PLS technique

There are of course also difficulties when using the PLS technique ... 

The PLS technique gives a stepwise solution for the regression model, which converges to the least squares solution. The final model is the sum of a series of submodels. It can handle multiple response variables, highly correlated predictor variables grouped into several blocks and underdetermined systems, where the number of samples is less than the number of predictor variables. Our model (not including the error terms) is ... 

This same data set was analyzed using the DCLS method with unsuccessful results (see Section 5.2.1.2). Analyzing the data with PLS reveals wh the classical approach failed. The number of factors required for the PLS models ranges from four to six when the system only contains three independent sources of variability (four components whose concentrations add to unity). This indicates that the system does not obey the assumptions of the DCLS model (e.g., linear additivity). The PLS technique has been able to model this even though the source and form of the violation is not known. 

In an earlier review of the applications of photoluminescence (PL) techniques to the characterization of adsorption, catalysis, and photocatalysis (Anpo and Che, 1999), we addressed the basic principles of PL and the importance of PL measurements for understanding of (photo)catalytic processes. This chapter describes more recent developments and focuses on investigations of catalysts in the working state, with an emphasis on the role of local structure on photocatalytic reactions determined with PL and related techniques. 

Details on the instruments available for collecting PL spectra are reported in refs. [11, 78]. One of the main points to be stressed is that, because of the high sensitivity of the PL technique, the sample cell has to be made from high-quality fused silica with no impurities, such as Suprasil. 

From these early studies, the PL technique, which was initially aimed at confirming the observahon of surface sites, was gradually extended to explore other related aspects, such as surface structure, decay of the excited states and surface reactivity. 

Polarized Light Screen (PLS). The PLS technique (23,24) was used extensively to obtain Immediate information about the macroscopic phase behavior of solutions. Diffuse light is transmitted through a polarizer and an analyzer. The sample is placed between the two polarizers, and system behavior is observed as shown in Figure 1. 

The PLS technique makes isotropy, birefringence, and scattering easy to identify, and shows interfacial phenomena (such as critically diffuse regions) at a constant temperature. 

Since PLS technique is sensitive to outliers and scaling, outliers should be removed and data should be scaled prior to modeling. After data pretreatment, the number of latent variables (PLS dimensions) to be retained in the model is determined. Cumulative prediction sum of squares (CUM-PRESS) versus the number of latent variables or prediction sum of squares (PRESS) versus the number of latent variables plots are used for this purpose. It is usually enough to consider the first few PLS dimensions for monitoring activities, while more PLS dimensions are needed for prediction in order to improve the accuracy of predictions. 

We have studied the synthesis of InAs nano-sized crystalline precipitates in crystalline silicon by means of the co-implantation of As+ (245 keV, 5xl016 cm2) and In+ (350 keV, 4.5xl016 cm 2) at 500 °C and annealing at 900 °C for 45 min. RBS, TEM/TED and PL techniques were used to characterize the implanted layers. The density of the precipitates equals to 1.2xlOn cm 2. The most of the crystallites are from 2 nm to 8 nm in size. The precipitates are located within at the depths of 100 to 350 nm. A broad line at 1.3 pm is found in low-temperature PL spectra of co-implanted and annealed silicon crystals This line can be attributed to donor-acceptor pair recombination between In and As atoms which occupy the substitutional sites in the silicon lattice. 

Hasegawa K, Funatsu K. Advanced PLS techniques in chemometrics and their applications to molecular design. In Lodhi H, Yamanishi Y, editors. Chemoinformatics and Advanced Machine Learning Perspectives Complex Computational Methods and Collaborative Techniques. Hershey IGI Publishing 2011. p 145-168. 

What are the problems with the PLS technique One problem, like the question of deciding dimensionality, is shared with MLR and PCR. Why fit a linear model The imposition of simple linear relationships on nature might be thought of as expecting too much . Fortunately, simple or at least fairly simple linear relationships often do hold and linear models do quite a... 

Different decompositions of X can now be selected by different choices of wa). The methods for direct decomposition for PCA and PLS techniques are outlined below. 

Frequently, laser-induced breakdown spectrometry (LIBS) requires multivariate regression to solve complex problems. The first paper that was found dates back to 2000 and was related to jewellery studies. Amador-Hernandez et al. showed that PLS models were highly satisfactory for measuring Au and Ag in Au-Ag-Cu alloys. This study was further completed by Jurado-Lopez and Luque de Castro, who compared the hybridized LIBS-PLS technique with analytical scanning microscopy, ICP-OES, FAAS and LIBS. Although the... 

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