Low Rank Determination Using Least Squares.
Abstract
In this report we discuss a technique for determining the rank of a matrix of a special type. The matrix is assumed to be composed of a matrix which has very low rank relative to its magnitude and a noise matrix component. The objective is to determine the rank of the 'underlying' matrix. The basic approach explored here is to exploit the observation that the rows of a low rank matrix are linear combinations of a small number of those rows. Therefore if we select 'basis' rows carefully, it should be true that the rows of the noisy matrix can be closely approximated by such linear combinations. The approximation is performed easily in a least squares sense and leads to an algorithm which appears to be quite robust and efficient. Its performance is similar in reliability to the use of SVD-based algorithms but with a cost comparable to Gauss elimination or LU factorization.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 05, 1995
- Accession Number
- ADA313644
Entities
People
- Peter R. Turner
Organizations
- Naval Air Warfare Center