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SLR-MVTC: Smooth Low-Rank Multi-View Tensor Clustering
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Proposes SLR-MVTC, which learns orthogonal-projection latent features per view, stacks them into a tensor, and minimizes a smooth tensor nuclear norm (low-rank part of FFT low-frequency slices) for direct multi-view clustering.
Problem
Multi-view tensor clustering methods use a two-stage pipeline (learn affinity/embedding, then K-means) and either ignore within-view local similarity or weight local and global high-order correlations equally.
Approach
Learn shared latent features directly from multi-view data while imposing a smooth tensor nuclear norm (STNN) on the feature tensor: FFT along the sample dimension isolates low-frequency components for within-view smoothness, and nuclear-norm low-rank approximation of those components captures cross-view correlations.
Key results
- SLR-MVC reports ACC of 92.90% on ORL, 72.84% on CCV, 85.49% on ALOI 100, and 99.60% on Reuters, with best reported results on most datasets.
- On CIFAR100, SLR-MVTC reaches 98.36% ACC, comparable to EBMGC-GNF (99.96%) but reported as roughly ten times faster.
- Ablation removing the low-frequency part (w/o LF) drops ACC substantially, e.g. from 98.36% to 89.09% on CIFAR100 and from 72.84% to 43.92% on CCV.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · ORL | ACC: 90.80(2.58) -> 92.90(1.49) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · ORL | ACC: 91.12(1.20) -> 92.90(1.49) | Helped |
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · CCV | ACC: 43.92(0.24) -> 72.84(2.07) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · CCV | ACC: 72.53(3.70) -> 72.84(2.07) | Helped |
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · ALOI 100 | ACC: 67.95(2.05) -> 85.49(1.51) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · ALOI 100 | ACC: 84.16(1.05) -> 85.49(1.51) | Helped |
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · Reuters | ACC: 43.90(0.02) -> 99.60(0.00) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · Reuters | ACC: 96.44(0.00) -> 99.60(0.00) | Helped |
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · AwA fea | ACC: 74.40(1.69) -> 88.62(2.64) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · AwA fea | ACC: 88.49(1.13) -> 88.62(2.64) | Helped |
| Add the low-frequency component by using STNN rather than TNN (ablation) | SLR-MVTC · CIFAR100 | ACC: 89.09(1.45) -> 98.36(0.56) | Helped |
| Add the low-rank component by using STNN rather than TLFC (ablation) | SLR-MVTC · CIFAR100 | ACC: 91.25(2.67) -> 98.36(0.56) | Helped |
Surprising findings
- EBMGC-GNF achieves higher ACC than SLR-MVTC on CIFAR100 (99.96% vs 98.36%), which the paper acknowledges.
- Removing the low-rank component leaves ACC nearly unchanged on several datasets (e.g. ORL 91.12 vs 92.90), suggesting the low-frequency smoothness term drives most of the gain.
Limitations
- Hyperparameters (lambda, gamma, L) are chosen by brute-force search over the evaluation data, so tuning is not held out.
- Performance is not uniformly best: EBMGC-GNF is slightly higher on CIFAR100 and some baselines are stronger on specific metrics.
- Scope limited to six datasets and K-means post-processing on the averaged features.
Experimental setup
Datasets: ORL CCV ALOI 100 Reuters AwA CIFAR100
Benchmarks: ORL CCV ALOI 100 Reuters AwA fea CIFAR100
Metrics: ACC NMI F-score Precision Recall ARI CPU time
Baselines: BMVC FPMVS-CAG AWMVC S2MVTC EBMGC-GNF sMERA-MVC CFMVC-ETR Orth-NTF
Builds on: Tensor nuclear norm (t-SVD) Tensor low-frequency component (TLFC) ADMM S2MVTC
Closest papers by meaning
- S2MVTC: a Simple yet Efficient Scalable Multi-View Tensor Clustering (CVPR 2024 · similarity 0.92)
- Large-scale Multi-view Tensor Clustering with Implicit Linear Kernels (CVPR 2025 · similarity 0.90)
- Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model (ICLR 2024 · similarity 0.89)
- From Dictionary to Tensor: A Scalable Multi-View Subspace Clustering Framework with Triple Information Enhancement (NeurIPS 2024 · similarity 0.89)
- Low-Rank Kernel Tensor Learning for Incomplete Multi-View Clustering (AAAI 2024 · similarity 0.89)
- EDISON: Enhanced Dictionary-Induced Tensorized Incomplete Multi-View Clustering with Gaussian Error Rank Minimization (ICML 2024 · similarity 0.88)
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