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Exploring a Principled Framework for Deep Subspace Clustering
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Proposes PRO-DSC, a deep subspace clustering framework that adds a log-det representation regularizer to the self-expressive model to prevent feature collapse and learn union-of-orthogonal-subspaces representations, evaluated on CLIP features across six image benchmarks.
Problem
Deep subspace clustering methods based on the self-expressive model suffer from catastrophic feature collapse of learned representations and lack guarantees that representations form a union of subspaces (UoS).
Approach
Add a concave log-det surrogate of rank on the learned representations to the self-expressive objective, prove this prevents collapse under a condition on gamma, alpha and lambda_max(M), show optimal representations align with eigenspaces and form orthogonal subspaces under a compatibly structured coherence condition, and implement scalably with neural reparameterization of the coefficients plus a
Key results
- PRO-DSC on CLIP features reaches 97.2% ACC / 92.8% NMI on CIFAR-10 and 77.3% ACC on CIFAR-100, outperforming TEMI (73.7%) and CPP (75.4%) on CIFAR-100.
- On ImageNet-Dogs-15, PRO-DSC achieves 84.0% ACC versus 83.0% for CPP and on ImageNet-1k 65.0% ACC versus 64.0% for TEMI.
- Ablation: removing the log-det term causes collapse, with CIFAR-10 ACC dropping from 97.2 to 56.9 when the self-expressive term alone is used with the block-diagonal regularizer (and similar drops for other combinations).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · CIFAR-10 | ACC: 96.9 -> 97.2 | Helped |
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · CIFAR-20 | ACC: 67.7 -> 71.6 | Helped |
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · CIFAR-100 | ACC: 75.4 -> 77.3 | Helped |
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · Tiny-ImageNet-200 | ACC: 64.5 -> 69.8 | Helped |
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · ImageNet-Dogs-15 | ACC: 83.0 -> 84.0 | Helped |
| Use PRO-DSC instead of the strongest listed baseline | CLIP-feature clustering · ImageNet-1k | ACC: 64.0 -> 65.0 | Helped |
| Add the log-determinant representation loss L1 (ablation) | PRO-DSC · CIFAR-10 | ACC: 56.9 -> 97.2 | Helped |
| Add the self-expressive loss L2 (ablation) | PRO-DSC · ImageNet-Dogs-15 | ACC: 10.5 -> 84.0 | Helped |
| Drop the explicit coefficient regularizer r(C) (ablation) | PRO-DSC · CIFAR-10 | ACC: 97.2 -> 97.0 | No clear effect |
| Replace block-diagonal regularizer with nuclear norm of C (ablation) | PRO-DSC · CIFAR-100 | ACC: 77.3 -> 75.2 | No clear effect |
| Replace block-diagonal regularizer with L1 norm of C (ablation) | PRO-DSC · CIFAR-100 | ACC: 77.3 -> 76.4 | No clear effect |
| Replace block-diagonal regularizer with squared Frobenius norm of C (ablation) | PRO-DSC · CIFAR-100 | ACC: 77.3 -> 75.2 | No clear effect |
Surprising findings
- The specific choice of regularizer (block-diagonal, l1, Frobenius, nuclear norm, or none) has little effect on performance, attributed to the structured representations learned by the log-det term.
- Removing the log-det term leads to catastrophic collapse, with ImgNetDogs-15 ACC falling to 10.5% in one ablation setting.
Limitations
- Theoretical guarantee of the compatibly structured coherence condition is not proven in general; only empirically observed.
- Results rely on pretrained CLIP features rather than end-to-end training from raw images.
Experimental setup
Datasets: CIFAR-10 CIFAR-20 CIFAR-100 ImageNet-Dogs-15 TinyImageNet-200 ImageNet-1k
Benchmarks: CIFAR-10 CIFAR-20 CIFAR-100 TinyImageNet-200 ImageNet-Dogs-15 ImageNet-1k
Metrics: clustering accuracy (ACC) normalized mutual information (NMI) subspace-preserving representation error (SRE) time (s) memory (MiB)
Baselines: k-means spectral clustering SSCOMP EnSC SENet SCAN TEMI CPP DSCNet EDESC
Builds on: self-expressive model (DSCNet) maximal coding rate reduction (MCR^2) MLC CPP
Closest papers by meaning
- A Critique of Self-Expressive Deep Subspace Clustering (ICLR 2021 · similarity 0.94)
- Deep Subspace Clustering Networks (NeurIPS 2017 · similarity 0.94)
- Efficient Deep Embedded Subspace Clustering (CVPR 2022 · similarity 0.94)
- LRSC: Learning Representations for Subspace Clustering (AAAI 2021 · similarity 0.94)
- Multi-Scale Fusion Subspace Clustering Using Similarity Constraint (CVPR 2020 · similarity 0.91)
- Neural Collaborative Subspace Clustering (ICML 2019 · similarity 0.91)
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