Partial least squares models prediction

Nord, L.I., Fransson, D. and Jacobsson, S.P. (1998). Prediction of Liquid Chromatographic Retention Times of Steroids by Three-Dimensional Structiure Descriptors and Partial Least Squares Modeling. Chemom.InteliLab.Syst, 44,257-269. 

Two analytical techniques optical absorbance of Safiranin-O-stained cartilage sections and energy dispersive X-ray analysis have been used by Joshua Bowden, Lew Rintoul, Thor Bostrom, James Pope, and Edeline Wentrup-Byme to construct partial least squares models from Fourier transform infra red spectral data which can then be used to predict the constituents in native, degraded or even engineered cartilage. 

Figure 3, Y predicted plot for a partial least square model obtainedfrom oxidised samples of a material containing Fe(II)-stearate as prooxidant (black) with predicted corresponding degradation states for a material with a commercial prooxidant (grey). (Reproduced with permission from reference 20. Copyright 2005 by Authors.)...

Daszykowski M, Vander Heyden Y, Walczak B. Robust partial least squares model for prediction of green tea antioxidant capacity from chromatograms. J Chromatogr A 2007 1176 12-8. 

Another problem is to determine the optimal number of descriptors for the objects (patterns), such as for the structure of the molecule. A widespread observation is that one has to keep the number of descriptors as low as 20 % of the number of the objects in the dataset. However, this is correct only in case of ordinary Multilinear Regression Analysis. Some more advanced methods, such as Projection of Latent Structures (or. Partial Least Squares, PLS), use so-called latent variables to achieve both modeling and predictions. 

Partial Least Squares Regression, also called Projection to Latent Structures, can be applied to estabfish a predictive model, even if the features are highly correlated. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Partial least squares regression (PLS). Partial least squares regression applies to the simultaneous analysis of two sets of variables on the same objects. It allows for the modeling of inter- and intra-block relationships from an X-block and Y-block of variables in terms of a lower-dimensional table of latent variables [4]. The main purpose of regression is to build a predictive model enabling the prediction of wanted characteristics (y) from measured spectra (X). In matrix notation we have the linear model with regression coefficients b ... 

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

Percent renal clearance was modeled for a set of 130 compounds from the literature using partial least squares applied to 3-D VolSurf or 2-D Molconn-Z descriptors [74]. The model based on VolSurf descriptors gave the best prediction... 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

Luco JM (1999) Prediction of the brain-blood distribution of a large set of drugs from structurally derived descriptors using partial least-squares (PLS) modeling. J Chem Inf Comput Sci 39 396 104. 

Experience in this laboratory has shown that even with careful attention to detail, determination of coal mineralogy by classical least-squares analysis of FTIR data may have several limitations. Factor analysis and related techniques have the potential to remove or lessen some of these limitations. Calibration models based on partial least-squares or principal component regression may allow prediction of useful properties or empirical behavior directly from FTIR spectra of low-temperature ashes. Wider application of these techniques to coal mineralogical studies is recommended. 

This problem is overcome by the Bio View sensor, which offers the possibility to monitor the whole spectral range simultaneously, and by using suitable data analysis and mathematical methods like chemometric regression models 11061. Real-time fluorescence measurement can be used more effectively comparing time-consuming off-line methods. Partial least squares (PLS) calibration models were developed for simultaneous on-line prediction of the cell dry mass concentration (Fig. 5), product concentration (Fig. 6), and metabolite concentrations (e. g., acetic acid, not shown) from 2D spectra. 

The total solid (dry matter) content of potato can be obtained by freeze-drying. Dry matter content is determined from the difference in the weight of potato samples before and after freeze-drying. The potato dry matter can also be estimated from the specific gravity measurements. In recent years, near infrared (NIR) spectroscopy has been used to measure specific gravity of potatoes. The NIR spectra (700-1100 nm) of potato samples are acquired, and partial least squares (PLS) regression analysis can be used to develop a predictive model for specific gravity (Scanlon et al., 1999). 

---