Feature-Label Modal Alignment for Robust Partial Multi-Label Learning

Yu Chen; Weijun Lv; Yue Huang; Xiaozhao Fang; Jie Wen; Yong Xu; Guanbin Li

cs.LGApr 10, 2026

Feature-Label Modal Alignment for Robust Partial Multi-Label Learning

Authors: Yu Chen, Weijun Lv, Yue Huang, Xiaozhao Fang, Jie Wen, Yong Xu, Guanbin Li

Organizations: School of Automation, Guangdong University of Technology, Guangzhou 510006, China · Shenzhen Key Laboratory of Visual Object Detection and Recognition, Harbin Institute of Technology, Shenzhen 518055, China · School of Computer Science and Engineering, Sun Yat-Sen University, Guangzhou 510275, China

Abstract

In partial multi-label learning (PML), each instance is associated with a set of candidate labels containing both ground-truth and noisy labels. The presence of noisy labels disrupts the correspondence between features and labels, degrading classification performance. To address this challenge, we propose a novel PML method based on feature-label modal alignment (PML-MA), which treats features and labels as two complementary modalities and restores their consistency through systematic alignment. Specifically, PML-MA first employs low-rank orthogonal decomposition to generate pseudo-labels that approximate the true label distribution by filtering noisy labels. It then aligns features and pseudo-labels through both global projection into a common subspace and local preservation of neighborhood structures. Finally, a multi-peak class prototype learning mechanism leverages the multi-label nature where instances simultaneously belong to multiple categories, using pseudo-labels as soft membership weights to enhance discriminability. By integrating modal alignment with prototype-guided refinement, PML-MA ensures pseudo-labels better reflect the true distribution while maintaining robustness against label noise. Extensive experiments on both real-world and synthetic datasets demonstrate that PML-MA significantly outperforms state-of-the-art methods, achieving superior classification accuracy and noise robustness.

Figures & tables

Fig. 1: An example of partial multi-label learning. The candidate label set contains both ground-truth labels (in black: ”lake,” ”cloud,” ”sun,” and ”tree”) and noisy labels (in red: ”mountain,” ”sea,” ”grass,” and ”bird”).

Symbol	Description
$\mathbf{X}\in\mathbb{R}^{n\times d}$	Feature matrix of $n$ instances with $d$ dimensions
$\mathbf{Y}\in\{0,1\}^{n\times c}$	Candidate label matrix with $c$ label classes
$\mathbf{R}\in\mathbb{R}^{n\times c}$	Pseudo-label matrix ( $0\leq r_{ij}\leq y_{ij}$ )
$\mathbf{Q}\in\mathbb{R}^{c\times c}$	Orthogonal basis matrix ( $\mathbf{Q}^{\top}\mathbf{Q}=\mathbf{I}_{c}$ )
$\mathbf{P}_{1}\in\mathbb{R}^{d\times m}$	Feature projection matrix
$\mathbf{P}_{2}\in\mathbb{R}^{c\times m}$	Pseudo-label projection matrix ( $\mathbf{P}_{2}^{\top}\mathbf{P}_{2}=\mathbf{I}_{m}$ )

TABLE I: Summary of key notations.

Fig. 2: Overview of the proposed PML-MA framework. The method comprises: (1) Label Low-Rank Orthogonal decomposition ( $\mathcal{L}_{LRO}$ ) decomposes candidate labels $\mathbf{Y}$ into orthogonal basis $\mathbf{Q}$ and pseudo-labels $\mathbf{R}$ ; (2) Global Modal Alignment ( $\mathcal{L}_{GMA}$ ) projects features $\mathbf{X}$ and pseudo-labels $\mathbf{R}$ into a common subspace via $\mathbf{P}_{1}$ and $\mathbf{P}_{2}$ ; (3) Local Modal Alignment ( $\mathcal{L}_{LMA}$ ) preserves neighborhood structures using similarity relationships; (4) Multi-peak Class Prototype learning ( $\mathcal{L}_{MCP}$ ) models the multi-peak distribution where instance $\mathbf{x}_{i}$ with pseudo-labels $\mathbf{r}_{i}=[0.7,0.8,0.4,0]$ (yielding $d_{ii}=1.9$ ) is guided by multiple class prototypes. The final classifier $\mathbf{P}_{2}\mathbf{P}_{1}^{\top}$ is derived from the aligned projection matrices.

