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70 D. S. de Sousa et al.
Supervised
Unsupervised
ClassificationRegression Clustering
Partial least
square -
PLS
Random forest –
Linear regressio n
Sparse linear
regression
Lasso regression
RF
Artificial neural
networks – ANNs
(CNNs, DNNs,
RNNs)
Decision trees
Support vector regression - SVR
Gradient
boosted trees
Nearest
neighbor
Support vector machine - SVMs
Natural language processing – NLP
(Kernel methods
and Bayesian
classifier)
Random forest
classifier
Naive Bayes - NBs
Decision trees
classifier
Linear
discriminant
analysis - LDA
Artificial neural
networks – ANNs
Gradient boosting
K-means
Hierarchical
clustering
Artificial neural
networks – ANNs
(Kohonen maps,
autoencoders)
Hidden Markov
model
Gaussian
mixture
Mean shift
Fig. 4.3 Examples of machine learning methods used in drug discovery followed by their classication based on their use and nature
Among these methods, NNs, which will be discussed in more detail later, along with Random Forest (RF) and Support Vector Machine (SVM), are the most widely employed approaches in drug design. [15]
RF is an ensemble ML method that combines multiple decision trees to make predictions. This algorithm extends the capabilities of decision trees while addressing their limitations. Its distinctive feature resides in creating an ensemble of decision trees during the training process, with each tree derived from a random sample of the training data, a procedure commonly referred to as bootstrapping. Furthermore, when splitting nodes in the tree, only a random subset of features is considered, which reduces correlation and enhances the models robustness. To make predictions, Random Forest employs a majority vote mechanism in classi­cation tasks, selecting the most frequently predicted class by individual trees, and it averages tree predictions in regression tasks. A key advantage of Random Forest is its ability to mitigate over tting. This is achieved by allowing individual trees to be highly customized to the training data, while the combination of predictions from multiple trees results in a more general and accurate model. Additionally, Random Forest provides a measure of feature importance for each attribute used in training, which facilitates feature selection and aids in understanding which variables have the greatest impact on predictions [ 15, 40].
SVM is a class of ML algorithms widely employed for classication and regres­sion tasks. These models are rooted in convex optimization theory, aiming to nd the decision hyperplane that best separates classes within a feature space. The primary goal of SVM is to maximize the margin between data points from different classes,
4 Machine Learning and Neural Network Methods Applied to Drug Discovery 71
which contributes to the robust generalization of the model to unseen data. In cases where data are not linearly separable, SVM can resort to kernel functions, which map data to a higher-dimensional space, enabling efcient separation of nonlinear clas­ses. This ability to handle complex, nonlinearly separable data makes SVM a powerful tool in various ML and pattern recognition applications [15, 41, 42].
Both RF and SVM are relevant methods in drug design and related applications. They offer different approaches to modeling and solving complex problems, and their selection often depends on the specic characteristics of the data and the nature of the problem at hand. RFs ensemble nature enhances robustness, while SVMs emphasis on nding optimal decision boundaries makes it suitable for classication tasks, even with complex data sets [15, 42].
2.1 Neural Networks
The human brain is a marvel of complexity and power, exhibiting an astonishing capacity to process vast amounts of information in a short period. At its core, the brain operates through intricate networks of neurons, which are responsible for the transmission and processing of information. This remarkable mechanism has inspired numerous researchers to emulate its functionality, particularly the experi­ential learning process. This endeavor has given rise to what we know as neural networks, also called articial neural networks (ANNs) [38].
ANNs have been meticulously designed to address a wide range of tasks span­ning from the simplest to the most complex, all within a rema rkably short period. This ability to solve a broad spectrum of issues promptly stems from the founda­tional design of ANNs, which closely mirror the biological functioning of the human brain. This structure comprises a multitude of interconnected articial neurons, which operate together to process information and make decisions. Within the architecture of an ANN, each component performs similarly to the organization of the human brain [38]. To illustrate these components, we will begin by presenting different forms of ANNs, which vary in compl exity and operating principles.
