Chemometrics is the science of extracting information from
chemical systems by data-driven means. It is a highly interfacial
discipline, using methods frequently employed in core data-analytic
disciplines such as
multivariate statistics,
applied mathematics, and
computer science, in order to address problems in
chemistry,
biochemistry,
medicine,
biology and
chemical engineering. In this way, it mirrors several other interfacial ‘-metrics’ such as
psychometrics and
econometrics.
Introduction
Chemometrics is applied to solve both descriptive and predictive
problems in experimental life sciences, especially in chemistry. In
descriptive applications, properties of chemical systems are modeled
with the intent of learning the underlying relationships and structure
of the system (i.e., model understanding and identification). In
predictive applications, properties of chemical systems are modeled with
the intent of predicting new properties or behavior of interest. In
both cases, the datasets can be small but are often very large and
highly complex, involving hundreds to thousands of variables, and
hundreds to thousands of cases or observations.
Chemometric techniques are particularly heavily used in
analytical chemistry and
metabolomics,
and the development of improved chemometric methods of analysis also
continues to advance the state of the art in analytical instrumentation
and methodology. It is an application driven discipline, and thus while
the standard chemometric methodologies are very widely used
industrially, academic groups are dedicated to the continued development
of chemometric theory, method and application development.
Origins
Although one could argue that even the earliest analytical
experiments in chemistry involved a form of chemometrics, the field is
generally recognized to have emerged in the 1970s as computers became
increasingly exploited for scientific investigation. The term
‘chemometrics’ was coined by Svante Wold in a grant application 1971,
[1]
and the International Chemometrics Society was formed shortly
thereafter by Svante Wold and Bruce Kowalski, two pioneers in the field.
Wold was a professor of organic chemistry at Umeå University, Sweden,
and Kowalski was a professor of analytical chemistry at University of
Washington, Seattle.
Many early applications involved multivariate classification,
numerous quantitative predictive applications followed, and by the late
1970s and early 1980s a wide variety of data- and computer-driven
chemical analyses were occurring.
Multivariate analysis was a critical facet even in the earliest
applications of chemometrics. The data resulting from infrared and
UV/visible spectroscopy are often easily numbering in the thousands of
measurements per sample. Mass spectrometry, nuclear magnetic resonance,
atomic emission/absorption and chromatography experiments are also all
by nature highly multivariate. The structure of these data was found to
be conducive to using techniques such as
principal components analysis (PCA), and
partial least-squares
(PLS). This is primarily because, while the datasets may be highly
multivariate there is strong and often linear low-rank structure
present. PCA and PLS have been shown over time very effective at
empirically modeling the more chemically interesting low-rank structure,
exploiting the interrelationships or ‘latent variables’ in the data,
and providing alternative compact coordinate systems for further
numerical analysis such as
regression,
clustering, and
pattern recognition.
Partial least squares in particular was heavily used in chemometric
applications for many years before it began to find regular use in other
fields.
Through the 1980s three dedicated journals appeared in the field:
Journal of Chemometrics,
Chemometrics and Intelligent Laboratory Systems, and
Journal of Chemical Information and Modeling.
These journals continue to cover both fundamental and methodological
research in chemometrics. At present, most routine applications of
existing chemometric methods are commonly published in
application-oriented journals (e.g.,
Applied Spectroscopy, Analytical Chemistry, Anal. Chim. Acta.
, Talanta
).
Several important books/monographs on chemometrics were also first
published in the 1980s, including the first edition of Malinowski’s
"Factor Analysis in Chemistry",
[2] Sharaf, Illman and Kowalski’s "Chemometrics",
[3] Massart
et al. "Chemometrics: a textbook",
[4] and "Multivariate Calibration" by Martens and Naes.
[5]
Some large chemometric application areas have gone on to represent new domains, such as molecular modeling and
QSAR,
cheminformatics, the ‘-omics’ fields of
genomics,
proteomics,
metabonomics and
metabolomics, process modeling and
process analytical technology.
An account of the early history of chemometrics was published as a series of interviews by Geladi and Esbensen.
[6][7]
Techniques
Multivariate calibration
Many chemical problems and applications of chemometrics involve
calibration.
The objective is develop models which can be used to predict properties
of interest based on measured properties of the chemical system, such
as pressure, flow, temperature,
infrared,
Raman,
NMR spectra and
mass spectra.
