Online subspace learning and imputation by Tensor-Ring decomposition.

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Partially observed high-order streaming data presents a significant challenge in data analysis.
• Existing online low-rank tensor completion methods often rely on traditional decomposition techniques like CP and Tucker.
• Tensor Ring decomposition offers advantages in expressing high-order data and estimating missing values.

Purpose of the Study:

• To propose novel online subspace learning and imputation methods for high-order streaming data.
• To leverage the strengths of Tensor Ring decomposition for improved data completion.
• To address limitations of traditional tensor decomposition methods in online settings.

Main Methods:

• Development of an online Tensor Ring subspace learning and imputation model.
• Formulation using exponentially weighted least squares with Frobenius norm regularization of TR-cores.
• Implementation of alternating recursive least squares and stochastic-gradient algorithms for optimization.

Main Results:

• The proposed methods effectively exploit time-varying subspaces in streaming data.
• Demonstrated superior performance compared to conventional Tensor Ring completion methods.
• Outperformed state-of-the-art online methods in streaming data completion across various missing ratios and noise levels.

Conclusions:

• The novel Tensor Ring-based methods provide an effective solution for online low-rank tensor completion.
• These methods offer significant improvements in handling missing data and noise in high-order streaming datasets.
• The approach is promising for applications requiring real-time analysis of complex, incomplete data streams.