Online Nonconvex Robust Tensor Principal Component Analysis.

Area of Science:

• Multiway data analysis
• Machine learning
• Signal processing

Background:

• Robust tensor principal component analysis (RTPCA) using tensor singular value decomposition (t-SVD) separates low-rank and sparse components from multiway data.
• Online RTPCA (ORTPCA) efficiently processes sequential tensor data for streaming applications.
• Existing ORTPCA methods face accuracy loss due to approximating tensor multirank with the convex tensor nuclear norm (TNN).

Purpose of the Study:

• To propose a novel online nonconvex RTPCA (ONRTPCA) method for enhanced tensor subspace tracking.
• To address the modeling errors in existing ORTPCA methods by employing a tighter approximation of tensor rank.
• To adaptively track varying subspaces in streaming data by incorporating a dynamic forgetting window.

Main Methods:

• Application of the tensor Schatten-norm for a more accurate tensor rank approximation.
• Deduction of a lemma to facilitate online updates of the Schatten-norm components.
• Development of the ONRTPCA algorithm for efficient tensor subspace tracking.
• Integration of a dynamic forgetting window for adaptive subspace tracking.

Main Results:

• The proposed ONRTPCA method demonstrates superior subspace tracking accuracy compared to state-of-the-art methods.
• The method achieves a high convergence speed.
• Low memory requirements are maintained, enhancing computational and storage efficiency.
• Experimental validation on synthetic and real-world video data confirms the effectiveness of the approach.

Conclusions:

• The ONRTPCA method offers a significant improvement in tensor subspace tracking accuracy for streaming data.
• The use of the tensor Schatten-norm and dynamic forgetting window effectively mitigates tracking errors and adapts to changing data patterns.
• The method provides an efficient and accurate solution for analyzing large-scale multiway data streams.