# Revisiting Sparsity Constraint Under High-Rank Property in Partial Multi-Label Learning

arXiv: https://arxiv.org/abs/2505.20938 · HTML: https://mlsanity.com/paper/2505.20938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 5 of 5)

- [Multi-Label Learning with Global and Local Label Correlation](https://mlsanity.com/paper/1704.01415/) (2017)
- [Instance-Aware Hashing for Multi-Label Image Retrieval](https://mlsanity.com/paper/1603.03234/) (2016)
- [Expand Globally, Shrink Locally: Discriminant Multi-label Learning with Missing Labels](https://mlsanity.com/paper/2004.03951/) (2020)
- [Multi-label Classification with High-rank and High-order Label Correlations](https://mlsanity.com/paper/2207.04197/) (2022)
- [Deep Partial Multi-Label Learning with Graph Disambiguation](https://mlsanity.com/paper/2305.05882/) (2023)

## Abstract (arXiv)

Partial Multi-Label Learning (PML) extends the multi-label learning paradigm to scenarios where each sample is associated with a candidate label set containing both ground-truth labels and noisy labels. Existing PML methods commonly rely on two assumptions: sparsity of the noise label matrix and low-rankness of the ground-truth label matrix. However, these assumptions are inherently conflicting and impractical for real-world scenarios, where the true label matrix is typically full-rank or close to full-rank. To address these limitations, we demonstrate that the sparsity constraint contributes to the high-rank property of the predicted label matrix. Based on this, we propose a novel method Schirn, which introduces a sparsity constraint on the noise label matrix while enforcing a high-rank property on the predicted label matrix. Extensive experiments demonstrate the superior performance of Schirn compared to state-of-the-art methods, validating its effectiveness in tackling real-world PML challenges.