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5 Clustering of Small Molecules 121
Table 5.1 Resources to perform small molecules
Name Clustering method Pros and cons Reference
ChemBioSe-
rver 2.0
(available as
web app)
ChemMine
tools (available as web
app)
Deep-Clustering (available as
Python code)
Hierarchical and affinity propagation clustering
Hierarchical clustering,
multidimensional scaling
(MDS), and binning clustering
VAE (Variational Auto
Encoder) & K-means
AE (Auto encoder) & K-means
Pros: Compound fingerprints
can be provided by the user or
generated on-site using 166-bit
MACCS Open Babel fingerprint
from .sdf or .mol files. In the
case of hierarchical clustering,
the user can select among different distances, linkage
approaches, and thresholds. A
tutorial is available on the site.
Results are stored for a week
Cons: Despite the tutorial and
the availability of a supporting
paper, the information on the
fundamentals of the affinity
propagation clustering may be a
bit scarce
Pros: Compounds can be inputted using SMILES notation, as .
sdf or using PubChem CIDs.
They can also be drawn online.
The user can tune different
parameters. A tutorial is available online. Depending on the
clustering methods, the output
can be exported graphically or as
tables/.csv file. Past jobs are
accessible. Free support available
Cons: Even for small sized data
sets, jobs run rather slowly.
Despite the tutorial and the
availability of a supporting
paper, the details of the procedures are a bit scarce, though
most of them use very welldocumented functions
implemented in R
Pros: The clustering procedure
exploits both local and global
molecular features. It can be
applied to large-scale chemical
libraries. The supporting paper
describes the clustering procedure in detail
Cons: Unavailability as web
application
[25]
[4]
[21]
(continued)
122 A. Talevi et al.
Table 5.1 (continued)
Name Clustering method Pros and cons Reference
ChemmineR
(R package)
hclust
(R function)
RDKIT (collection of
cheminformatics and
machinelearning software written
in C++ and
Python)
iRaPCA
(available as
web app and
Python code)
SOMoC
(available as
a web app
and Python
code)
Hierarchical clustering:
Maximum Common Substructure (MCS) Search.
Nonhierarchical clustering:
K-means clustering
Different hierarchical clustering
methods (Ward, single, complete, and average linkage,
among others)
Sphere exclusion and fuzzy
clustering
Hybrid clustering method using
molecular descriptors and
K-means
Non-hierarchical clustering
using EState1 fingerprints and
UMAP
Pros: ChemmineR is a popular
cheminformatics package, with
plenty of documentation and an
active community forum and
blog available through their
developers. The developers welcome community-contributed
resources
Pros: This is a well-documented
R function to perform hierarchical clustering based on different
combinations of distances and
linkage methods. In fact, it has
been used to build some other
clustering resources listed here
Pros: Large community of users.
Community forum is available.
Well documented
Cons: Time-consuming, these
methods can be slow to run and
are best used on small sets
(no more than a few hundred
molecules) of small molecules
Pros: The developers have validated their approach across
29 data sets of different sizes,
obtaining better metrics than
several classic approximations.
The user can tune different
parameters and input their own
molecular descriptor sets to perform the clustering. Allows iterative sub-clustering. Free
support is available. The
supporting paper describes the
clustering procedure in detail
Cons: Long computer times for
large-scale libraries. Low
interpretability
Pros: The developers have validated their approach across
29 data sets of different sizes and
obtained better metrics than
several classic approximations.
The user can tune different
parameters. Free support is
available. The supporting paper
describes the clustering
[12]
[53]
[24]
[38]
[38]
(continued)
5 Clustering of Small Molecules 123
Table 5.1 (continued)
Name Clustering method Pros and cons Reference
procedure in detail. Compatible
with large-scale libraries.
Cons: Relatively low
interpretability
clValid
(R package)
NbClust
(R package)
cclust
(R package)
MASSA
(Python
code)
Variety of methods for validating the results from a cluster
analysis.
Clustering validity indexes can
be applied to outputs of two
clustering algorithms: K-means
and hierarchical agglomerative
clustering (HAC), by varying all
combinations of a number of
clusters, distance measures, and
clustering methods
Convex Clustering methods
include the K-means algorithm,
the On-line Update algorithm
(Hard Competitive Learning),
and the Neural Gas algorithm
(Soft Competitive Learning)
Explores the biological, physicochemical, and structural
spaces of molecules using PCA,
hierarchical clustering analysis
and K-modes
– [8]
Pros: Provides 30 indexes that
determine the number of groups
in a data set. The user can
simultaneously evaluate several
clustering schemes while varying the number of clusters.