Data Set	avg.#CLs	PML-MA	PML-PLR	FBD-PML	PML-ND	P-LENFN	PAMB	PML-NI	PARTICLE	PML-fp
Mirflickr	3.35	.169±.004	.171±.003	.170±.003	.185±.004	.173±.004	.171±.032	.224±.006	.174±.037	.216±.002
Music-emotion	5.29	.208±.004	.210±.001	.212±.004	.211±.005	.213±.004	.210±.003	.254±.009	.221±.004	.238±.017
Music-style	6.04	.114±.006	.115±.003	.117±.006	.116±.005	.116±.005	.115±.004	.159±.012	.125±.004	.166±.023
YeastBP	18.84	.033±.002	.034±.002	.035±.002	.076±.003	.041±.002	.034±.007	.037±.002	.026±.012	.040±.002
emotions	3	.202±.021	.204±.019	.218±.022	.210±.020	.226±.023	.205±.020	.312±.056	.235±.022	.377±.004
	4	.209±.015	.215±.018	.235±.019	.228±.020	.247±.022	.221±.022	.500±.047	.253±.022	.705±.013

TABLE II: Comparison of PML-MA with other state-of-the-art PML algorithms on HAMMING LOSS (mean

\pm

std), where the best experimental performance (the smaller the better) is shown in boldface and the suboptimal is shown with an underscore.

Data Set	avg.#CLs	PML-MA	PML-PLR	FBD-PML	PML-ND	P-LENFN	PAMB	PML-NI	PARTICLE	PML-fp
Mirflickr	3.35	.108±.008	.109±.006	.116±.007	.113±.005	.118±.005	.112±.038	.126±.007	.127±.103	.124±.003
Music-emotion	5.29	.235±.007	.236±.008	.238±.008	.242±.006	.246±.009	.234±.007	.246±.008	.362±.014	.458±.114
Music-style	6.04	.137±.012	.136±.009	.138±.010	.137±.008	.138±.010	.135±.005	.137±.010	.221±.010	.445±.231
YeastBP	18.84	.195±.011	.208±.010	.225±.011	.215±.009	.256±.011	.230±.011	.220±.011	.404±.033	.269±.012
emotions	3	.156±.038	.158±.030	.172±.032	.165±.028	.180±.031	.160±.021	.188±.029	.250±.035	.293±.015
	4	.165±.029	.172±.025	.185±.026	.178±.027	.192±.027	.177±.032	.211±.027	.263±.029	.407±.014

TABLE III: Comparison of PML-MA with other state-of-the-art PML algorithms on RANKING LOSS (mean

\pm

std), where the best experimental performance (the smaller the better) is shown in boldface and the suboptimal is shown with an underscore.

Data Set	avg.#CLs	PML-MA	PML-PLR	FBD-PML	PML-ND	P-LENFN	PAMB	PML-NI	PARTICLE	PML-fp
Mirflickr	3.35	.176±.018	.183±.014	.196±.016	.189±.015	.282±.011	.275±.093	.296±.024	.198±.012	.292±.011
Music-emotion	5.29	.420±.012	.424±.013	.444±.017	.432±.015	.476±.019	.428±.032	.478±.019	.585±.036	.690±.140
Music-style	6.04	.331±.022	.338±.018	.349±.019	.342±.016	.356±.019	.343±.011	.345±.018	.405±.017	.620±.254
YeastBP	18.84	.544±.033	.548±.028	.560±.032	.552±.030	.597±.015	.564±.023	.553±.029	.999±.000	.685±.018
emotions	3	.235±.070	.241±.028	.255±.030	.246±.027	.298±.059	.244±.026	.299±.050	.307±.069	.458±.000
	4	.283±.050	.297±.032	.318±.033	.309±.034	.329±.035	.333±.060	.355±.064	.324±.050	.542±.000

TABLE IV: Comparison of PML-MA with other state-of-the-art PML algorithms on ONE-ERROR (mean

\pm

std), where the best experimental performance (the smaller the better) is shown in boldface and the suboptimal is shown with an underscore.

