3.) The O2PLS method, the best of both worlds
O2PLS (ref 2,3) is a recent development of the OPLS method (ref 1), that you may have heard of. The idea of OPLS is to separate the systematic variation in X into two parts, an Y-related part, and an Y-orthogonal part. The Y-orthogonal part may be part of the model, but is useless for prediction of Y. As shown in the papers, the main benefit is model interpretation, and pure profile estimation (ref 4), while maintaining the predictive ability of the PLS method. Interpreting the scores and loadings of the Y-orthogonal components in the model will often highlight problems with experimental setup, drift, baseline or presence of non-linearities or may simply indicate a side reaction, unknown constituents in the sample and so on.
O2PLS (ref 2,3), is an extension of OPLS when you are after the relationship between two data blocks X and Y. Hence, you get for each X and Y, a set of components that describe the joint X-Y overlapping variation. These components reap the nice properties of both both canonical correlation and PLS2, without suffering from any of their problems, e.g. the problem of canonical correlation to estimate matrix inverse and to handle noise, and the problem of PLS2 being uni-directional.
In addition, the third model structure, the Y-orthogonal components and the X-orthogonal components, describe the unique (non-correlated) and systematic variation in either data set, that neither PLS2 nor canonical correlation explicitly contains. Along with this follows a number of diagnostics, e.g. how much of the variation in the X-block is overlapping with the Y-block, how much variation is non-overlapping in X (Y-orthogonal variation), and how much is non-overlapping in Y (X-orthogonal variation).
Below, I have posted a number of references, 1-4 are method papers, and 5-7 are applications of O2PLS we have worked on in PAT with the pharma industry, GlaxoSmithKline. There are also other papers as well in the transcriptomic and metabolomics application areas (no references provided here).
best regards,
Johan Trygg,
Chemometrics group/Umeå University
Original OPLS references
1.) Trygg J, Wold S. Orthogonal projections to latent structures, O-PLS. J. Chemometrics, 2002; 16: 119-128. [http://www3.interscience.wiley.com/cgibin/ abstract/89015377/]
2.) Trygg J, O2-PLS for qualitative and quantitative analysis in multivariate calibration. J. Chemometrics, 2002; 16: 283-293 [http://doi.wiley.com/10.1002/cem.724]
3.) Trygg J, Wold S, O2-PLS, a two-block (X-Y) latent variable regression (LVR) method with an integral OSC filter. J. Chemometrics, 2003; 17: 53-64.[ http://doi.wiley.com/10.1002/cem.775]
4.) Prediction and spectral profile estimation in multivariate calibration, J. Chemometrics. 2004; 18:166-172 http://www3.interscience.wiley.com/cgibin/abstract/93518542/]
5.) Gabrielsson J, Jonsson H, Airiau C, Schmidt B, Escott R, Trygg J, OPLS methodology for analysis of pre-processing effects on spectroscopic data, Chemometr. Intell. Lab. Syst., 84 (1-2): 153-158 DEC 1 2006 [http://dx.doi.org/10.1016/j.chemolab.2006.03.013]
6.) Gabrielsson J, Jonsson H, Airiau C, Schmidt B, Escott R, Trygg J. Multi-block strategies for analysis of process analytical and spectroscopical data, Journal of Chemometrics, 2006, Early view http://www3.interscience.wiley.com/cgibin/ abstract/114103585/]
7.) Gabrielsson J, Airiau C, Schmidt B, Jonsson H, Escott R, Trygg J, Combining process and spectroscopic data to improve batch modeling, AIChE Journal, 52 (9): 3164-3172 Sep 2006 [http://dx.doi.org/10.1002/aic.10932]
