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Deep-Union Completion
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Proposes Deep Union Completion (DUC), a deep autoencoder with a pseudo-completion layer and closed-form clustering layer that completes missing data under a latent union-of-subspaces model.
Problem
Matrix completion with large amounts of missing data fails when real data does not follow low-rank, high-rank, or deep completion models; naive filling biases structure discovery, creating a chicken-and-egg problem with clustering.
Approach
Learn a non-linear embedding whose latent representation lies in a union of subspaces, using a learned pseudo-completion layer to fill missing entries, an autoencoder to embed, and a closed-form projector-based clustering layer that identifies the UoS without explicit clustering regularizers.
Key results
- Abstract claims DUC outperforms state-of-the-art clustering accuracy by more than 40% across over 10 real datasets.
- DUC achieved zero completion error on COIL20 with up to 60% missing data, per the paper's results section.
- Zero-filling in the same architecture consistently diverges from the true model, showing the pseudo-completion layer's importance (about 50% clustering and 30% completion degradation reported on synthetic data).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DUC instead of the next-best algorithm | DUC · COIL20, Extended Yale B, and ORL | clustering accuracy: more than a staggering 40% | Helped |
| Add the pseudo-completion layer (ablation) | DUC · Synthetic data, most nontrivial cases of K and d | clustering accuracy: an average of 50% | Helped |
| Add the pseudo-completion layer (ablation) | DUC · Synthetic data, most nontrivial cases of K and d | completion accuracy: 30% | Helped |
Surprising findings
- On synthetic data, baselines designed for the idealized setting are competitive with DUC, which is only comparable to them there.
- DUC slightly outperforms the zero-fill variant even at 0% missing data, which the authors attribute to added model complexity.
Limitations
- Performance on synthetic data is only comparable to baselines, which the authors attribute to idealized baseline conditions.
- The number of subspaces K must be chosen (e.g., number of classes) or estimated via SVD thresholds, and regression datasets lack natural K and d.
- Training has no fixed epoch count; termination depends on learning rate schedule, and no pretraining is used.
Experimental setup
Datasets: COIL20 Extended Yale B ORL Boston Housing Period Changer Heart Disease Human Activity Recognition Using Smartphones Oxford-IIIT Pet 102 Category Flower synthetic union-of-subspaces data
Benchmarks: COIL20 Extended Yale B ORL Boston Housing Period Changer Heart Disease Human Activity Recognition Using Smartphones Oxford-IIIT Pet 102 Category Flower synthetic union-of-subspaces data
Metrics: completion error (normalized Frobenius norm) clustering accuracy
Baselines: SimpleFill K-Nearest Neighbors imputation Iterative Imputer SoftImpute MIDAS SSC-MC SSC-EWFZ GSSC EM MSC zero-fill DUC
Builds on: high-rank matrix completion autoencoder subspace clustering (Ji et al. 2017) subspace clustering
Closest papers by meaning
- Online High Rank Matrix Completion (CVPR 2019 · similarity 0.88)
- A Pairwise Pseudo-likelihood Approach for Matrix Completion with Informative Missingness (NeurIPS 2024 · similarity 0.84)
- Generalization Analysis of Deep Non-linear Matrix Completion (ICML 2024 · similarity 0.84)
- Exploring a Principled Framework for Deep Subspace Clustering (ICLR 2025 · similarity 0.84)
- Symmetric Matrix Completion with ReLU Sampling (ICML 2024 · similarity 0.82)
- Matrix Completion with Incomplete Side Information via Orthogonal Complement Projection (ICML 2025 · similarity 0.82)
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