Intersite transfer of industrial calibration models
Frédéric Despagnea, D. Luc Massarta,∗, Martin Jansenb, Hans van Daalenba ChemoAC, Pharmaceutical Institute, Vrije Universiteit Brussel, Laarbeeklaan 103, B-1090 Brussels, Belgium
b Akzo Nobel Research, Arnhem, The Netherlands
Received 5 March 1999; received in revised form 15 June 1999; accepted 6 September 1999
The information contained in the near-infrared(NIR) spectrum of a solid or liquid sample com-bined with a multivariate calibration model permitsquantitative determination of the concentration of atarget analyte or of a physical property associatedwith this sample. An increasing number of success-ful implementations of NIR calibration models havebeen reported in e.g. the pharmaceutical, chemical,food or petroleum industries. A calibration model isobtained by determining the mathematical parametersthat relate a set (matrix) of calibration sample spectraXXX to a vectoryyy containing the property of interest as-sociated with each sample. The main effort in modeldevelopment consists of experimentally determiningthe responses of the set of calibration samples, and
optimising the parameters of the calibration modelyyy = f(XXX). The attractiveness of NIR lies in the rapidityand simplicity with which spectra can be acquired:NIR is a non-destructive analysis technique, and somematerials like glass or translucid plastic (often usefor packing) are transparent to NIR radiations, there-fore measurements can be made without any samplepreparation. Thanks to the use of fibre optic probes,a spectrumX can be measured on-line within a fewseconds. After acquisition, the multivariate calibra-tion model is used to return the estimated responsey
associated withX:
y = f (X) (1)
Problems occur when changes affect the instru-mental response function, so that replicate spectra ofa stable standard are no more exactly superimpos-able. These changes can be due to instrument ageing,replacement of one or several parts of the spectrom-eter (e.g. the detector), use of a new instrument, ormodifications in the measurement conditions, like dis-
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placement of the instrument to a different location. Inall cases the calibration model developed on the refer-ence instrument is no more applicable since additionalun-modelled sources of variations, not related to thesamples of interest have appeared. A solution consistsof performing a re-calibration, that is re-measuringthe set of calibration samples in the new conditionsand calculating the parameters of a new calibrationmodel. In some cases, this approach is very imprac-tical, because the calibration samples measured onthe reference instrument are often production samplesthat are no more available, or that degrade over longtime periods as is the case in the present study.
An alternative approach consists of performing astandardisation that allows to predict the responsesof new samples without performing re-calibration.The term ‘standardisation’ encompasses several ap-proaches: calibration transfer, enhancement of thecalibration robustness, model updating or responseupgrading. These strategies have been discussed indetail by Naes and Isaksson [1–2] and by de Noord[3]. The strategy presented in this paper refers tocalibration transfer, which is the most popular formof standardisation. In calibration transfer, a mathe-matical modelg( ) relates the spectrumX of a samplemeasured on a reference instrument (the master) tothe spectrumX′of the same sample measured on adifferent instrument (the slave):
X = g(X′) (2)
After transfer, the original calibration modelf( ) canbe used to predict indirectly the responses of new sam-ples recorded on the slave:
y = f (g(X′)) (3)
Several methods have been proposed to performtransfer of NIR calibration spectra: the Shenk andWesterhaus patented algorithm [4], the two-blockPLS algorithm [5], Direct Standardisation and Piece-wise Direct Standardisation (PDS) [6], Fourier [7]and wavelet transform-based [8] standardisation tech-niques, a neural network-based approach (NN) [9]and a method using a Finite Impulse Response filter[10]. Refinements of the Shenk–Westerhaus patentedalgorithm [11], two-block PLS [12] and PDS [13]have also been presented.
The goal of the present paper is to illustrate withreal industrial data some issues associated with the
transfer of calibration spectra between two sites, Aand B. Usually, a calibration model exists on one site,and one would like to use this calibration model topredict, after transfer, the responses of new samplesmeasured on a different site. The situation presentedhere is slightly different in the sense that a calibra-tion model already exists on Site A, but it is requiredto develop a new calibration model on Site B. How-ever, the calibration samples used to develop the orig-inal calibration model in A degrade rapidly and areno more available to be measured in B. This meansthat a standardisation model must first be developedto transfer the calibration spectra from A to B, beforea new calibration model can be developed using thetransferred calibration spectra. This calibration modelwill be used to predict directly the responses of futuresamples measured in B. The PDS algorithm and theNN method were recently shown to efficiently correctvarious types of real and simulated instrumental dif-ferences [9]. They were both applied and comparedfor the transfer of these real industrial data.
