On principal component analysis in L1
Four formulations of principal component analysis in L1 norm were developed by Galpin and Hawkins (Comput. Statist. Data Anal. 5 (1987) 305), QPmax, QPmin, LPmax, and LPmin. Choulakian (Comput. Statist. Data Anal. 37 (2001)135) claimed that of the four formulations, only QPmax produces a non-trivial solution. The objective is to present counter-examples that illustrate that the QPmin and LPmin formulations also give non-trivial solutions that may be unique except for the sign.
principal component analysis l1 norm