Robust Tensor Tracking with Missing Data and Outliers: Novel Adaptive CP Decomposition and Convergence Analysis

Canonical Polyadic (CP) decomposition is a powerful multilinear algebra tool for analyzing multiway (a.k.a. tensor) data and has been used for various signal processing and machine learning applications. When the underlying tensor is derived from data streams, adaptive CP decomposition is required....

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Vydáno v:IEEE transactions on signal processing Ročník 70; s. 1 - 16
Hlavní autoři: Thanh, Le Trung, Abed-Meraim, Karim, Trung, Nguyen Linh, Hafiane, Adel
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Témata:
Adaptation models
adaptive algorithm
Adaptive algorithms
CANDECOMP/PARAFAC (CP) decomposition
Convergence
Data analysis
Data models
Data transmission
Decomposition
Engineering Sciences
Linear programming
Loading
Machine learning
Mathematical analysis
Missing data
outlier
Outliers (statistics)
Robustness
Signal and Image processing
Signal processing
Signal processing algorithms
streaming tensor
Tensors
Tracking
ISSN:1053-587X, 1941-0476
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Shrnutí:Canonical Polyadic (CP) decomposition is a powerful multilinear algebra tool for analyzing multiway (a.k.a. tensor) data and has been used for various signal processing and machine learning applications. When the underlying tensor is derived from data streams, adaptive CP decomposition is required. In this paper, we propose a novel method called robust adaptive CP decomposition (RACP) for dealing with high-order incomplete streaming tensors that are corrupted by outliers. At each time instant, RACP first performs online outlier rejection to accurately detect and remove sparse outliers, and then performs tensor factor tracking to efficiently update the tensor basis. A unified convergence analysis of RACP is also established in that the sequence of generated solutions converges asymptotically to a stationary point of the objective function. Extensive experiments were conducted on both synthetic and real data to demonstrate the effectiveness of RACP in comparison with state-of-the-art adaptive CP algorithms.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3201640