Nbclust offers functionalities to
visualize the results of various
indices
Pros: cclust offers a variety of
convex clustering methods and
provides several clustering
indexes. It can handle complex
data sets with large numbers of
data points and dimensions.
Cons: The interpretation of
clustering results can be difficult, especially for highdimensional data sets or those
with complex structures
Initial evaluation of the algorithm in the context of QSAR/
QSPR modeling to split data sets
into training and test sets produced models with low variability and better values for
validation metrics, even when
the descriptors used in the
QSAR/QSPR were different
from those used in the separation
of training and test sets, Generates graphical representations
that can provide further insights
into the data
[14]
[63]
[51]
124 A. Talevi et al.
Table 5.2 Questions to answer when planning a clustering study
Have you checked relevant literature on the subject?
Is there some prior clue about the structure of the data that can serve as an external validation
criterion?
If so, do you trust the data? Can you do anything to minimize data noise and data mislabeling?
Would it be convenient for you to include a feature-selection step?
What internal cluster validation index(es) will you include?
Would you address cluster replicability?
Has any bias been reported for the clustering method(s) of choice?
of the authors is that in the real world a ground truth, a ground cluster structure of
real data, does not exist (especially if we use clustering as a truly unsupervised
approximation, with no preconception or prior labeling of the data points). This view
seems in line with the notion of clusterability. As pointed out by Ackerman and
Ben-David [2], “if a data set is hard to cluster then it does not have a meaningful
clustering structure.” However, we accept that some representations of the data are
more useful for speci fic purposes, and their usefulness depends on the value criteria
of the user.
This leads us to the problem of variable selec tion, an old debate that has not yet
been fully settled. Ketchen et al. [27] describe three fundamental approaches to the
selection of relevant features for a clustering experiment: inductive, deductive, and
cognitive.
The inductive approach considers as many variables as possible because it is not
known a priori which features provide the best differentiation among observations;
thus, using as many clustering variables is likely to maximize the chances of
discovering significant differences [28, 34]. In contrast, the deductive and cognitive
approaches (pre)select the feature space based on either theoretic knowledge or
expert judgment. The (often vast) universe of possible features is thus pruned to a
more limited and, in principle, meaningful number based on previous knowledge .
The preceding concepts are captured, in one way or another, by clustering
approaches that incorporate dimensionality-reduction and/or feature-selection
steps, although the latter have rarely been applied in the field of small molecule
clustering [42]. Small molecules are often represented by high-dimensional vectors
(i.e., a large pool of global and/or local molecular features), which, for different
reasons (to facilitate visual representation, reduce computational cost, and/or capture
orthogonal and significant feature projections), are often pre-processed using dimensionality reduction techniques, such as Principal Component Analysis (PCA) [38]or
the Uniform Manifold Approximation and Projection (UMAP) approaches
[24, 38]. Hadipour et al. [21] recently reported an open-source deep clustering
approach, in which dimensionality-reduction techniques wer e implemented serially.
First, the authors resorted to PCA on sets of global and local molecular features,
leading to a representation comprising 243 features, which was then subjected to
further dimensionality reduction using autoencoders.
5 Clustering of Small Molecules 125
In particular, McKelvey’s view is well embodied by subspace clustering approximations, which attempt to find relevant cluster structures in different subspaces of
the feature space. In this way, large pools of variables could be exploited through
smaller subsets, either through systematic exploration (computationally very
demanding for high numbers of features) or stoch astic, until combinations of variables useful for the problem in question are found, without a priori selection of
variables biased by the researcher’s prior knowledge (and lack of knowledge!). For
example, starting from descriptor sets provided by the user, the iRaPCA approach
[38] explores stochastic subsets of molecular descriptors where cohesive and wellseparated clusters can be found, as judged by the silhouette coefficient or other
validity measures. Each of the so-obtained clusters can be further divided, iteratively, into sub-clusters. iRaPCA has shown, without iterations, consistent and
almost optimal behavior in benchmarking experiments across 29 data sets of variable
sizes [38, 39].
