Optimal Personalized Subspace Learning for Multi-view Tensor Observations

Kangxiang Qin; Zeyu Li; Xinbing Kong; Wang Zhou

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arXiv · 2609.30720

Optimal Personalized Subspace Learning for Multi-view Tensor Observations

Kangxiang Qin·Zeyu Li·Xinbing Kong·Wang Zhou

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Abstract

In this work, we model the observed multi-view tensors by decomposing the underlying signal in each view into two components: (i) the shared component that captures common dynamics across all views, and (ii) the private component that accounts for view-wise unique variations. To decouple the shared and private components, we introduce a novel Tucker personalized subspace principal component analysis (TPS-PCA) approach for tensors, which admits a one-step closed-form solution and serves as an ideal surrogate for our extended tensor-version personalized PCA (TP-PCA), adapted from the seminal work by \cite{shi2024personalized}. The theoretical analysis reveals that the proposed TPS-PCA estimators reach the minimax lower bound in terms of view-wise tensor decoupling, whereas the TP-PCA estimators only achieve a rate of average decoupling error across views, which is still slower than that of the TPS-PCA estimators. Extensive numerical experiments are conducted on synthetic and real datasets, demonstrating the wide applicability of the proposed method in fields including power management, financial analysis, and activity recognition.

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BibTeX RIS

Kangxiang Qin, Zeyu Li, Xinbing Kong, Wang Zhou. 2026-09-25. Optimal Personalized Subspace Learning for Multi-view Tensor Observations. https://arxiv.org/abs/2609.30720

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