Examples include the development of multivariate models relating 1)
multi-wavelength spectral response to analyte concentration, 2)
molecular descriptors to biological activity, 3) multivariate process
conditions/states to final product attributes. The process requires a
calibration or training data set, which includes reference values for
the properties of interest for prediction, and the measured attributes
believed to correspond to these properties. For case 1), for example,
one can assemble data from a number of samples, including concentrations
for an analyte of interest for each sample (the reference) and the
corresponding infrared spectrum of that sample. Multivariate calibration
techniques such as partial-least squares regression, or principal
component regression (and near countless other methods) are then used to
construct a mathematical model that relates the multivariate response
(spectrum) to the concentration of the analyte of interest, and such a
model can be used to efficiently predict the concentrations of new
samples.
Techniques in multivariate calibration are often broadly categorized as classical or inverse methods.
[5][8]
The principal difference between these approaches is that in classical
calibration the models are solved such that they are optimal in
describing the measured analytical responses (e.g., spectra) and can
therefore be considered optimal descriptors, whereas in inverse methods
the models are solved to be optimal in predicting the properties of
interest (e.g., concentrations, optimal predictors).
[9]
Inverse methods usually require less physical knowledge of the chemical
system, and at least in theory provide superior predictions in the
mean-squared error sense,
[10][11][12] and hence inverse approaches tend to be more frequently applied in contemporary multivariate calibration.
The main advantages of the use of multivariate calibration techniques
is that fast, cheap, or non-destructive analytical measurements (such
as optical spectroscopy) can be used to estimate sample properties which
would otherwise require time-consuming, expensive or destructive
testing (such as HPLC-MS). Equally important is that multivariate
calibration allows for accurate quantitative analysis in the presence of
heavy interference by other analytes. The selectivity of the analytical
method is provided as much by the mathematical calibration, as the
analytical measurement modalities. For example near-infrared spectra,
which are extremely broad and non-selective compared to other analytical
techniques (such as infrared or Raman spectra), can often be used
successfully in conjunction with carefully developed multivariate
calibration methods to predict concentrations of analytes in very
complex matrices.
Classification, pattern recognition, clustering
Supervised multivariate classification techniques are closely related
to multivariate calibration techniques in that a calibration or
training set is used to develop a mathematical model capable of
classifying future samples. The techniques employed in chemometrics are
similar to those used in other fields – multivariate discriminant
analysis, logistic regression, neural networks,
regression/classification trees. The use of rank reduction techniques in
conjunction with these conventional classification methods is routine
in chemometrics, for example discriminant analysis on
principal components or
partial least squares scores.
Unsupervised classification (also termed
cluster analysis)
is also commonly used to discover patterns in complex data sets, and
again many of the core techniques used in chemometrics are common to
other fields such as machine learning and statistical learning.
Multivariate curve resolution
In chemometric parlance, multivariate curve resolution seeks to
deconstruct data sets with limited or absent reference information and
system knowledge. Some of the earliest work on these techniques was done
by Lawton and Sylvestre in the early 1970s.
[13][14] These approaches are also called self-modeling mixture analysis,
blind source/signal separation,
and spectral unmixing. For example, from a data set comprising
fluorescence spectra from a series of samples each containing multiple
fluorophores, multivariate curve resolution methods can be used to
extract the fluorescence spectra of the individual fluorophores, along
with their relative concentrations in each of the samples, essentially
unmixing the total fluorescence spectrum into the contributions from the
individual components. The problem is usually ill-determined due to
rotational ambiguity (many possible solutions can equivalently represent
the measured data), so the application of additional constraints is
common, such as non-negatively, unmodality, or known interrelationships
between the individual components (e.g., kinetic or mass-balance
constraints).
[15][16]
Other techniques
Experimental design
remains a core area of study in chemometrics and several monographs are
specifically devoted to experimental design in chemical applications.
[17][18]
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.
[19]
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
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.
[20] Chemometric model selection usually involves the use of tools such as
resampling (including bootstrap, permutation, cross-validation).
Multivariate statistical process control (MSPC), modeling and optimization accounts for a substantial amount of historical chemometric development.
[21][22][23]
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,
[24] or the newer term
process analytical technology continues to draw heavily on chemometric methods and MSPC.
Multiway methods are heavily used in chemometric applications.
[25][26]
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.