Data Set	avg.#CLs	PML-MA	PML-PLR	FBD-PML	PML-ND	P-LENFN	PAMB	PML-NI	PARTICLE	PML-fp
Mirflickr	3.35	.225±.004	.225±.005	.229±.078	.231±.004	.226±.006	.228±.007	.227±.005	.239±.054	.226±.012
Music-emotion	5.29	.402±.007	.404±.008	.408±.011	.406±.009	.407±.010	.410±.010	.409±.009	.510±.012	.589±.097
Music-style	6.04	.204±.014	.198±.010	.201±.012	.200±.011	.196±.009	.195±.008	.196±.013	.284±.013	.491±.206
YeastBP	18.84	.263±.009	.270±.010	.285±.012	.280±.011	.357±.016	.299±.049	.289±.009	.423±.162	.368±.015
emotions	3	.297±.030	.298±.028	.301±.032	.299±.030	.316±.029	.300±.036	.325±.026	.357±.045	.371±.029
	4	.297±.035	.305±.030	.310±.031	.308±.029	.324±.032	.312±.028	.339±.031	.356±.031	.469±.009

TABLE V: Comparison of PML-MA with other state-of-the-art PML algorithms on COVERAGE (mean

\pm

std), where the best experimental performance (the smaller the better) is shown in boldface and the suboptimal is shown with an underscore.

Data Set	avg.#CLs	PML-MA	PML-PLR	FBD-PML	PML-ND	P-LENFN	PAMB	PML-NI	PARTICLE	PML-fp
Mirflickr	3.35	.833±.011	.825±.010	.815±.015	.820±.012	.798±.007	.791±.019	.786±.009	.813±.136	.792±.005
Music-emotion	5.29	.633±.010	.630±.010	.615±.013	.628±.011	.610±.012	.626±.011	.608±.012	.506±.016	.435±.093
Music-style	6.04	.743±.017	.742±.010	.735±.014	.740±.012	.731±.016	.741±.007	.739±.015	.657±.012	.472±.200
YeastBP	5.93	.418±.020	.410±.020	.380±.023	.406±.021	.339±.015	.356±.022	.404±.022	.108±.016	.286±.009
emotions	3	.814±.043	.812±.020	.800±.030	.808±.025	.781±.033	.810±.017	.777±.028	.747±.035	.675±.005
	4	.800±.026	.790±.030	.775±.035	.785±.032	.768±.028	.783±.036	.749±.034	.739±.033	.581±.003

TABLE VI: Comparison of PML-MA with other state-of-the-art PML and MLL algorithms on AVERAGE PRECISION , where the best experimental performance (the larger the better) is shown in boldface and the suboptimal is shown with an underscore.

Panel of Figure 9 — Fig. 3: Results of PML-MA against other approaches with the Nemenyi test(CD = 2.1934 at 0.05 significance level).

Evaluation metric	$\ F_{F}$	Critical value
Hamming Loss	23.1348
Ranking Loss	71.4812
One Error	54.1232	1.9785
Coverage	51.7904
Average precision	128.4977

TABLE VII: Summary of FRIEDMAN STATISTICS

\ F_{F}

FOR EACH EVALUATION METRIC AT 0.05 SIGNIFICANCE LEVEL (# APPROACHES

k

= 9, DATA SETS

N

= 30).

Panel of Figure 11 — Fig. 4: Results of PML-MA with varying values of trade-off parameters on birds dataset.