2.1.1 Perceptron
As previously pointed out, a perceptron is the simplest model of a neural network, with its main characteristic being that it has only a single layer, hence the name Single-Layer Articial Neural Network. To understand how it operates, we can break down its core components and processes. Inputs (x) represent the numerical values provided to the perceptron (independent variables), while weights (w) are adjustable parameters that determine the relative importance of these inputs, which are ne-tuned during training. A bias (b) is a constant value added to the weighted sum of inputs, allowing control of the output. The operation of the perceptron can be summarized by the equation for the weighted sum (Z ), which is calculated as the sum
72 D. S. de Sousa et al.
of the products of inputs and their corresponding weights, plus the bias, as represented in Eq. 4.1:
b
þx1w1þ ...þ xnwn: ð4:1Þ
0
Z =
n
xiwi= x0w
i = 0
A node (neuron), which in the case of a perceptron is singular, serves as a processing unit that receives Z, as input and applies an acti vation function ( f ) which in this model is essential a step function. The primary purpose of this activation function is to generate the output, the dependent variable (Y ), as established in Eq. 4.2 [43, 44].
Y = fZðÞ=
1ifZ > 0, 0ifZ ≤ 0:
ð4:2Þ
The perceptrons outputs represent the nal results, commonly used for tasks like binary classication. However, its main limitation is that, since it only consists of a single neuron, it is primarily suitable for addressing linearly separable problems. Nevertheless, understanding the operation of the perceptron is essential as it lays the foundation for comprehending more intricate neural network models with multiple layers and interconnected neurons. These advanced models have the capacity to express probabilities or continuous values, making them applicable to a wider range of complex tasks [43, 44]. Figure 4.4 illustrates a perceptrons structure, aiding in the visualization of its basic components.
2.1.2 Multilayer Neural Networks
A Multilayer Neural Network or multilayer perceptron (MLP) as the name suggests represents an advanced form of neural network that incorporates the presence of more than one layer of interconnected neurons, resulting in a more intricate archi­tecture when compared to the traditional perceptron. The fundamental structure of an MLP closely resembles that of a perceptron, comprising an input layer that receives input data, one or more hidden layers that process and transform these data, and an output layer that furnishes the nal network output following processing. These layers play distinct roles and perform specic functions within the network [45, 46].
The input layer is the initial layer of the network and is designed to accept input data, which may encompass features, characteristics, or information fed into the network for processing. This layer does not engage in any calculations but simply conveys the data to the intermediary layers [45, 46].
The hidden layers are the heart of the MLP and are tasked with processing input data through mathematical operations such as weight multiplication, bias addition, and applying activation functions. These layers are termed hiddenbecause their
4 Machine Learning and Neural Network Methods Applied to Drug Discovery 73
x
1
Neuron
Output
Input Layer
Fig. 4.4 Representative diagram of the architecture of a perceptron
operations are not directly observable in the network training process but are essential in feature extraction and data representation [45 , 46].
The output layer constitutes the nal layer of the network and generates the ultimate output, which may take the form of a prediction, classication, or any other desired outcome based on the specic problem at hand. The structure and the number of neurons in this layer depend on the nature of the task for which the network is being designed [45, 46]. Figure 4.5 illustrates an example of the generic structure of an MLP, providing a visual aid for understanding its fundamental components.
In the case of these models, the increase in the number of layers and neurons allows for the execution of more complex and nonlinear tasks, as the models capacity for representation and learning becomes more sophisticated. This is due to the enhanced ability to express and adapt to intricate patterns in the data. As part of this process, new activation functions can be applied, with the most common ones being the ReLU and sigmoid functions [47, 48].
The ReLU (Rectied Linear Unit) activation function is widely used due to its simplicity and effectiveness in overcoming gradient vanishing problems. It
74 D. S. de Sousa et al.
Fig. 4.5 Architecture of a multilayer neural network: 7 input neurons (blue), 15 neurons in the rst hidden layer (gray), 8 neurons in the second hidden layer (gray), and 2 neurons in the output layer (green)
Input Layer
Output
Layer
Hidden Layers
transforms negative values into zero while leaving positive values unchanged, as expressed in Eq. 4.3 [47, 48].
fZðÞ=
Z if Z 0,
0ifZ < 0:
ð4:3Þ
On the other hand, the sigmoid function is a classic activation function that is often used in output layers of neural networks, especially in binary classication problems. It maps input values to the range from 0 to 1, which is useful for estimating probabilities [47, 48]. The expression that represents this function is shown in Eq. 4.4.
fZðÞ=
1
1 þ e
-z
ð4:4Þ
Moreover, there are other activation functions, such as the hyperbolic tangent (tanH) and the parametric rectied linear unit (PReLU), which also are important in different contexts and can be chosen based on the characteristics of the problem being addressed [47 , 48]. Table 4.1 summarizes the other activation functions.