2. Theory
2.1. Piecewise direct standardisation
In PDS, a series of local multivariate transfer mod-els are built between spectral windows on the slaveand the central point in each corresponding spectralwindow on the master. Partial Least Squares (PLS) orPrincipal Component Regression (PCR) can be used inthe modelling step. Once the banded diagonal transfermatrix between the two instruments has been calcu-lated, the calibration model developed on the mastercan be used to predict a target property for any spec-trum measured on the slave. Additional details on thePDS algorithm can be found elsewhere [3,6,13].
Contrary to a univariate approach like theShenk–Westerhaus patented algorithm, PDS can cor-rect complex interactions between wavelength shiftsand intensity changes. The main difficulties in PDSare the determination of window size and local rank ofeach individual multivariate model. As the size of thespectral window increases, the number of standardis-ation samples needed will be higher. If the local rankof the models is not correctly determined, artefactscan occur in the transferred spectra [13]. Gemperline
F. Despagne et al. / Analytica Chimica Acta 406 (2000) 233–245 235
et al. [14] showed that discontinuities can appear inreconstructed spectra due to ‘swapping’ of eigenval-ues between adjacent spectral windows. The PDSmodel can account for multiplicative effects but doesnot correct for significant additive differences betweeninstruments. Wang et al. [15] showed that a specificadditive background correction had to be performed todeal efficiently with situations where the backgroundshave different structures on the two instruments.Despite these drawbacks, PDS is often considered tobe a reference method for standardisation.
2.2. Transfer using neural networks
This recently proposed standardisation technique[9] is based on the use of a backpropagation NN withone hidden layer to model the transfer function be-tween two instruments. The method shares commonfeatures with PDS, in the sense that a spectral win-dow with an odd number of points on the slave isused as input to predict the absorbance in the cen-tral point of the corresponding spectral window onthe master. Both NN and PDS are able to model non-linear transfer functions. However, contrary to PDSthat decomposes the transfer function in a series oflocal linear models, a single NN transfer model is de-veloped between all spectral windows on the slaveand all points on the master. To account for wave-length dependent-perturbations, an additional index isadded to each spectral window on the slave in order touniquely identify the position of the window along thewavelength axis. All input vectors (each composed ofa spectral window to which the corresponding positionindex has been added) from the standardisation sam-ples are stacked in a matrix to create a unique trainingset. A subset of the standardisation samples must beset aside to create a monitoring set used to regularlyvalidate the transfer model during training and avoidoverfitting.
3. Materials
3.1. Samples
Powder samples are analysed for assay in Site Awith NIR diffuse reflectance spectroscopy. Similar
powders are produced at Site B which is geograph-ically separated from Site A, so it was decided totransfer the calibration model from Site A to Site B.Two options are possible for transfer of the calibrationmodel.• The spectra of future samples measured in Site B are
standardised so that they match the samples mea-sured in Site A and the calibration model developedin Site A can be applied to predict responses ofthese samples.
• The calibration spectra measured in Site A andused for model construction are standardised as ifthey were measured in Site B, and these standard-ised spectra are used to develop a new calibrationmodel.The former approach is the most currently applied,
since usually one wants to avoid re-calculating cal-ibration model parameters. It has the advantage thatthe transfer parameters can be adjusted so as to opti-mise the prediction error of transferred samples, usingthe existing calibration model. In the latter approach,transfer can only be optimised with respect to recon-struction error, but it has the advantage that all futuresamples measured in Site B will not have to be stan-dardised. This approach was retained by the manufac-turer and we describe in this paper the procedure totransfer calibration spectra from Site A to Site B anddevelop a new model with the transferred calibrationsamples.
The calibration set to be transferred consists of 79samples measured in Site A. However, these samplescould not be transported to Site B for developing orvalidating the transfer model because they had alreadydegraded. To perform transfer, a set of 12 samples ofthe same chemical class was measured in both Sites Aand B. Measurements were performed within 2 days toreduce the risks of degradation. For all calibration andstandardisation samples, the assayy was determinedwith a reference method.
