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

Abstract

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 $\bar{A}$ 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 $\bar{A}$ 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 $\bar{A}$ from a suboptimal state to the desired $\bar{A}^*$, 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\%.