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Multi-Label Ranking Loss Minimization for Matrix Completion
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Proposes multi-label ranking loss minimization (MLRM), which converts an incomplete matrix into a pairwise column-ranking matrix and solves a nuclear-norm plus l1 factorized objective, outperforming matrix completion baselines on movie recommendation, drug-target interaction, and multi-label learning.
Problem
Standard matrix completion minimizes rank plus Hamming-style element-wise loss, which can yield ambiguous recoveries of missing entries under low-rank assumptions.
Approach
Replace the Hamming/element-wise loss with a Frobenius approximation to a pairwise column-ranking matrix derived from multi-label ranking loss, with unknown entries set to neutral values, and combine it with a FNNM-style low-rank plus sparse side-information decomposition, followed by a per-row offset correction.
Key results
- On MovieLens, MLRM-p (p=0.1) reaches MAE 0.8046-0.8552 across sampling rates, best at 0.1 to 0.9 observation rates except for FNNM at 0.9 level comparison is close; MLRM ranks first in 2 of 5 rates.
- On DTI, MLRM achieves average rank 1.6 versus 1.9 for FNNM among inductive methods; FNNM is better overall in 4 of 10 cases.
- On 7 MLL datasets, MLRM ranks first in 31 of 35 settings with average rank 1.11 versus 2.43 for the next best (SIMC).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use pairwise ranking loss minimization (MLRM) instead of the compared completion methods | Matrix completion · MovieLens | MAE: 0.9502±0.0016 -> 0.8552±0.0022; 0.8799±0.0019 -> 0.8465±0.0019; 0.8453±0.0027 -> 0.8530±0.0017; 0.8201±0.0032 -> 0.8546± | Mixed |
| Use MLRM instead of FNNM | DTI prediction · Enzymes and GPCRs | AUC: Enzymes: 0.6422±0.0072 -> 0.5836±0.0068; GPCRs: 0.5999±0.0135 -> 0.6459±0.0192 | Mixed |
| Use MLRM instead of the compared multi-label learning methods | Multi-label learning · Arts, Business, Computers, Education, Health, Recreation, Society | AP | Helped |
| Add inductive learning on side information (ablation) | MLRM · MovieRec | MAE | Helped |
| Add result correction (ablation) | MLRM · MovieRec | MAE | Helped |
| Add inductive learning on side information (ablation) | MLRM · MovieRec | MAE | No clear effect |
| Add result correction (ablation) | MLRM · DTI and MLL | AUC and AP | No clear effect |
Surprising findings
- On DTI, MLRM does not dominate; FNNM is better in several settings, and MLRM is weaker at low sampling rates in multi-label learning.
Limitations
- Assumes ranking relations between entries, which may not apply to nominal values.
- Pairwise ranking matrix scales as nm^2/2, leading to high time and space complexity; column sampling needed for large matrices.
- Performance weaker at low observation rates in multi-label learning and on some DTI settings.
Experimental setup
Datasets: MovieLens-100K Enzymes GPCRs Arts Business Computers Education Health Recreation Society
Benchmarks: MovieLens-100K Enzymes GPCRs 7 multi-label learning datasets (Arts, Business, Computers, Education, Health, Recreation, Society)
Metrics: MAE AUC AP
Baselines: FPCA SIMC FNNM InMC SMDkM
Builds on: FNNM multi-label ranking loss singular value thresholding inductive matrix completion
Closest papers by meaning
- Optimal Discrete Matrix Completion (AAAI 2016 · similarity 0.87)
- Clipped Matrix Completion: A Remedy for Ceiling Effects (AAAI 2019 · similarity 0.86)
- Mixture Matrix Completion (NeurIPS 2018 · similarity 0.86)
- Scalable Completion of Nonnegative Matrix with Separable Structure (AAAI 2016 · similarity 0.86)
- Convex Co-Embedding for Matrix Completion with Predictive Side Information (AAAI 2017 · similarity 0.85)
- Bipartite Ranking From Multiple Labels: On Loss Versus Label Aggregation (ICML 2025 · similarity 0.83)
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