ANALYSIS OF NONNEGATIVE LEAST SQUARES ALGORITHMS

Abstract

Nonnegative least squares problems (NNLS) which are least squares solutions that are constrained to take nonnegative values often arise in many applications like image processing, data mining, etc. There have been several approaches to solve such a problem like the active set method by Lawson and Hanson, FNNLS by Bro and Jong, the Quasi-Newton minimization method, and Randomized projections methods. In this thesis, we evaluated the performance properties of all these algorithms by implementing them in MATLAB and compared the results. The results obtained showed that Randomized projections seem to work very efficiently, producing results around 3 times faster than Quasi-Newton method with a relative error of 3.25% for randomly generated matrices using MATLAB.