JOURNAL OF CHEMOMETRICS, zyxwvutsr VOL. zyxwvuts 2, 231-246 zyxwvu (1988) NOTES ON THE HISTORY AND NATURE OF PARTIAL LEAST SQUARES (PLS) MODELLING PAUL GELADI Norwegiun Computing Center, P. B. 114 Blindern, zyxwv N-0314 Oslo 3, Norway Research Group for Chemometrics, Umed University, S-90187 Umed, Sweden AND SUMMARY The growing awareness of the need for non-deterministicand distribution-free (soft) models combined with an iterative algorithm for finding latent variables led to the construction of partial least squares models. There have been separate developments in the humanistic and the natural sciences, with stress on different aspects and a different terminology. The historical development is described and some key topics are explained. KEY WORDS Partial least squares models History of PLS Soft versus hard modelling Latent variables Path models INTRODUCTION Partial least squares (PLS) is the name for a class of methods, used for relating blocks of variables measured on sets of objects. Modelling with PLS has a large potential as a method of data analysis in many branches of science. This total potential is still rather unused, but PLS is starting to enj'oy widespread acceptance among scientists. In this process overview is lost. Widely different branches of science are using identical PLS algorithms with differences in nomenclature and totally different algorithms with varying goals are put in the same basket because of the name PLS. The pioneering work of PLS was largely done by Professor Herman Wold who worked at different universities in Sweden. This is described in the section on prehistory, spanning the period from the 1930s to the mid 1960s. The section on history describes the developments from the early 1970s to the early 1980s, when the basis for PLS modelling was elaborated and interest grew among econometricians and sociologists. The section on PLS in chemistry describes the introduction and use of one subset of PLS models, mainly comprising regression modelling from 1980 onwards. The ideas of PLS modelling are closely connected with the evolution of chemometrics as a discipline. Just a small sample from the recent literature, the new journals Journal of Chemometrics and Chemometrics and Intelligent Laboratory Systems, will show that interest in PLS is very much alive.'-' It is hoped that looking back at the historical development of PLS will bring understanding and transparency to some of the confused users of it. A historical overview can never be complete, but at this stage anything pointing in the right direction may be felt as useful. Because of the historical nature of this text, reference is made to key publications and all the 0886-9383/88/04023 1-16$08.00 1988 by John Wiley zyxwvuts & Sons, Ltd. Received 26 October 1987 Revised 11 January 1988