Combinatorial and High-Throughput Screening of Materials ...

ACS Combinatorial Science
possible to recognize these relationships with far greater speed
and not necessarily depending on a priori models, provided the
availability of the relevant data. The predictive aspect of data
mining tasks can serve for both classification and regression
operations. Data mining, which is an interdisciplinary blend of
statistics, machine learning, artificial intelligence, and pattern
recognition, is viewed to have four core tasks:
Cluster analysis seeks to find groups of closely related observations
and is valuable in targeting groups of data that may have
well behaved correlations and can form the basis of physics-based
as well statistically based models. Cluster analysis when integrated
with CHT experimentation, can serve as a powerful tool
for rapidly screening combinatorial libraries.
Predictive modeling helps build models for targeted objectives
(e.g., a specific materials property) as a function of input or
exploratory variables. The success of these models also helps
refine the relevance of the input parameters.
Association analysis is used to discover patterns that describe
strongly associated features in data (for instance the frequency of
association of a specific materials property to materials chemistry).
Such an analysis over extremely large data sets is made possible
with the development of very high-speed search algorithms and
can help to develop heuristic rules for materials behavior governed
by many factors.
Anomaly detection does the opposite by identifying data or
observations significantly different from the norm. To be able to
identify such anomalies or outliers are critical in CHT experiments
and high throughput screening especially to quantitatively
assess uncertainty and accuracy of results and distinguish between
true “discoveries” and false positives.
Massive data generated from high-troughput characterization
tools leads to the need for effective data analysis and interpretation
to identify the trends and relationships in the data. 9
Advanced mathematical and statistical techniques are used in
CHT screening to determine, often by indirect means, the
properties of substances that otherwise would be very difficult
to measure directly. 82,83 These techniques have been successfully
applied for visualization and pattern recognition, 84,85 lead identification
and optimization, 86,87 process optimization, 66,88 and
development of predictive models and quantitative structure
activity relationships (QSARs) and quantitative structure
property relationships (QSPRs). 85,89,90 The implementation
of multivariate calibration improves analysis selectivity when
spectroscopic or any other types of measurements are performed
with relatively low resolution instruments. 91,92
Multivariate data analysis techniques are essential analytical
tools for in combinatorial materials science. The attractiveness of
partial least-squares (PLS) method has been demonstrated for
in situ monitoring of combinatorial reactions using single-bead
FTIR spectroscopy. 93 Using these tools, quantitative and qualitative
analysis of combinatorial samples was performed with IR
spectra with severely overlapped bands. A limitation of PLS
method is in the ability to reveal only the changes due to reaction
but it cannot provide spectra for pure components. 93 This
limitation can be overcome by using other multivariate analysis
tools such as evolving factor analysis and multivariate curve
resolution methods. 8
In combinatorial materials science, pattern recognition techniques
find similarities and differences between samples of
combinatorial libraries, serve as a powerful visualization and
descriptor-identification tool, and can warn of the occurrence
of abnormalities in the measured data. 84 These techniques can
REVIEW
reveal correlated patterns in large data sets obtained from
combinatorial experiments, large databases or simulations, can
determine the structural relationship among screening hits, and
can significantly reduce data dimensionality to make it more manageable
in the database with the minimal loss of information.
79 81,94
Methods of pattern recognition include principal components
analysis (PCA), hierarchical cluster analysis (HCA), soft independent
modeling of class analogies (SIMCA), neural networks,
and some others. 95,96
PCA is a widely used approach to search for patterns by
seeking to reduce the dimensionality of data because it provides
an unsupervised and robust way for analysis of multivariate data.
PCA projects the data set onto a subspace of lower dimensionality
with removed collinearity. PCA achieves this objective by
explaining the variance of the data matrix in terms of the weighted
sums of the original variables without significant loss of information.
These weighted sums of the original variables are called
principal components (PCs). Each PC is a suitable linear
combination of all the original variables. The first PC accounts
for the maximum variance (eigenvalue) in the original data set.
The second PC is orthogonal (uncorrelated) to the first and
accounts for most of the remaining variance. Thus, the mth PC is
orthogonal to all others and has the mth largest variance in the set
of PCs. Once the N PCs have been calculated using eigenvalue/
eigenvector matrix operations, only M PCs with variances above
a critical level are retained. This M-dimensional PC space has
retained most of the information from the initial N-dimensional
variable space, by projecting it into orthogonal axes of high
variance and forming a suitable PCA model. 18
In PCA, the scores plots show the relations between analyzed
samples, while the loadings plots show the relations between
analyzed variables. To ensure the quality of the data analyzed
using PCA, several statistical tools are also available. Multivariate
control charts use two statistical indicators of the PCA model such
as Hotelling’s T 2 and Q values plotted as a function of combinatorial
sample or time. The significant principal components of the
PCA model are used to develop the T 2 -chart and the remaining
PCs contribute to the Q-chart. The Hotelling’s T 2 statistic is the
sum of normalized squared scores and is a measure of the variation
in each sample within the PCA model. The T 2 contributions
describe how individual variables contribute to the Hotelling’s T 2
value for a given sample. The Q residual is the squared prediction
error and describes how well the PCA model fits each sample. It is
a measure of the amount of variation in each sample not captured
by principal components retained in the model. The graphical
representation of PCA with T 2 and Q statistics for multiple
samples in the PCA model is illustrated in Figure 5.
It is important not only to discover a target feature in a
combinatorial library but also to glean from these combinatorial
experiments the variations in the library. An illustrative example
can be provided from combinatorial polymer libraries of polyanhydrides
(see Figure 6), which are important biomaterials for
biomedical applications and drug delivery because of their
degradation and erosion properties. 97 For drug delivery applications,
the choice of correct chemistry and management of various
degradation factors (for example, kinetics of drug release and
polymer-drug interaction) are essential for proper drug stabilization.
High throughput FTIR screening has been shown to be an
appropriate tool for screening compositional libraries of polyanhydride
copolymers. FTIR spectra (see Figure 6A, B) and
images (see Figure 6C) were utilized for the PCA-based tracking of
the subtle changes in chemistry of polyanhydride copolymers. 98
586 dx.doi.org/10.1021/co200007w |ACS Comb. Sci. 2011, 13, 579–633