Editing Chemometrics (section)

===Other techniques===
'''[[design of experiments|Experimental design]]''' remains a core area of study in chemometrics and several monographs are specifically devoted to experimental design in chemical applications.<ref name="Deming1987">{{cite book |first1=S. N. |last1=Deming |first2=S. L. |last2=Morgan |title=Experimental design: a chemometric approach |publisher=Elsevier |year=1987 |isbn=978-0444427342 }}</ref><ref name="Bruns2006">{{cite book |first1=R. E. |last1=Bruns |first2=I. S. |last2=Scarminio |first3=B. |last3=de Barros Neto |title=Statistical design – chemometrics |publisher=Elsevier |location=Amsterdam |year=2006 |isbn=978-0444521811 }}</ref>  Sound principles of experimental design have been widely adopted within the chemometrics community, although many complex experiments are purely observational, and there can be little control over the properties and interrelationships of the samples and sample properties.

'''[[Signal processing]]''' is also a critical component of almost all chemometric applications, particularly the use of signal pretreatments to condition data prior to calibration or classification.  The techniques employed commonly in chemometrics are often closely related to those used in related fields.<ref name="Wentzell2000">{{cite book |first1=P. D. |last1=Wentzell |first2=C. D. |last2=Brown |chapter=Signal Processing in Analytical Chemistry |title=Encyclopedia of Analytical Chemistry |editor-first=R. A. |editor-last=Meyers |publisher=Wiley |year=2000 |pages=9764–9800 }}</ref> Signal pre-processing may affect the way in which outcomes of the final data processing can be interpreted.<ref>{{Cite journal|last1=Oliveri|first1=Paolo|last2=Malegori|first2=Cristina|last3=Simonetti|first3=Remo|last4=Casale|first4=Monica|date=2019|title=The impact of signal pre-processing on the final interpretation of analytical outcomes – A tutorial|journal=Analytica Chimica Acta|language=en|volume=1058|pages=9–17|doi=10.1016/j.aca.2018.10.055|pmid=30851858|bibcode=2019AcAC.1058....9O |s2cid=73727614 }}</ref>

'''Performance characterization, and figures of merit'''  Like most arenas in the physical sciences, chemometrics is quantitatively oriented, so considerable emphasis is placed on performance characterization, model selection, verification & validation, and [[figure of merit|figures of merit]].  The performance of quantitative models is usually specified by [[root mean squared error]] in predicting the attribute of interest, and the performance of classifiers as a true-positive rate/false-positive rate pairs (or a full ROC curve).  A recent report by Olivieri et al. provides a comprehensive overview of figures of merit and uncertainty estimation in multivariate calibration, including multivariate definitions of selectivity, sensitivity, SNR and prediction interval estimation.<ref>{{cite journal |first1=A. C. |last1=Olivieri |first2=N. M. |last2=Faber |first3=J. |last3=Ferre |first4=R. |last4=Boque |first5=J. H. |last5=Kalivas |first6=H. |last6=Mark |title=Guidelines for calibration in analytical chemistry Part 3. Uncertainty estimation and figures of merit for multivariate calibration |journal=Pure and Applied Chemistry |volume=78 |year=2006 |issue=3 |pages=633–650 |doi=10.1351/pac200678030633 |s2cid=50546210 |url=https://zenodo.org/record/894416 |doi-access=free }}</ref>  Chemometric model selection usually involves the use of tools such as [[resampling (statistics)|resampling]] (including bootstrap, permutation, cross-validation).

'''Multivariate [[statistical process control]] (MSPC)''', modeling and optimization accounts for a substantial amount of historical chemometric development.<ref>{{cite journal |first1=D. L. |last1=Illman |first2=J. B. |last2=Callis |first3=B. R. |last3=Kowalski |title=Process Analytical Chemistry: a new paradigm for analytical chemists |journal=American Laboratory |volume=18 |year=1986 |pages=8–10 }}</ref><ref>{{cite journal |first1=J. F. |last1=MacGregor |first2=T. |last2=Kourti |title=Statistical control of multivariate processes |journal=Control Engineering Practice |volume=3 |year=1995 |issue=3 |pages=403–414 |doi=10.1016/0967-0661(95)00014-L }}</ref><ref>{{cite journal |first1=E. B. |last1=Martin |first2=A. J. |last2=Morris |title=An overview of multivariate statistical process control in continuous and batch process performance monitoring |journal=Transactions of the Institute of Measurement & Control |volume=18 |year=1996 |issue=1 |pages=51–60 |doi=10.1177/014233129601800107 |bibcode=1996TIMC...18...51M |s2cid=120516715 }}</ref>  Spectroscopy has been used successfully for online monitoring of manufacturing processes for 30–40 years, and this process data is highly amenable to chemometric modeling.  Specifically in terms of MSPC, multiway modeling of batch and continuous processes is increasingly common in industry and remains an active area of research in chemometrics and chemical engineering.  Process analytical chemistry as it was originally termed,<ref>{{cite journal |first1=T. |last1=Hirschfeld |first2=J. B. |last2=Callis |first3=B. R. |last3=Kowalski |title=Chemical sensing in process analysis |journal=[[Science (journal)|Science]] |volume=226 |year=1984 |issue=4672 |pages=312–318 |doi=10.1126/science.226.4672.312 |pmid=17749872 |bibcode=1984Sci...226..312H |s2cid=38093353 }}</ref> or the newer term [[process analytical technology]] continues to draw heavily on chemometric methods and MSPC.

'''Multiway methods''' are heavily used in chemometric applications.<ref>{{cite book |first1=A. K. |last1=Smilde |first2=R. |last2=Bro |first3=P. |last3=Geladi |title=Multi-way analysis with applications in the chemical sciences |publisher=Wiley |year=2004 }}</ref><ref>{{cite journal |first1=R. |last1=Bro |first2=J. J. |last2=Workman |first3=P. R. |last3=Mobley |first4=B. R. |last4=Kowalski |title=Overview of chemometrics applied to spectroscopy: 1985–95, Part 3—Multiway analysis |journal=Applied Spectroscopy Reviews |volume=32 |year=1997 |issue=3 |pages=237–261 |doi=10.1080/05704929708003315 |bibcode=1997ApSRv..32..237B }}</ref>  These are higher-order extensions of more widely used methods.  For example, while the analysis of a table (matrix, or second-order array) of data is routine in several fields, multiway methods are applied to data sets that involve 3rd, 4th, or higher-orders.  Data of this type is very common in chemistry, for example a liquid-chromatography / mass spectrometry (LC-MS) system generates a large matrix of data (elution time versus m/z) for each sample analyzed.  The data across multiple samples thus comprises a [[data cube]].  Batch process modeling involves data sets that have time vs. process variables vs. batch number.  The multiway mathematical methods applied to these sorts of problems include [[PARAFAC]], trilinear decomposition, and multiway PLS and PCA.