Robust Low-rank Tensor Decomposition with the Criterion

Area of Science:

• Data Science
• Scientific Computing
• Signal Processing

Background:

• Tensor data is increasingly prevalent in science and engineering.
• Existing tensor decomposition methods struggle with outliers.
• Robustness against outliers is crucial for reliable data analysis.

Purpose of the Study:

• To develop a robust Tucker decomposition estimator.
• To address the challenge of outliers in tensor data analysis.
• To improve the performance of tensor decomposition in high-rank scenarios.

Main Methods:

• Introduced the Tucker-L1 estimator based on the L1 criterion.
• Conducted numerical experiments to evaluate performance.
• Validated the method on real-world applications including fMRI, fluorescence data, and image classification.

Main Results:

• Tucker-L1 demonstrates empirically stronger recovery performance than existing alternatives.
• The method shows improved robustness in challenging high-rank scenarios.
• Data-driven rank selection is feasible using cross-validation or hold-out validation.

Conclusions:

• Tucker-L1 offers a robust solution for tensor decomposition in the presence of outliers.
• The method is effective for various scientific applications, including denoising and feature extraction.
• Tucker-L1 provides a valuable tool for analyzing complex, noisy tensor data.