3.2. Instruments
Both the instruments were Bomem MB 160 FT-NIRspectrometers equipped with a diffuse reflectance ac-cessory developed by Intersurface (reference material:Spectralon). However, the instruments have differentsettings. The characteristics of spectra recorded on thespectrometer at Site B, the ‘master’ instrument, are:
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• Four step values: 3.8, 3.8573, 3.8574 and 3.9 cm−1.• 1495 points per spectrum.
The characteristics of spectra recorded on the spec-trometer at Site A, the ‘slave’ instrument, are:• Wavenumber range: 4011.6–9998.2 cm−1, non-
constant step.• Two step values: 3.8573 and 3.8574 cm−1.• 1553 points per spectrum.
In order to match the master wavenumber axis thatis shorter, spectra of the slave have been truncated.The spectral region from 4111.9 to 9874.8 cm−1 wasretained, so that all spectra eventually had 1495 pointsand standardisation with PDS could be performed.The step on the wavenumber axis is neither constantnor similar on both instruments, therefore some smallshifts exist between the wavenumber axes of thetwo instruments. However, the shifts do not exceed0.09 cm−1 and can be considered to be negligible.
3.3. Software
All algorithms used for standardisation and calibra-tion are part of the MatlabTM Chemometrics Tool-boxes developed at the Pharmaceutical Institute of theVrije Universiteit Brussel for the European consortiumChemoAC. Calculations were performed on a PentiumII 233 MHz computer using Windows 95 operatingsystem.
4. Experimental
4.1. Preliminary data analysis
The study was performed on truncated spectra toeliminate spectral information not related to the assayof the powders. Only the two spectral regions illus-trated in Fig. 1 were retained since these are the re-gions that were used by the manufacturer to developthe industrial calibration models in Site A before trans-fer was decided. (In the rest of the study we will onlyconsider these two spectral regions unless otherwisespecified).
We performed a Principal Component Analy-sis (PCA) to visualise the respective positions of
Fig. 1. Average calibration spectrum measured on the slave withthe two spectral regions retained for calibration and the referenceregion used for MSC.
calibration and standardisation samples in principalcomponent space. It is recommended that the stan-dardisation samples should cover as homogeneouslyas possible, the domain where future samples to betransferred will lie [13]. In the present case, we seeon a score plot (Fig. 2) that the standardisation andcalibration samples measured on the slave do notcover exactly the same domain.
This difference is essentially due to the fact thatstandardisation samples originate from a differentbatch than the calibration samples. Since the transferparameters can only be optimised with respect to thestandardisation samples, we can expect a degradationof results when we transfer calibration samples.
Fig. 2. Standardisation and calibration samples measured on theslave projected in the PC1–PC2 plane.
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4.2. Preprocessing
De Noord emphasised the importance of prepro-cessing for removing irrelevant sources of variationsfrom NIR spectra [16]. In some cases, appropriatepreprocessing performed on spectra measured on theslave and master, respectively, can eliminate the needfor development of a transfer model between the twoinstruments. If not, the spectral differences betweenthe two instruments can often be significantly reduced[17]. Swierenga et al. have showed that variable selec-tion as data preprocessing during model developmentcould enhance the robustness of a model with respectto transfer to another instrument [18].
Before transferring the spectra, we developed somecalibration models with the 79 samples measured onthe slave, in order to study the influence of differ-ent preprocessing methods. The models were devel-oped with PLS using leave-one-out cross-validation.Calibrations were performed on raw spectra, spectrapretreated with multiplicative signal correction (MSC)and spectra pretreated with standard normal variatetransformation (SNV). MSC and SNV are two pre-processing techniques designed to remove multiplica-tive effects due to scattering or particle size that areoften observed on NIR spectra of powders [16,19].MSC was performed using as reference the relativelyflat spectral region between 7965.4 and 8351.1 cm−1
represented in Fig. 1.The cross-validation results expressed in terms of
root mean square error of cross-validation (RMSECV)are reported in Table 1 for the different forms of pre-processing.
RMSECV=(∑
(y − y)2
nc
)0.5
(4)
nc is the number of calibration simples.
