A FAST NON-NEGATIVITY-CONSTRAINED LEAST-SQUARES ALGORITHM

In this paper a modification of the standard algorithm for non-negativ ity-constrained linear least squares regression is proposed. The algor ithm is specifically designed for use in multiway decomposition method s such as PARAFAC and N-mode principal component analysis. In those me thods the typical situation is that there is a high ratio between the numbers of objects and variables in the regression problems solved. Fu rthermore, very similar regression problems are solved many times duri ng the iterative procedures used. The algorithm proposed is based on t he defacto standard algorithm NNLS by Lawson and Hanson, but modified to take advantage of the special characteristics of iterative algorith ms involving repeated use of non-negativity constraints. The principle behind the NNLS algorithm is described in detail and a comparison is made between this standard algorithm and the new algorithm called FNNL S (fast NNLS). (C) 1997 John Wiley & Sons, Ltd.