# A Fresh Look at Generalized Category Discovery through Non-negative Matrix Factorization

arXiv: https://arxiv.org/abs/2410.21807 · HTML: https://mlsanity.com/paper/2410.21807/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 79 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [iBOT: Image BERT Pre-Training with Online Tokenizer](https://mlsanity.com/paper/2111.07832/) (2021)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [DeiT III: Revenge of the ViT](https://mlsanity.com/paper/2204.07118/) (2022)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Masked Siamese Networks for Label-Efficient Learning](https://mlsanity.com/paper/2204.07141/) (2022)
- [Learning to Discover Novel Visual Categories via Deep Transfer Clustering](https://mlsanity.com/paper/1908.09884/) (2019)
- [Generalized Category Discovery](https://mlsanity.com/paper/2201.02609/) (2022)
- [Open-World Semi-Supervised Learning](https://mlsanity.com/paper/2102.03526/) (2021)
- [A Unified Objective for Novel Class Discovery](https://mlsanity.com/paper/2108.08536/) (2021)
- [AutoNovel: Automatically Discovering and Learning Novel Visual Categories](https://mlsanity.com/paper/2106.15252/) (2021)
- [Parametric Classification for Generalized Category Discovery: A Baseline Study](https://mlsanity.com/paper/2211.11727/) (2022)
- [Dynamic Conceptional Contrastive Learning for Generalized Category Discovery](https://mlsanity.com/paper/2303.17393/) (2023)

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

- [Category Discovery: An Open-World Perspective](https://mlsanity.com/paper/2509.22542/) (2025)
- [Unlocking Optical Prior: Spectrum-Guided Knowledge Transfer for SAR Generalized Category Discovery](https://mlsanity.com/paper/2604.22174/) (2026)

## Abstract (arXiv)

Generalized Category Discovery (GCD) aims to classify both base and novel images using labeled base data. However, current approaches inadequately address the intrinsic optimization of the co-occurrence matrix barA based on cosine similarity, failing to achieve zero base-novel regions and adequate sparsity in base and novel domains. To address these deficiencies, we propose a Non-Negative Generalized Category Discovery (NN-GCD) framework. It employs Symmetric Non-negative Matrix Factorization (SNMF) as a mathematical medium to prove the equivalence of optimal K-means with optimal SNMF, and the equivalence of SNMF solver with non-negative contrastive learning (NCL) optimization. Utilizing these theoretical equivalences, it reframes the optimization of barA and K-means clustering as an NCL optimization problem. Moreover, to satisfy the non-negative constraints and make a GCD model converge to a near-optimal region, we propose a GELU activation function and an NMF NCE loss. To transition barA from a suboptimal state to the desired barA^*, we introduce a hybrid sparse regularization approach to impose sparsity constraints. Experimental results show NN-GCD outperforms state-of-the-art methods on GCD benchmarks, achieving an average accuracy of 66.1% on the Semantic Shift Benchmark, surpassing prior counterparts by 4.7%.