Partial cross-validation

L Stable and S. Wold, Partial least square analysis with cross-validation for the two-class problem a Monte Carlo study. J. Chemometrics, 1 (1987) 185-196. 

M. Stone and R.J. Brooks, Continuum regression cross-validated sequentially constructed prediction embracing ordinary least sqaures, partial least squares, and principal component regression. J. Roy. Stat. Soc. B52 (1990) 237-269. 

Figure 18 Regression equation obtained from partial-least-squares data cross-validated in Figure 17.

On the other hand, the prediction by content approach is applicable regardless of the variety of sorting pathways. It may be applied to partial sequences, which are now massively produced day by day. In addition, this approach allows a simple and unified treatment, which is convenient for objective testing (e.g., cross validation). However, there is no guarantee that the amino acid composition of proteins in each localization site is well conserved. Even when a clear tendency is observed for a known set of proteins, it can be an artifact resulting from the deviation of data because the size of known proteins for each site is often insufficient to perform reliable statistical analyses. It is also evident that this approach cannot handle the differences among isoforms with different localization (see Section III,K,3). 

For partial least-squares (PLS) or principal component regression (PCR), the infrared spectra were transferred to a DEC VAX 11/750 computer via the NIC-COM software package from Nicolet. This package also provided utility routines used to put the spectra into files compatible with the PLS and PCR software. The PLS and PCR program with cross-validation was provided by David Haaland of Sandia National Laboratory. A detailed description of the program and the procedures used in it has been given (5). 

Ekins et al. (163) used the rat ortholog 2B6 to generate a pharmacophore model and compared these findings with a partial least squares (PLS) model using MS-WHIM descriptors. The model was constructed using 16 B-lymphoblastoids and yielded a good cross-validated r2 of 0.607. The analysis included molecular surface properties (size) together with positive elec-... 

A more complex method is described by WOLD [1978], who used cross-validation to estimate the number of factors in FA and PCA. WOLD applied the NIPALS (non linear iterative partial least squares) algorithm and also mentioned its usefulness in cases of incomplete data. 

Cramer, R.D., Bunce, J.D., Patterson, D.E. and Frank, I.E., Cross-validation, bootstrapping, and partial least squares compared with multiple regression in conventional QSAR studies, Quant. Struct.-Act. Relat., 7, 18-25, 1988. 

Quantitative structure-activity/pharmacokinetic relationships (QSAR/ QSPKR) for a series of synthesized DHPs and pyridines as Pgp (type I (100) II (101)) inhibitors was generated by 3D molecular modelling using SYBYL and KowWin programs. A multivariate statistical technique, partial least square (PLS) regression, was applied to derive a QSAR model for Pgp inhibition and QSPKR models. Cross-validation using the leave-one-out method was performed to evaluate the predictive performance of models. For Pgp reversal, the model obtained by PLS could account for most of the variation in Pgp inhibition (R2 = 0.76) with fair predictive performance (Q2 = 0.62). Nine structurally related 1,4-DHPs drugs were used for QSPKR analysis. The models could explain the majority of the variation in clearance (R2 = 0.90), and cross-validation confirmed the prediction ability (Q2 = 0.69) [ 129]. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

There is an approach in QSRR in which principal components extracted from analysis of large tables of structural descriptors of analytes are regressed against the retention data in a multiple regression, i.e., principal component regression (PCR). Also, the partial least square (PLS) approach with cross-validation 29 finds application in QSRR. Recommendations for reporting the results of PC A have been published 130). 

Intermediate Least Squares regression (ILS) is an extension of the Partial Least Squares (PLS) algorithm where the optimal variable subset model is calculated as intermediate to PLS and stepwise regression, by two parameters whose values are estimated by cross-validation [Frank, 1987]. The first parameter is the number of optimal latent variables and the second is the number of elements in the weight vector w set to zero. This last parameter (ALIM) controls the number of selected variables by acting on the weight vector of each mth latent variable as the following ... 

Here c is the collision velocity, the asymptotic coefficient is expressed through the atom ionization potential I, and in atoinic units it is etjual to n = / (see also formula (23)). This formula is valid for transfer of an. s—electron or in the case when transitions for states with given quantum numbers may be separated. In particular, the partial cross sections of resonant charge exchange in the chlorine case are given in Table 4. 

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