Cross validation segmented

SIMCA is a supervised pattern recognition technique, which needs to have the data classrhed manually or done using HCA. SIMCA then performs PCA on each class with a sufficient number of factors retained to account for most of the variation within classes. The number of factors retained is very important. If too few are selected, the information in the model set can become distorted. By using a procedure called cross validation, segments of the data are omitted during PCA, and the omitted data are predicted and compared to the actual value. This is repeated for every data element until each point has been excluded once from the determination. The PCA model that yields the minimum prediction error for the omitted data is retained. 

With cross-validation [28], the same objects are used both for model estimation and testing. A few objects are left out from the calibration data set and the model is calibrated on the remaining objects. Then the values for the left-out objects are predicted and the prediction residuals are computed. The process is repeated with another subset of the calibration set, and so on until every object has been left out once then all prediction residuals are combined to compute the validation residual variance and root mean square error in prediction (RMSEP). It is of utmost importance that the user is aware of which level of cross-validation one wants to validate. For example, if one physical sample is measured three times, and the objective is to establish a model across samples, the three replicates must be held out in the same cross-validation segment. If the objective is to validate the repeated measurement, keep out one replicate for all samples and generate three cross-validation segments. The calibration variance is always the same it is the validation... 

Figure 3.13 shows the result of this procedure for groups 3 and 4 from the glass vessels data from Section 1.5.3 (n = 20, m 13, (Janssen et al. 1998)). The cross validation procedure with four segments is repeated 100 times, resulting in 100... 

The underlying assumption is further that this procedure leads to information as to the future performance of the full iV-object model but this is an equally flawed assumption. This procedure has patently no link to any new data set, new measurements , generated after the model has been established and cross-validated. In reality, all that cross-validation delivers is a measure of internal training set stability with respect to sub-setting (sequential exclusion of one object, or one segment). 

K.H. Esbensen and T.T. Lied, Principles of image cross-validation (ICV) representative segmentation of image data structures, in Techniques and Applications of Hyperspectral Image Analysis, H. Grahn and P. Geladi (eds). Chap. 7. (155-180), John Wiley Sons, Ltd, Chichester, 2007. 

The experimental crystallization temperature prediction model was evaluated using 13-segment cross-validation (full cross-validation) this can be considered acceptable for such small sample data sets, albeit only furnishing indicative estimates [2]. 

Figure 9.10 PLS-1 model for the average particle size in chambers 2 and 3. Sensors C and D were used in this model based on four PLS components. The model was validated with segmented cross validation with 10 segments. Predicted versus measured (top) and predicted and measured (bottom).

Acoustic spectra were calibrated using PLS regression with six ammonia concentration levels. The reference concentration levels were 0, 0.5, 1, 2, 5 and 8% ammonia, with five replicate measurements at each level. Figure 9.23 shows the PLS-R prediction results validated with two-segment cross-validation (commonly referred to as a test set switch). 

NB This pilot study included only six concentration levels with a five-component PLS model there is a virtual certainty of over fitting the model. Even a two-segment cross validation is no absolute guarantee [2], but does supply the only possible validation basis with any credibility. However, the results in Figure 9.23 indicate and substantiate satisfactory possibilities for continuing to the type of extended calibration work needed in a full-fledged industrial calibration setting. 

Figure 9.23 Prediction resuits for ammonia, validated with two-segment cross validation (test set switch). Slope = 0.96. RMSEP = 0.48% ammonia.

An independent issne is that all the most important parameter validations are both based on identical 10-segment cross-validations as well as proper test sets. The prediction results for granule moisture content have here been displayed in a time-dependent fashion, which is most relevant for the industrial process operators. 

The full-scale industrial experiment demonstrated the feasibility of a convenient, nonintrusive aconstic chemometric facility for reliable ammonia concentration prediction. The training experimental design spanned the industrial concentration range of interest (0-8%). Two-segment cross-validation (test set switch) showed good accnracy (slope 0.96) combined with a satisfactory RMSEP. It is fully possible to further develop this pilot study calibration basis nntil a fnll industrial model has been achieved. There wonld appear to be several types of analogous chemical analytes in other process technological contexts, which may be similarly approached by acoustic chemometrics. 

Schedule of the leave-one-out cross-validation scheme. Any cross-validation procedure will perform in the same way although considering more samples at each validation segment. 

Figure 10.16. Cross-validation results using PARAFAC models with one to seven components. For each model a cross-validation was performed using 17 segments.

Full details of prediction results for each of 168 reference membrane proteins are enclosed in the Supplementary Material (Table IV). We used cross-validation (5-fold, Methods) and the KYTDO scale ( 1). All of 168 proteins were correctly predicted as membrane proteins having at least one transmembrane segment. With 100% correct transmembrane topology 130 proteins were predicted. A total of 631 transmembrane helices were correctly predicted out of a total number of 662 expected transmembrane segments. Only 36 TMH were overpredicted and 31 underpredicted. Of individual residues in TMH configuration 12273 out of 14374 were correctly predicted, 2033 overpredicted and 2101 underpredicted. The performance parameters (Methods) are then Aj = 0.712, = 95.3%,... 

Another example of applying chemometrics to separations data is depicted in Figures 8 and 9. Here, interval PLS (iPLS) was applied to blends of oils in order to quantify the relative concentration of olive oil in the samples (de la Mata-Espinosa et al., 2011b). iPLS divides the data into a number of intervals and then calculates a PLS model for each interval. In this example, the two peak segments which presented the lower root mean square error of cross validation (RMSECV) were used for building the final PLS model. 

The original spectra were subjected to MSC before MWPLSR, SCMWPLS, and multivariate analysis were applied. All 48 skin spectra were employed to build PLS calibration models. The model performance was validated by use of the four segments cross-validation method (12 spectra per segment) and the RMSEV was calculated. 

Systematic segmented cross-validation leaves out a whole group of objects at a time. A typical example is when there are replicated measurements of one physical sample. Depending on the objective one may either take out all replicates for each physical sample or replicate n for all objects. 

Clear liquid velocity (ft/sec) through the downcomer is then found by multiplying DL by 0.00223. The correlation is not valid if Pl - pv is less than 301b/ft (very high pressure systems). For foaming systems, DL should be multiplied by 0.7. Frank recommends segmental downcomers of at least 5% of total column cross-sectional area, regardless of the area obtained by this correlation. 

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