Problem
Research questions and friction points this paper is trying to address.
multi-view tensor
personalized subspace learning
shared and private components
tensor decoupling
principal component analysis
Optimal Personalized Subspace Learning for Multi-view Tensor Observations
🤖 AI Summary
This study addresses the challenge of disentangling shared and private components in multi-view tensors by proposing Tucker Personalized Subspace Principal Component Analysis (TPS-PCA). Grounded in tensor decomposition theory, the method achieves efficient signal separation through closed-form solutions. Notably, this work establishes the first view-wise minimax lower bounds for decoupling, overcoming the theoretical limitations inherent in conventional average error rate analyses. Extensive experiments across diverse domains, including power systems and finance, demonstrate that TPS-PCA consistently delivers superior performance and broad applicability. By offering rigorous theoretical guarantees alongside practical utility, this approach introduces a new paradigm for multi-view tensor analysis.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Multi-view Tensor
Personalized Subspace PCA
Tucker Decomposition
Minimax Lower Bound
Signal Decoupling
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