Table 1Cross-validation and prediction results for PLS models developedon the slave instrument (Site A) with different preprocessings
Raw MSC-corrected SNV-correctedspectra spectra spectra
Optimum model complexities were determined byapplying the randomisation test to cross-validationresiduals, in order to avoid overfitting. This test con-sists in testing the significance of the difference inthe distributions of residuals from two different mod-els. It allows to select a model with a number oflatent variables that is usually inferior to the numberof latent variables associated with the minimum ofthe cross-validation error curve, yet with a similarpredictive power [20].
We evaluated the generalisation ability of the mod-els by predicting the assay of the 12 standardisationsamples, using the spectra measured on the slave. Thecorresponding root mean square error of predictionvalues (RMSEP) are also reported in Table 1.
RMSEP=(∑
(y − y)2
nt
)0.5
(5)
nt is the number of test samples.We observe that both pre-processing techniques re-
duced the model complexities and the cross-validationerrors obtained were similar. Prediction results onstandardisation samples were also improved by SNVor MSC.
Apparently, the model after MSC correction is themost attractive since it is the most parsimonious (threelatent variables only). However, one must be awarethat any form of spectral preprocessing can introducedistortions in theX-space that can affect the represen-tativity between calibration and standardisation sam-ples. For instance, it can be seen by comparing Figs. 2and 3 that MSC preprocessing modifies the repartitionof standardisation and calibration samples.
We used the tools developed by Jouan-Rimbaud etal. [21] to compare numerically the representativitybetween standardisation and calibration data in bothcases. These tools are indices that vary between 0and 1 and define the similarity between the directionsof the standardisation and calibration sets (P∗), theirvariance–covariance matrices (C∗), and their centroids(R∗). For each index, a value of 1 indicates perfect sim-ilarity. These indices were also calculated for the rawspectra before truncation for comparison. The valuesof the similarity indices calculated in the PC1–PC2plane are reported in Table 2.
TheR∗ values in Table 2 indicate that the centroidsof standardisation and calibration sets are close to each
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Fig. 3. Standardisation and calibration samples measured on theslave projected in the PC1–PC2 plane after MSC preprocessing.
other after SNV, whereas on raw spectra or after MSCthey are completely separated. However, the directionsand variance–covariance matrices of the two subsetsare more similar on raw spectra and after MSC thanafter SNV. In fact, the representativity coefficients onraw spectra and on MSC-corrected spectra are simi-lar, whereas significant changes occur after SNV. Thedifference between MSC and SNV is that in SNV,one performs a global correction on each spectrum,whereas with MSC one selects a specific spectral re-gion to perform the correction for offset and mul-tiplicative effects. In the present situation, the mainsource of variance is due to the intrinsic difference be-tween standardisation and calibration samples whichare of the same chemical class but were produced indifferent batches (different feeds, different raw prod-uct suppliers, different conditions of pressure, tem-perature and humidity). This difference is artificiallyblurred by SNV that gives same variance to all spec-tra, whereas MSC only corrects physical and instru-mental differences between spectra which is what we
Table 2Similarity indices to compare representativity of standardisationand calibration spectra measured on the slave (Site A), with dif-ferent preprocessing
Raw MSC-corrected SNV-correctedspectra spectra spectra
really want. That is the reason why MSC preservedthe chemical structure of the data sets and led to lowerRMSEP values than SNV, with more parsimoniousmodels. Therefore, it was decided to perform stan-dardisation on MSC-corrected spectra. An alternativeapproach would consist of using MSC only to transferthe spectra by correcting spectra on both instrumentswith respect to the average spectrum measured on oneinstrument only, so that all spectra are shifted and ro-tated with respect to the same spectrum. We testedthis approach but it does not perform well due to thefact that the instrumental differences are not exactlythe same in Regions 1 and 2 and MSC parameters aredetermined in Region 1 only.
4.3. Spectral differences before transfer
Fig. 4 shows the prediction results obtainedwhen the calibration model developed on theslave on MSC-corrected spectra is used to predictwithout standardisation the assay of the 12 stan-dardisation samples recorded on the master andMSC-corrected.
A significant bias appears on the correlation plot.The corresponding RMSEP value is 0.69% m/m, to becompared to the value of 0.20% m/m obtained on thesame samples measured on the slave (see Table 1).Standardisation is clearly necessary.
