Nonconvex Low-Rank Tensor Representation with Deep Priors for Multiview Subspace Clustering

Yao Fu, Dong Hu, Zhi Wang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:31854-31876, 2026.

Abstract

Multiview subspace clustering (MvSC) has shown remarkable potential in exploring underlying structures of high-dimensional data. However, existing MvSC methods still suffer from two shortcomings: (1) the commonly use of convex low-rank approximations inadequately capture high-order correlations across views, while sensitivity to noise and outliers degrades clustering performance, and (2) they lack the ability to preserve global correlations and local geometric patterns simultaneously. To address these issues, we propose a novel nonconvex regularized MvSC model with deep prior, which not only accurately characterizes the intrinsic low-rank structure and suppresses the effect of outliers, but also preserves local structural properties through deep networks. By mathematically analyzing the optimal solution of the optimization problem in our proposed model, we develop an efficient ADMM-based algorithm with provable convergence guarantees to solve it. Extensive experiments on various datasets demonstrate the superiority of the proposed model. MATLAB code is available at https://github.com/wangzhi-swu/NRDN-MvSC.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-fu26g, title = {Nonconvex Low-Rank Tensor Representation with Deep Priors for Multiview Subspace Clustering}, author = {Fu, Yao and Hu, Dong and Wang, Zhi}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {31854--31876}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/fu26g/fu26g.pdf}, url = {https://proceedings.mlr.press/v306/fu26g.html}, abstract = {Multiview subspace clustering (MvSC) has shown remarkable potential in exploring underlying structures of high-dimensional data. However, existing MvSC methods still suffer from two shortcomings: (1) the commonly use of convex low-rank approximations inadequately capture high-order correlations across views, while sensitivity to noise and outliers degrades clustering performance, and (2) they lack the ability to preserve global correlations and local geometric patterns simultaneously. To address these issues, we propose a novel nonconvex regularized MvSC model with deep prior, which not only accurately characterizes the intrinsic low-rank structure and suppresses the effect of outliers, but also preserves local structural properties through deep networks. By mathematically analyzing the optimal solution of the optimization problem in our proposed model, we develop an efficient ADMM-based algorithm with provable convergence guarantees to solve it. Extensive experiments on various datasets demonstrate the superiority of the proposed model. MATLAB code is available at https://github.com/wangzhi-swu/NRDN-MvSC.} }
Endnote
%0 Conference Paper %T Nonconvex Low-Rank Tensor Representation with Deep Priors for Multiview Subspace Clustering %A Yao Fu %A Dong Hu %A Zhi Wang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-fu26g %I PMLR %P 31854--31876 %U https://proceedings.mlr.press/v306/fu26g.html %V 306 %X Multiview subspace clustering (MvSC) has shown remarkable potential in exploring underlying structures of high-dimensional data. However, existing MvSC methods still suffer from two shortcomings: (1) the commonly use of convex low-rank approximations inadequately capture high-order correlations across views, while sensitivity to noise and outliers degrades clustering performance, and (2) they lack the ability to preserve global correlations and local geometric patterns simultaneously. To address these issues, we propose a novel nonconvex regularized MvSC model with deep prior, which not only accurately characterizes the intrinsic low-rank structure and suppresses the effect of outliers, but also preserves local structural properties through deep networks. By mathematically analyzing the optimal solution of the optimization problem in our proposed model, we develop an efficient ADMM-based algorithm with provable convergence guarantees to solve it. Extensive experiments on various datasets demonstrate the superiority of the proposed model. MATLAB code is available at https://github.com/wangzhi-swu/NRDN-MvSC.
APA
Fu, Y., Hu, D. & Wang, Z.. (2026). Nonconvex Low-Rank Tensor Representation with Deep Priors for Multiview Subspace Clustering. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:31854-31876 Available from https://proceedings.mlr.press/v306/fu26g.html.

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