Mathematical Problems in Engineering
Volume 2 (1996), Issue 1, Pages 63-93

Partial least-squares: Theoretical issues and engineering applications in signal processing

Fredric M. Ham and Ivica Kostanic

Florida Institute of Technology, 150 West University Boulevard, Melbourne 32901-6988, Florida, USA

Received 20 March 1995

Copyright © 1996 Fredric M. Ham and Ivica Kostanic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we present partial least-squares (PLS), which is a statistical modeling method used extensively in analytical chemistry for quantitatively analyzing spectroscopic data. Comparisons are made between classical least-squares (CLS) and PLS to show how PLS can be used in certain engineering signal processing applications. Moreover, it is shown that in certain situations when there exists a linear relationship between the independent and dependent variables, PLS can yield better predictive performance than CLS when it is not desirable to use all of the empirical data to develop a calibration model used for prediction. Specifically, because PLS is a factor analysis method, optimal selection of the number of PLS factors can result in a calibration model whose predictive performance is considerably better than CLS. That is, factor analysis (rank reduction) allows only those features of the data that are associated with information of interest to be retained for development of the calibration model, and the remaining data associated with noise are discarded. It is shown that PLS can yield physical insight into the system from which empirical data has been collected. Also, when there exists a non-linear cause-and-effect relationship between the independent and dependent variables, the PLS calibration model can yield prediction errors that are much less than those for CLS. Three PLS application examples are given and the results are compared to CLS. In one example, a method is presented using PLS for parametric system identification. Using PLS for system identification allows simultaneous estimation of the system dimension and the system parameter vector associated with a minimal realization of the system.