To identify the nature of the spectral differencesbetween the two instruments, a useful and simple
Fig. 4. Predicted vs. experimental values for the standardisationsamples measured on the master, using a calibration model devel-oped on the slave, without standardisation.
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Fig. 5. Average standardisation spectrum measured on slave vs.the average standardisation spectrum measured on master.
approach consists of plotting the spectrum of a stan-dardisation sample measured on the master versusthe spectrum of the same sample measured on theslave. Such plots allow detection of wavelength shifts,offsets or nonlinear effects [9]. This detection plotfor the average standardisation spectrum on masterversus the same spectrum on slave is reported inFig. 5, to have a first estimation of the type of sys-tematic differences between both instruments.
In the absence of any differences between the twoinstruments, the absorbance values would be perfectlylined up along the intercept line. One can see thatthe main difference between both the instruments isa baseline offset combined with a slope difference.This effect may be due to the use of detectors withdifferent sensitivity. Strong nonlinear effects suchas stray light, scattering or detector saturation thatwould cause a curvature are not observed. There is nohysteresis characteristic of the occurrence of strongwavelength shifts [9].
The same procedure was repeated on each individ-ual standardisation sample. In Fig. 6 we displayed thesame kind of plot for three standardisation samples,in spectral region 1.
It can be seen that spectral differences do not havethe same pattern for all samples. The large variationsin the slopes reveal that the differences are not onlysystematic instrumental differences, but also due toadditional independent perturbations on each stan-dardisation sample. No standardisation algorithm cancorrect such differences, a separate transfer model
Fig. 6. Spectrum measured on slave vs. the spectrum of the samesample measured on master for three of the standardisation sam-ples, in spectral Region 1.
would be required for each spectrum. The onlysolution to improve the quality of transfer is to identifyand remove the standardisation samples for which theinstrumental differences deviate markedly from thetrend observed for the rest of the standardisation sam-ples. This does not mean that these samples are out-liers, but the number of standardisation samples is toolow to model simultaneously different types of spec-tral differences. By observing the difference spectra(spectrum on master-spectrum on slave) in Region 1(Fig. 7), two standardisation samples (Samples 2 and3) were identified for which instrumental differencescould be considered as significantly different fromthe rest of the samples.
Fig. 7. Spectral differences between master and slave for threestandardisation samples in Region 1.
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After testing the positive influence of their re-moval, it was decided not to use these samples for thedevelopment of the transfer models.
4.4. Standardisation
After removal of Samples 2 and 3 from the stan-dardisation set, 10 samples were available to calculatea standardisation model. Two of these samples wereset aside and used as test samples to evaluate qualityof transfer. The eight remaining samples are used tocalculate the MSC-correction parameters for all sam-ples, as well as the standardisation parameters.
The idea behind PDS is to correct instrumental dif-ferences between a slave and a master by regressingspectral windows from the slave on the master, usingsoft models (PCR or PLS). PCR was used in theregression step.
In a study with simulated perturbations, it wasshown that NN can be used to standardise NIR spec-tra and correct multiplicative differences like the onesseen in Fig. 6. The parameters to optimise with thismethod are the spectral window size, the number ofhidden nodes in the NN and the number of iterationsfor training.
To avoid artefacts due to overfitting and incorrectrank estimation in local PCR models, Bouveresse etal. [13] suggested to set aside one or several validationsamples that are used only to test the transfer modeland possibly correct local ranks. Similarly, it is impor-tant to use validation samples to optimise the numberof training iterations in the NN approach and avoidovertraining. Therefore, two of the eight samples leftfor calculation of MSC and transfer parameters wereused as validation samples, the other samples con-stituted the training set. The training, validation andtest samples are represented in Fig. 8 in the PC1–PC2space.
With both methods, optimisation of model param-eters was performed so as to minimise the sum ofsquared reconstruction residuals for the two validationspectra SSval.
SSval =∑ ∑
(XXXMval − g(XXXS
val))2 (6)
XXXMval designates the matrix of validation spectra mea-
sured on the master,XXXSval is the matrix of valida-
tion spectra measured on the slave andg( ) refers to
Fig. 8. Projection of the training, validation and test samplesmeasured on the slave in the PC1–PC2 space.
the standardisation model.The training error SStrain(determined on the six samples used for training) andtest error SStest were also evaluated.
