# Expand Globally, Shrink Locally: Discriminant Multi-label Learning with Missing Labels

arXiv: https://arxiv.org/abs/2004.03951 · HTML: https://mlsanity.com/paper/2004.03951/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2020.

## Built on by (most cited first, 9 of 9)

- [One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement](https://mlsanity.com/paper/2206.00517/) (2022)
- [Reliable Representation Learning for Incomplete Multi-View Missing Multi-Label Classification](https://mlsanity.com/paper/2303.17117/) (2023)
- [Masked Two-channel Decoupling Framework for Incomplete Multi-view Weak Multi-label Learning](https://mlsanity.com/paper/2404.17340/) (2024)
- [Multi-View Factorizing and Disentangling: A Novel Framework for Incomplete Multi-View Multi-Label Classification](https://mlsanity.com/paper/2501.06524/) (2025)
- [Adaptive Disentangled Representation Learning for Incomplete Multi-View Multi-Label Classification](https://mlsanity.com/paper/2601.05785/) (2026)
- [A Survey on Incomplete Multi-label Learning: Recent Advances and Future Trends](https://mlsanity.com/paper/2406.06119/) (2024)
- [Revisiting Sparsity Constraint Under High-Rank Property in Partial Multi-Label Learning](https://mlsanity.com/paper/2505.20938/) (2025)
- [Least-Ambiguous Multi-Label Classifier](https://mlsanity.com/paper/2509.10689/) (2025)
- [When Semantically Consistent Encoding Meets View-Label Heterogeneity Modeling: A Unified Framework for Incomplete Multi-View Multi-Label Learning](https://mlsanity.com/paper/2609.07525/) (2026)

## Abstract (arXiv)

In multi-label learning, the issue of missing labels brings a major challenge. Many methods attempt to recovery missing labels by exploiting low-rank structure of label matrix. However, these methods just utilize global low-rank label structure, ignore both local low-rank label structures and label discriminant information to some extent, leaving room for further performance improvement. In this paper, we develop a simple yet effective discriminant multi-label learning (DM2L) method for multi-label learning with missing labels. Specifically, we impose the low-rank structures on all the predictions of instances from the same labels (local shrinking of rank), and a maximally separated structure (high-rank structure) on the predictions of instances from different labels (global expanding of rank). In this way, these imposed low-rank structures can help modeling both local and global low-rank label structures, while the imposed high-rank structure can help providing more underlying discriminability. Our subsequent theoretical analysis also supports these intuitions. In addition, we provide a nonlinear extension via using kernel trick to enhance DM2L and establish a concave-convex objective to learn these models. Compared to the other methods, our method involves the fewest assumptions and only one hyper-parameter. Even so, extensive experiments show that our method still outperforms the state-of-the-art methods.