2.1.3 Types of Neural Networks
Neural networks not only vary in the number of neurons and layers but can also take on various formats that directly inuence their operating principle s, opening a wider range of applications and distinct purposes. This gives rise to a variety of neural
4 Machine Learning and Neural Network Methods Applied to Drug Discovery 75
Table 4.1 Mathematical for­mulations of other examples of activation functions
Name Equation
Identity f(Z ) = Z
TanH
ArcTan f(Z ) = tan
PReLU
ELU
SoftPlus f(Z ) = ln (1 + e
fZðÞ=
fZðÞ=
fZðÞ=
2
-2Z
1þe
-1
(Z)
Zif Z≥0,
αZif Z< 0:
α eZ- 1ðÞif Z < 0
- 1
Zif Z≥ 0,
Z
)
network architectures [38, 45]. Figure 4.6 illustrates the most well-known types of neural networks.
It is possible to observe in Fig. 4.6 that neural network methods vary fundamen­tally in shape, neuron composition, operating direction, and activation functions. The purpose of this chapter is not to explain how all these methods work, so we will highlight some more widely used methods in the eld of drug discovery. For this, we will divide them into two categories: Feedforward and Rec urrent Neural Network.
Feedforward
The feedforward models are a fundamental category in the eld of ANNs due to their simple and effective approach. Essentially, they follow the principle of a unidirec­tional ow of information, from input to output, without the formation of cycles or loops. This characteristic makes feedforward methods especially suitable for han­dling tasks that do not involve temporal or sequential dependencies, such as classi­cation tasks. The perceptron itself, one of the pioneering concepts in the eld of neural networks, is a classic example of this approach [38, 46, 49].
The operation of a feedforward method is relatively simple but effective. Initially, a set of input information is provided to the model. This information is then processed by a series of layers of neurons. Each neuron in a layer performs a weighted linear combination of the input values and applies a nonlin ear activation function. This activation function is essential because it introduces nonlinearity into the network, allowing it to capture complex relationships in the data. This is important for the ability of neural networks to model real-world problems, which often involve nonlinear relationships [ 38, 46, 49].
The feedforward approac h encompasses a variety of algorithms and architectures that are widely used in different application domains. Some notable examples include Radial Basis Function (RBF) networks and Convolutional Neural Networks (CNN) [38, 45, 50].
RBF
The structure of an RBF is typically the same as that of a Multilayer Perceptron, but it utilizes radial functions as activation functions [49], as described in Eq. 4.5.
76 D. S. de Sousa et al.
Perceptron
CNN
LSTM
Autoencoder
GRU
Hopfield Network
Deep FeedforwardFeedforward
RNN
Sparse autoencoder
Kohonen Network
Input node
Backfed Input node
Recurrent node
Fig. 4.6 Architecture representation of some types of neural networks
Hidden node
Memory node with gates
Output node
n
f xðÞ=
wiφ x - c
i = 1
Kernel
ðÞ ð4:5Þ
kk
Convolution /pool
Memory node
Match Input output node
i
In this context, where the input is modeled as a vector x from the set of real numbers of N dimensions, n is the number of neurons in the hidden layer, c center vector for neuron i, and w
is the weight of neuron i in the linear output neuron.
i
is the
i
4 Machine Learning and Neural Network Methods Applied to Drug Discovery 77
Functions that depend only on the distance from a center vector are radially symmetric about that vector, hence the name radial basis. In the basic form, all inputs are connected to each hidden neuron. The norm is typically taken to be the Euclidean distance, and the radial basis function is commonly taken to be Gaussian [50].
The main characteristic of RBF networks is their ability to approximate complex functions with an approach based on the nonlinear representation of data. This is particularly useful in probl ems where the relationship between input and output data cannot be easily modeled by linear functions. Additionally, RBF networks have the ability to adapt automatically to training data, adjusting the weights and centers of the neurons in the hidden layer [45, 50].
CNN
A Convolutional Neural Network stands as a widely employed neural network architecture in tasks linked to image and video processing. This technology proves indispensable in elds such as computer vision, pattern recognition, and ML applied to visual data [5153].
Drawing inspiration from the workings of the human visual cortex, CNNs operate through convolutional layers, responsible for applying convolution operations to input images. This convolution entails the use of lters to extract features such as edges, textures, and relevant patterns in the image. Following the convolutional layers, pooling layers come into play, tasked with reducing the spatial dimension of feature maps, and preserving crucial infor mation while decreasing the networks parameter count. Proceeding with the process, fully connected layers are employed to make decisions based on the previously extracted features. These layer s resemble those found in traditional neural networks, where outputs are computed using adjustable weights [5153].