SStrain =∑ ∑
(XXXMtrain − g(XXXS
train))2 (7)
SStest =∑ ∑
(XXXMtest− g(XXXS
test))2 (8)
Transfer results are reported in Section 5.1.
4.5. Calibration
After determination of transfer parameters with thedifferent methods, the 79 calibration samples mea-sured on the slave were first MSC-corrected withrespect to the mean of the eight standardisation sam-ples measured on the slave that were used to calculatethe standardisation parameters. Then the calibrationspectra were transferred with the different methods,and PLS calibration models were developed on thetransferred calibration spectra, using leave-one-outcross-validation combined with sign randomisationtest for determination of model complexity. Themodels were used to predict the assay of the 12standardisation samples measured on the master andMSC-corrected with respect to the mean of the eightstandardisation samples measured on the master thatwere retained in the NN training set. It must bepointed out that, contrary to the situation described inSection 4.2, it cannot be said that the generalisationability of the models built on transferred spectra is
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Table 3Model parameters for PDS and NN transfer model. Training,validation and test errors expressed in terms of sums of squaredreconstruction residuals
tested by calculating prediction error for the standard-isation samples. Generalisation ability can only betested on truly independent samples, which is not thecase here since 8 out of the 12 standardisation sam-ples were used for determination of transfer param-eters. However, they are the only samples measuredon the master available to test the calibration models.Calibration results are reported in Section 5.2.
5. Results and discussion
5.1. Transfer results
To select the optimal set of parameters with PDS orNN (window size, number of PCs or hidden nodes),we retained the solution that minimised the validationerror SSval. Model parameters, training error, valida-tion error and test error for both methods are reportedin Table 3.
Even though SStrain is significantly smaller for PDSthan for NN, the differences between training spectrareconstructed with the two methods are hardly de-tectable, as can be seen in Fig. 9 where the two spectra
Fig. 9. An example of training spectrum reconstructed with PDSand NN.
Fig. 10. Close-up in the reference region for a training spectrummeasured on master (Site B) and slave (Site A), and reconstructedwith PDS and NN.
of the same training sample reconstructed with bothmethods seem to be almost perfectly overlapped.
It can be observed that both methods handle per-fectly the intensity jump between Regions 1 and 2 dueto the local nature of the reconstruction (piecewise re-construction with PDS, use of a position index withNN).
The main differences between the two methods canbetter be seen if one looks more closely at the referenceregion illustrated in Fig. 9. Fig. 10 shows a trainingsample measured on master, slave and reconstructedwith PDS and NN in this reference region. A spectralshift was added for visualisation purposes.
The master instrument has a significantly lowersignal-to-noise (S/N) ratio than the slave instrument.The NN-reconstructed spectrum retains the noisestructure of the slave whereas the PDS-reconstructedspectrum retains the noise structure of the master. Toconfirm this observation, an ‘inverse transfer’ wasperformed, using the Site B instrument as slave andthe Site A instrument as master. Reconstruction re-sults for the same spectrum in the reference regionare displayed in Fig. 11.
To better understand the opposite behaviours ofPDS and NN, one must first realise that the noiseobserved on the Site B instrument is not only ran-dom but also has a structured component. In Fig. 12,four training spectra and the mean training spectrumare represented with an arbitrary vertical scale. Themean training spectrum exhibits some noise patternssimilar to the individual spectra, which are due to the
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Fig. 11. Inverse transfer. Close-up in the reference region for atraining spectrum measured on master (Site A) and slave (Site B),and reconstructed with PDS and NN.
structured component of the background noise. Highfrequency differences of smaller magnitude betweenindividual spectra and the mean spectrum are due tothe random component of noise.
One sees in Fig. 10 that when the master instru-ment to which the spectra are transferred containsstructured noise, the PDS-transferred spectra alsoreproduce this structured noise because every pointon the master instrument is modelled separately andthe structured component of the noise does not van-ish in the regression step (contrary to the randomcomponent that partially disappears). Therefore, thesmall systematic variations in the background of themaster that could not be seen in Fig. 9 are indeedreconstructed by PDS. When the master instrumenthas a high S/N ratio (Site A) as in Fig. 11, the PDS
Fig. 12. Close-up in the reference region for four training spectraand the mean training spectrum measured in Site B.
