A Split-and-Merge Approach for Singular Value Decomposition of Large-Scale Matrices

Area of Science:

• Numerical Analysis
• Computer Science
• Machine Learning

Background:

• Singular Value Decomposition (SVD) is a fundamental matrix factorization technique.
• Existing parallel SVD algorithms face challenges with large-scale datasets.
• Online eigen-analysis requires efficient, sequential processing capabilities.

Purpose of the Study:

• Introduce a new SVD algorithm with an embarrassingly parallel structure.
• Enable efficient implementation on distributed and multicore systems.
• Provide a serial option for online eigen-analysis and feature screening.

Main Methods:

• Developed a novel SVD algorithm employing a split-and-merge strategy.
• Designed for inherent parallelizability, suitable for distributed computing.
• Ensured serial implementation capability for sequential processing needs.

Main Results:

• The proposed algorithm exhibits an embarrassingly parallel structure.
• Demonstrated efficient implementation on distributed and multicore architectures.
• Showcased suitability for big data problems, including feature screening.

Conclusions:

• The new SVD algorithm offers significant advantages for big data analysis.
• Its parallel nature overcomes limitations of existing methods for large datasets.
• The algorithm is versatile, supporting both parallel and serial execution modes.