Fig. 5: The convergence curves of PML-MA on the synthetic datasets.

Component	Configuration and accordingly performance
$\mathcal{L}_{LRO}$	✓	✗	✓	✓
$\mathcal{L}_{GLMA}$	✓	✓	✗	✓
$\mathcal{L}_{MCP}$	✓	✓	✓	✗
emotions (avg.#CLs=4)	.800 $\pm$ .026	.793 $\pm$ .020	.785 $\pm$ .013	.796 $\pm$ .023
birds (avg.#CLs=4)	.597 $\pm$ .060	.590 $\pm$ .040	.584 $\pm$ .048	.595 $\pm$ .051
scene (avg.#CLs=5)	.813 $\pm$ .024	.811 $\pm$ .020	.807 $\pm$ .012	.810 $\pm$ .028

TABLE VIII: Ablation study results. Comparison of performance with and without each module, in metric Average precision . The best experimental performance is shown in boldface.

Panel of Figure 14 — Fig. 6: Comparative experiment of low rank orthogonal decomposition and low rank sparse decomposition on yeast and reference datasets.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Datasets	#Instance	#Dim	#Class	avg.#CLs	avg.#GLs
Mirflickr	10433	100	7	3.35	1.77
Music $\_$ emotion	6833	98	11	5.29	2.42
Music $\_$ style	6839	98	10	6.04	1.44
YeastBP	6139	6139	127	5.93	5.54
emotions	593	72	6	3, 4, 5	1.86
birds	645	260	19	3, 4, 5	1.01

Appendix

TABLE IX: General Information of The nine Multi-label datasets and four partial multi-label learning datasets.

Method	Hl	Rl	Oe	Cov	Ap	avg
PML-MA	2.0833	1.2500	1.2500	1.6000	1.1000	1.4567
PML-PLR	2.9167	2.2000	2.3333	2.1833	2.2333	2.3733
FBD-PML	5.2333	4.9167	4.5333	4.5000	4.5333	4.7433
PML-ND	3.4167	3.5333	3.4167	3.4667	2.9333	3.3533
P-LENFN	6.7167	6.2167	6.1500	6.2333	5.7167	6.2067
PAMB	5.8500	4.9333	6.3000	5.6667	5.7167	5.6933

Appendix

TABLE X: The Average Rankings of Each Method Across All Five Metrics (Transposed)

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Bringing Clustering to MLL: Weakly-Supervised Clustering for Partial Multi-Label Learning

Yu Chen, Weijun Lv, Yue Huang, Xuhuan Zhu+1

School of Automation, Guangdong University of Technology

Multi-Label Classification Learning with Noisy Labels Weakly Supervised Learning

Open paper AskPDF arXiv

Label noise in multi-label learning (MLL) poses significant challenges for model training, particularly in partial multi-label learning (PML) where candidate labels contain both relevant and irrelevant labels. While clustering offers a natural approach to exploit data structure for noise identification, traditional clustering methods cannot be directly applied to multi-label scenarios due to a fundamental incompatibility: clustering produces membership values that sum to one per instance, whereas multi-label assignments require binary values that can sum to any number. We propose a novel weakly-supervised clustering approach for PML (WSC-PML) that bridges clustering and multi-label learning through membership matrix decomposition. Our key innovation decomposes the clustering membership matrix

\mathbf{A}

into two components:

\mathbf{A} = \mathbfΠ \odot \mathbf{F}

, where

\mathbfΠ

maintains clustering constraints while

\mathbf{F}

preserves multi-label characteristics. This decomposition enables seamless integration of unsupervised clustering with multi-label supervision for effective label noise handling. WSC-PML employs a three-stage process: initial prototype learning from noisy labels, adaptive confidence-based weak supervision construction, and joint optimization via iterative clustering refinement. Extensive experiments on 24 datasets demonstrate that our approach outperforms six state-of-the-art methods across all evaluation metrics.

Abstract

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