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Large-scale Multi-view Tensor Clustering with Implicit Linear Kernels

CVPR 2025 · Learning theory and algorithms › Clustering · approach: Subspace clustering · 6 citations (OpenAlex)

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Shows that the tensor rotation trick in t-SVD-based multi-view tensor clustering leaks sample-order (label) information, and proposes LMTC, a linear-complexity large-scale multi-view tensor clustering method that drops the rotation and uses implicit linear kernels with a t-TNN constraint.

Problem

Multi-view tensor clustering methods using t-SVD with the tensor rotation trick inadvertently use sample sequential information (inadvertent label use), while existing large-scale multi-view clustering methods rely on matrix factorization or anchors and ignore pairwise similarity among all samples.

Approach

Remove the tensor rotation trick from tensor clustering to avoid order leakage, and incorporate pairwise similarity via implicit linear kernels (X_v^T X_v never formed explicitly) aligned with orthogonal latent representations regularized by t-TNN, solved by ALM with linear complexity in sample count.

Key results

• LMTC improves ACC over the second-best method by 0.22%, 1.90%, 4.12%, 3.51%, 2.73% and 0.20% on ORL, HW, BDGP, ALOI, DryBean and AwA respectively.
• Shuffling data drops ACC of tensor-rotation-based methods substantially, e.g. ASR-ETR on AwA falls from 67.70 to 9.41 and on YtVideo from 71.35 to 17.05.
• LMTC runs in about 1 to 24x less time than OPMC on ORL-scale data while staying competitive in accuracy, and scales to YtVideo (101,499 samples).

Measured effects reported in the paper

Surprising findings

• Tensor-rotation-based multi-view tensor clustering methods perform far worse when samples are shuffled, suggesting prior reported gains came from inadvertent use of sample order.
• On BDGP, OPMC has a 2.53% higher NMI than LMTC, though it requires about 24 times more time.

Limitations

• Hyperparameter lambda must be grid-searched, with performance sensitive to its value.
• Does not outperform OPMC on NMI for BDGP and is not the fastest method.

Experimental setup

Datasets: ORL HW BDGP ALOI DryBean AwA YtVideo

Benchmarks: ORL HW BDGP ALOI DryBean AwA YtVideo

Metrics: ACC NMI Purity running time

Baselines: RMKC BMVC LMSC OPMC EOMSC MCHBG ASR-ETR S2MVTC TBGL Orth-NTF

Builds on: t-SVD tensor nuclear norm OPMC Orth-NTF ASR-ETR

Closest papers by meaning

• S2MVTC: a Simple yet Efficient Scalable Multi-View Tensor Clustering (CVPR 2024 · similarity 0.91)
• Low-Rank Kernel Tensor Learning for Incomplete Multi-View Clustering (AAAI 2024 · similarity 0.90)
• SLR-MVTC: Smooth Low-Rank Multi-View Tensor Clustering (AAAI 2025 · similarity 0.90)
• Performance Gaps in Multi-view Clustering under the Nested Matrix-Tensor Model (ICLR 2024 · similarity 0.90)
• From Dictionary to Tensor: A Scalable Multi-View Subspace Clustering Framework with Triple Information Enhancement (NeurIPS 2024 · similarity 0.90)
• Scalable Federated One-Step Multi-View Clustering with Tensorized Regularization (AAAI 2025 · similarity 0.88)