SketchyCoreSVD: SketchySVD from Random Subsampling of the Data Matrix

Area of Science:

• Data Science
• Numerical Linear Algebra
• Machine Learning

Background:

• Singular Value Decomposition (SVD) is crucial for analyzing large datasets.
• Traditional SVD computation can be computationally expensive for massive matrices.

Purpose of the Study:

• To introduce SketchyCoreSVD, an efficient method for near-optimal rank-r SVD.
• To provide theoretical guarantees for the proposed method.
• To demonstrate the practical performance of SketchyCoreSVD on large-scale data.

Main Methods:

• SketchyCoreSVD constructs random sketches from subsampled rows and columns of the data matrix.
• The method computes the SVD based on these compact sketches.
• Theoretical analysis is provided under matrix incoherence assumptions.

Main Results:

• SketchyCoreSVD achieves near-optimal rank-r SVD computation.
• The method is validated on various large static and time-varying datasets.
• Performance is demonstrated to be effective for large-scale matrix decomposition.

Conclusions:

• SketchyCoreSVD offers an efficient and theoretically sound approach for computing SVD.
• The method is suitable for handling large and dynamic data matrices.
• This technique can significantly reduce the computational burden of SVD in practice.