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Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures
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Proposes a distribution-matching loss (adversarial, with orthonormality constraints) to identify shared components from unaligned multimodal linear mixtures, with milder conditions than ICA-based prior work and structural constraints (shared mixing, weak supervision) for further relaxation.
Problem
Identifying shared latent components across two modalities generated as linear mixtures of shared and private components when cross-modality samples are unpaired (unaligned).
Approach
Match distributions of linearly embedded multimodal data (adversarial distribution matching with whitening constraints) instead of paired CCA; identifiability follows from a geometric "modality variability" assumption plus either non-Gaussian independent content or hyper-rectangular content support, with structural constraints (shared mixing matrix, few paired samples) relaxing requirements furthe
Key results
- On Office-Home the proposed method averages 87.2% target accuracy vs 85.0% for CLIP and 72.4% for MCC.
- On Office-31 the proposed method averages 93.0% vs 91.2% for CLIP, with gains above 4% on W->A and D->A-type tasks.
- On single-cell RNA-ATAC, the method without paired samples reaches about 3x the k-NN accuracy of the CM-AE baseline, and one paired sample raises it to about 5x.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| post-process CLIP features with the proposed shared component method | CLIP ViT-L/14 · Office-31 average | classification accuracy: 91.2 -> 93.0 | Helped |
| post-process CLIP features with the proposed shared component method | CLIP ViT-L/14 · Office-Home average | classification accuracy: 85.0 -> 87.2 | Helped |
| use the proposed method without paired-sample supervision instead of CM-AE | RNA–ATAC shared representation · A549 RNA–ATAC test set | k-NN accuracy: around 3 times greater | Helped |
| add one paired sample of supervision (ablation) | Proposed RNA–ATAC shared representation · A549 RNA–ATAC test set | k-NN accuracy: around 5 times higher | Helped |
| increase the number of available paired samples (ablation) | Proposed RNA–ATAC shared representation · A549 RNA–ATAC test set | k-NN accuracy | Helped |
Surprising findings
- Distribution matching alone (unpaired) can already reach roughly 3x the k-NN accuracy of a paired-weakly-supervised baseline on single-cell data.
Limitations
- Identifiability conditions are sufficient but not shown to be necessary.
- Linear mixture model has limited expressiveness and needs preprocessing of real data.
- Results assume unlimited data; no finite-sample analysis.
Experimental setup
Datasets: Office-31 Office-Home A549 single-cell RNA/ATAC data
Benchmarks: Office-31 Office-Home A549 RNA-ATAC k-NN
Metrics: classification accuracy k-NN accuracy
Baselines: DANN ADDA DAN JAN CDAN MDD MCC CLIP CM-AE
Builds on: canonical correlation analysis independent component analysis GAN adversarial loss CLIP
Closest papers by meaning
- Connect, Collapse, Corrupt: Learning Cross-Modal Tasks with Uni-Modal Data (ICLR 2024 · similarity 0.86)
- Learning Shared Representations from Unpaired Data (NeurIPS 2025 · similarity 0.86)
- Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability (NeurIPS 2025 · similarity 0.86)
- On the Value of Cross-Modal Misalignment in Multimodal Representation Learning (NeurIPS 2025 · similarity 0.85)
- AlignMamba: Enhancing Multimodal Mamba with Local and Global Cross-modal Alignment (CVPR 2025 · similarity 0.85)
- Enhancing Multimodal Cooperation via Sample-level Modality Valuation (CVPR 2024 · similarity 0.85)
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