On the other hand, multi-view clustering has also attracted much attention lately
[13, 19, 57] and is better aligned with the idea of an underlying ground-truth
structure of the data (in which case any view of the data would origi nate from an
underlying latent space) . However, it has largely been overlooked in the field of
cheminformatics. Different views of the data may be integrated or combined because
of their complementarity (this can be of particular interest when the clustering
procedure is supervised via external labeling of the data) or based on their consensus
(returning to the idea that high-level stability should be verified across different
algorithms, features, and entities).
4 Conclusions
The principle of similarity (“guilty by association”) has been and is of great
importance in the field of cheminformatics and drug discovery, in which molecular
similarity (apparent or not) is used to identify new bioactive scaffolds, develop a
series of analogs around such scaffolds, and make predi ctive interpolations related to
physicochemical and biological properties of interest. However, in several ways, the
field of supervised machine learning has matured more rapidly than its unsupervised
counterpart. Not only is supervised learning much more widely used, but rigorous
internal and external validation of supervised models is common practice, while
validation of small molecule clustering experiments is much more sporadic. Furthermore, while supervised machine-learning procedures in the cheminformatics
field have rapidly assimilated the newest algorithms, small molecule clustering
still does not fully exploit recent progress such as subspace clustering and multiview clustering (with exceptions). A good part of the bibliography used in this
chapter comes from disciplines as distant and dissimilar as psychology, organizational management or marketing, image recognition, bioinformatics, etc. In addition,
of course, to pure mathematics. The progress that clustering theory has experienced
in other disciplines has spilled over, rather very slowly, to cheminformatics.
126 A. Talevi et al.
In a chemical universe that is expanding exponentially, as demonstrated by the
currently available ultra-large chemical libraries, the development and application of
specific clustering methods will allow the detection of unforeseen patterns in the data
and will accelerate the exploitation of this virtually infinite chemodiversity. It is no
longer possible to trust the human ability to detect molecular patterns, not only
because the vast number of accessible molecules cannot be encompassed humanly
but also because in such richness and chemical diversity, it is likely that relationships
that are not apparent and unnoticed to the naked eye will appear, the detection of
which requires higher levels of abstraction and the integration of chemical knowledge and advanced mathematics. Subspace clustering and multi-view clustering, still
largely unexplored in the field of chemistry, will provide solutions to the problem of
automatic or semi-automatic analysis of ultra-large chemical libraries.
Acknowledgments The three authors are members of CONICET and UNLP. They thank these
institutions and FONCYT (PICTs 2019-0984, 2019-1075, 2021-0720) for their financial support.
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Chapter 6
QSAR and Machine Learning Predictors
Philipe Oliveira Fernandes and Vinicius Gonçalves Maltarollo
Abstract This chapter de lves into the fundamental principles and applications of
quantitative structure–activity relationship (QSAR) and machine learning (ML)based predictors in the realm of drug design and chemical biology. QSAR establishes a quantitative relationship between the chemical structure of molecules and
their biological activities or physicochemical properties. The evolution of QSAR
from its first reports to its modern applications was covered comprising the theoretical foundations, encompassing descriptors, mathematical models (followed by brief
examples of ML applied to this field), and statistical validation techniques employed
in QSAR analysis. Interestingly, many recognized and accepted good practices and
validation protocols align with OECD guidelines for QSAR applications for regulatory purposes. In this sense, notably, the QSAR field becam e important outside of
the academic boundaries. Additionally, this chapte r discusses current challenges and
emerging trends in QSAR research, including the incorporation of machine learning
algorithms and big data analytics for enhanced predictive accuracy and applicability.
Overall, this chapter serves as a comprehensive guide for researchers and practitioners in understanding and leveraging QSAR as a pivotal tool in rational drug
design and chemical biology.
Keywords QSAR · Machine learning · Molecular descriptors · OECD principles
1 Historical Background
The Quantitative Structure–Activity Relationship (QSAR) field was introduced
when researchers tried to correlate the molecular structure of similar compounds to
a specific biological activity. This process can be traced back to 1863 when Cros first
reported a correlation between the toxicity of primary aliphatic alcohols and their
water solubility [1], a pioneer work in this field. Another notable work from the
P. O. Fernandes · V. G. Maltarollo (✉)
Departamento de Produtos Farmacêuticos, Faculdade de Farmácia, Universidade Federal de
Minas Gerais, Belo Horizonte, Minas Gerais, Brazil
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
V. G. Maltarollo (ed.), Computer-Aided and Machine Learning-Driven Drug
Design, Computer-Aided Drug Discovery and Design 3,
https://doi.org/10.1007/978-3-031-76718-0_6
131