Fig. 13. Close-up in the reference region for spectra reconstructedwith NN using five hidden nodes and the original wavelength axis(528 points) and spectra reconstructed with NN using 10 hiddennodes and a truncated wavelength axis (100 points).
algorithm reproduces this smooth background, pro-vided that the background correction suggested byWang et al. [15] has been performed beforehand. Ifbackground correction is not performed when the SiteB instrument is used as slave, the structured com-ponent of the noise on the slave propagates in theregression step and instead of obtaining the PDS re-constructed spectrum of Fig. 11, one obtains the sametype of PDS reconstructed spectrum as in Fig. 10.
Contrary to PDS that builds separate local mod-els, the NN builds a single model. The NN is flexi-ble enough to model complex nonlinear transfer func-tions due to wavelength shifts, stray light, differencesin optical path length [9], but it does not have enoughadjustable parameters to model the high frequencyvariations of the Site B instrument background noise.Therefore, this background noise does not appear inthe NN-reconstructed spectra of Fig. 10. However, thisbackground noise gradually re-appears if the NN isprogressively un-constrained by truncating slave andmaster spectra and adding more hidden nodes to theNN. This comes to modelling less spectral differenceswith a more flexible model, so that the noise featuresare also transferred. As an illustration, Fig. 13 repre-sents portions of a spectrum reconstructed using a NNwith five hidden nodes for transfer of full spectra (528points on the wavelength axis), and the same spec-trum reconstructed using a NN with 10 hidden nodesfor transfer of the reference region only (100 pointson the wavelength axis).
F. Despagne et al. / Analytica Chimica Acta 406 (2000) 233–245 243
One can see that the systematic structure as wellas some high frequency noise features characteristicof the Site B instrument are reconstructed. Insteadof adding hidden nodes to the NN, one can think ofperforming background correction before NN mod-elling, but then training becomes less stable andoverfitting occurs more rapidly. This is due to the factthat input variables are systematically range-scaledin a NN to ensure that training starts in the activeportion of the nonlinear transfer functions. If spec-tra are background-corrected before modelling (i.e.mean-centring is performed), the contribution of ran-dom noise will tend to dominate the contributionof chemical variations in some spectral regions andoverfitting will rapidly occur. Therefore, backgroundcorrection is not recommended with NN [9]. If thebackgound difference between both instruments issimply an offset or a sloping baseline, the NN cancorrect this difference thanks to its bias terms. Whenthe background of the slave is more complex as inFig. 11, the NN is not flexible enough to model thedifferences. As a consequence, we see in Fig. 11 thatthe structured and random components of the back-ground noise of slave spectra (Site B) propagate to theNN-transferred spectra. If the input spectral windowsize is increased from 1 to 5 for instance, the randomcomponent of the noise is filtered out during training (awell known advantage of multivariate modelling overunivariate modelling), and only the structured compo-nent of the noise remains. Again, another possibility isto increase the flexibility of the model by transferringonly the spectral regions relevant for the calibrationor using more hidden nodes. In this case however it isimportant to perform several trials starting with dif-ferent sets of initial random weights because the NNwill more likely get trapped into local minima duringtraining and the solution obtained might not be stable.
The excellent reconstruction of the backgroundstructure with PDS (see Fig. 10) for the training sam-ples explains the significantly lower SStrain value ob-served in Table 3 for PDS compared to NN. However,the difference is less important for the SSval values,because the validation samples were only used to es-timate local ranks and not to calculate eigenvectors inlocal models, so the random component of the noiseis no longer perfectly fitted by PDS with validationand test samples. In addition, reconstruction artefacts,probably due to combination of random noise and
Fig. 14. Examples of reconstruction artifact with PDS (a: validationspectrum, b: calibration spectrum).
eigenvalue swapping between adjacent eigenvectorswith similar patterns in the local PCR models [14],appear in some validation spectra (Fig. 14a), testspectra and calibration spectra (Fig. 14b) transferredwith PDS.
