Built on by (most cited first, 2 of 2)

- [GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales](https://mlsanity.com/paper/2506.06634/) (2025)
- [Advanced spectral clustering for heterogeneous data in credit risk monitoring systems](https://mlsanity.com/paper/2509.00546/) (2025)

## Abstract (arXiv)

Spectral clustering, as a popular tool for data clustering, requires an eigen-decomposition step on a given affinity to obtain the spectral embedding. Nevertheless, such a step suffers from the lack of generalizability and scalability. Moreover, the obtained spectral embeddings can hardly provide a good approximation to the ground-truth partition and thus a k-means step is adopted to quantize the embedding. In this paper, we propose a simple yet effective scalable and generalizable approach, called Neural Normalized Cut (NeuNcut), to learn the clustering membership for spectral clustering directly. In NeuNcut, we properly reparameterize the unknown cluster membership via a neural network, and train the neural network via stochastic gradient descent with a properly relaxed normalized cut loss. As a result, our NeuNcut enjoys a desired generalization ability to directly infer clustering membership for out-of-sample unseen data and hence brings us an efficient way to handle clustering task with ultra large-scale data. We conduct extensive experiments on both synthetic data and benchmark datasets and experimental results validate the effectiveness and the superiority of our approach. Our code is available at: https://github.com/hewei98/NeuNcut.