Multidimensional Data Processing With Bayesian Inference via Structural Block Decomposition

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• Efficiently handling large multidimensional datasets is crucial for big-data processing.
• Low-rank tensor decomposition is a promising approach, but current models may not fully capture spatial information.
• Existing rank-1 components often use vector outer products, limiting effectiveness for complex datasets.

Purpose of the Study:

• To develop a novel tensor decomposition model for efficient and effective handling of large multidimensional datasets.
• To extend tensor decomposition beyond vector outer products to better capture spatial correlations.
• To establish a robust principal component analysis (RPCA) framework for tensor completion and data imputation.

Main Methods:

• Developed a new tensor decomposition model by extending the rank-1 component to a matrix outer product (Bhattacharya-Mesner product).
• Incorporated Bayesian inference within the framework for subtle matrix unfolding outer product.
• Applied the model to tensor completion and robust principal component analysis (RPCA) tasks.

Main Results:

• The proposed model effectively decomposes tensors compactly while preserving spatial characteristics.
• Demonstrated high desirability and effectiveness on real-world datasets for hyperspectral image completion/denoising, traffic data imputation, and video background subtraction.
• The matrix outer product approach enhances the capture of correlated spatial information in large-scale, high-order multidimensional data.

Conclusions:

• The novel tensor decomposition model using matrix outer products offers a significant advancement in big-data processing.
• The approach provides a tractable and effective method for analyzing complex multidimensional data.
• The framework is versatile, showing strong performance in various applications including image processing and data imputation.