COMMENTS ON THE NIPALS ALGORITHM

The Non-linear lterative Partial Least Squares(NIPALS)algorithm is used in principal componentanalysis to decompose a data matrix into score vectors and eigenvectors(loading vectors)plus a residualmatrix.N1PALS starts with some guessed starting vector.The principal components obtained by NIPALSdepends on the starting vector;the first principal component could not always be computed.Wold hassuggested a starting vector for NIPALS,but we have found that even if this starting vector is used,thefirst principal component cannot be obtained in all cases.The reason why such a situation occurs isexplained by the power method.A simple modification of the original NIPALS procedure to avoid gettingsmaller eigenvalues is presented.     

SHORT COMMUNICATION COMMENTS ON THE POWER METHOD

In a recent short communication,Miyashita et al.have commented on the weakness of the NIPALSalgorithm(equivalently the power method)for calculating the eigenvalues out of order.They offer adiagnostic to ascertain when this may have occurred and suggested a modification to the NIPALSalgorithm to avoid this situation.Further comments regarding the use of the power method andMiyashita's presentation of its weakness are warranted.The general inadequacies of methods fordecomposing a matrix with degenerate eigenvalues and their relationship to the orthogonal design ofexperiments are discussed.