On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis - Archive ouverte HAL Access content directly
Conference Papers Year : 2023

On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis

Abstract

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left| \langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant components are successively estimated from the noisy observation and subsequently subtracted, we leverage recent advances in random tensor theory in the regime of asymptotically large tensor dimensions to analytically characterize the estimated singular values and the alignment of estimated and true singular vectors at each step of the deflation procedure. Furthermore, this result can be used to construct estimators of the signal-to-noise ratios $\beta_i$ and the alignments between the estimated and true rank-1 signal components.

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hal-04271959 , version 1 (06-11-2023)

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Mohamed El Amine Seddik, Maxime Guillaud, Alexis Decurninge, José Henrique de M Goulart. On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis. IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2023), IEEE, Dec 2023, Los Sueños, Costa Rica. à paraître. ⟨hal-04271959⟩
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