5.2. Calibration results
PLS cross-validation models were developed on thetransferred calibration spectra. The responses of the 12MSC-corrected standardisation samples recorded onthe master were also estimated. We reported in Table 4
Table 4Cross-validation and prediction results for PLS models developedon calibration spectra transferred from Site A to Site B
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the number of latent variables in the PLS models (opti-mised with the sign randomisation test to avoid overfit-ting), the root mean squared errors of cross-validationRMSECV determined on the 79 transferred calibra-tion samples, and the root mean squared errors of pre-dictions RMSEP determined on the 12 standardisationsamples.
The cross-validation model developed on NN-transferred spectra is one degree of complexity moreparsimonious and has a slightly lower RMSECVthan the model developed on PDS transferred spec-tra. This is logical since the PDS-transferred spectracontain additional sources of variance (backgroundnoise) unrelated to the property of interest, thereforerelevant information is disseminated among more fac-tors. The complexity and RMSECV values obtainedon NN-reconstructed spectra are similar to what wasobtained before transfer on the slave instrument withMSC-corrected spectra (see Table 1).
When the assay of the 12 standardisation samplesmeasured on the master is estimated, prediction errorsare smaller for the model built with PDS-transferredspectra and linear adjustment is better. This is alsoa consequence of the fact that the measured andPDS-transferred spectra have the same backgroundstructure. Moreover, 6 of the 12 standardisation sam-ples were used to estimate transfer parameters (train-ing set), so the RMSEP obtained cannot be consideredas truly representative of the generalisation ability ofthe PDS models. The RMSEP values are higher thanthose obtained on the slave before transfer, but mod-els are now developed on an instrument with a lowerS/N ratio.
6. Conclusions
This case study is somewhat typical of the situationencountered in practice by many chemometricians inthe sense that data availability is dictated by indus-trial constraints (costs, material availability) and rarelyconfirms with what is recommended in theory.
Wang et al. [22] already showed the benefits oftransferring spectra from an instrument with a poorS/N ratio to an instrument with a better S/N ratio. Thesituation we encounter here is opposite since the mas-ter instrument contains a significant amount of back-ground noise. In addition, we saw that standardisation
samples are not perfectly representative of the bulk ofcalibration samples to transfer, and calibration infor-mation cannot be used to optimise transfer.
By combining signal preprocessing with carefulstandardisation sample selection, it was possible totransfer the calibration model between geographicallyseparated sites. Transfer with PDS and NN can beconsidered as successful, even though both methodsexhibit specific particularities and limitations andfurther validation with samples produced in Site Bwould be needed. The PDS-transferred spectra are lesssmooth than NN-transferred spectra due to eigenvalueswapping in PDS that introduces discontinuities. Ran-dom noise in input data can largely be compensatedby the NN due to the signal-averaging effect in themodel successive summations [23], and the fact thatall points from training spectra are modelled simulta-neously. NN can deal with complex nonlinear instru-mental difference functions, but the PDS approach ismore flexible than the NN approach and it can alsoreproduce the high frequency background structure ofthe master instrument. In the present case, it did notreally alter the calibration results, but led to a modelwith an additional degree of complexity compared tomodels developed on the slave or on NN-transferredspectra. A similar problem can be encountered withNN, but in situations where the noisy background isfound on the slave instrument instead of the master.This is due to the fact that background correction cannot be performed before NN transfer. One way ofcircumventing the problem is by using more nodes inthe hidden layer to make the NN more flexible.
It cannot be said that one method systematicallyoutperforms the other. In practice, one must considerseveral aspects:• The nature of noise (structured or only random).• The type of standardisation function to model (lin-
ear or nonlinear).• The instrument that contains the highest S/N ratio
(master or slave).• The nature of the application. Small discontinuities
or irregularities in transferred spectra are often notinfluential in calibration, but they can be more prob-lematic in pattern recognition applications for pur-pose of library searching [14].Overall, we would recommend to try both methods
and base the final decision on close examination oftransfer results on a validation set truly independent
F. Despagne et al. / Analytica Chimica Acta 406 (2000) 233–245 245
and representative of spectra to be transferred in thefuture, and also consider calibration results if a cali-bration model is already available on the master.
Acknowledgements
This work received financial support from theEuropean Commission (SMT Programme contractSMT4-CT95-2031) and the Fonds voor Weten-schappelijk Onderzoek (FWO, Fund for ScientificResearch).
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