Activation functions, such as ReLU, are applied at each layer to introduce non­linearities into the network, enabling the learning of more complex representations. Additionally, normalization layers, like Batch Normalization, can be incorporated to enhance the networks training [5153].
Recurrent Neural Networks
Recurrent Neural Networks (RNNs) constitute a type of neural network architecture designed to handle sequential or temporal data. Unlike conventional feedforward networks, RNNs feature feedback connections, allowing the output of a layer to be fed back into the input of the same layer. This capability enables the network to maintain an internal memory [49 , 5456].
The key concept in RNNs is their ability to process sequences of data. Each unit in an RNN layer retains an internal state updated based on the current input and the previous state, enabling the network to capture contextual information over time.
78 D. S. de Sousa et al.
However, traditional RNNs face certain limitations, such as the vanishing or exploding gradient problem, which hinders the training of long sequences. To overcome these issues, more advanced variants have emerged, such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). These architectures introduce memory control mechanisms that aid in preserving and forgetting infor­mation more effectively [5457].
LSTM
Long Short-Term Memory (LSTM) Networks emerge as a solution to the challenges faced by conventional RNNs when dealing with sequential data. While RNNs are widely employed for such tasks, they often struggle to capture long-term relation­ships. LSTMs offer a more effective approach, enabling the network to memorize and access relevant information across extensive sequences, proving particularly valuable in contexts where understanding temporal relationships is central [49, 57,
58].
The basic structure of an LSTM includes memory units called cells, each equipped with three gates: the input gate, the forget gate, and the output gate. These gates function as control mechanisms that regulate the amount of information that enters, is forgotten, or is transmitted [57, 58].
The LSTM operates at each time step, making decisions based on the character­istics of sequential data and the previous memory. This allows the network to learn complex temporal dependencies over time [57, 58].
The fundamental advantage of LSTMs lies in their ability to selec tively retain and discard information. This exibility makes LSTMs effective in modeling patterns in sequential data, applicable in various areas such as pattern recognition, machine translation, and time series prediction [57, 58].
GRU
Similar to LSTMs, Gated Recurrent Units, or GRUs, were developed to overcome the limitations of traditional RNNs. GRUs simplify the structure of LSTMs by combining the concept of memory units and gates into a single unit. They retain the ability to capture long-term information but with a more streamlined architecture [49, 57, 59].
In a GRU, we also nd two main gates: the update gate and the reset gate. The update gate determines how much of the previous memory should be retained, while the reset gate decides how much of the previous information should be forgotten. The simplicity of GRUs compared to LSTM s can result in more efcient computa­tion and faster training in certain situations [57, 59].
2.2 Deep Learning
Deep learning, within the broader context of ML, is an approach that surpasses the limitations of conventional neural networks by incorporating three or more layers.
4 Machine Learning and Neural Network Methods Applied to Drug Discovery 79
While traditional ML can be likened to a neural network with a single layer, deep learning expands upon this architecture, mimicking to some extent the complexity of the human brain [5, 18, 26, 33, 34].
By adding hidden layers, regardless of the method employed, the neural network gains the ability to learn and generalize from vast amounts of data. While a single neural layer can make basic predictions, additional layers enhance and rene the models accuracy. This expansion not only increases the systems complexity but also intensies its aptitude for learning [5, 18, 26, 33, 34].
As the neural network deepens, its capacity to extract abstract and hierarchical features from data signicantly improves. This feature enables the model to identify complex patterns, contributing to a deeper and more rened understanding of the data. The richness of data used during train ing not only forties the model but also empowers it to handle a broader range of situations, making it more versatile and adaptable [5, 18, 26, 33, 34].
Comparatively, while traditional ML may be effective for specic tasks with smaller data sets, deep learning excels in scenarios where the complexity and diversity of the data demand a more sophisticated approach [5, 18, 26, 33, 34].

3 Using Machine Learning

ML and NNs, as discussed earlier, exhibit a variety of approaches in terms of operation, structure, and purposes, offering a wide range of application possibilities. To employ ML in a specic application, it is essential to thoroughly understand the structure of the involved stages. In summary, these stages involve dening the problem, data collection, data preprocessing, model selection, model training, val­idation, model tuning, and prediction (Fig. 4.7). Each of these steps is of fundamen­tal importance in the development and successful application of solutions based on this approach.
3.1 Problem Denition
In the ML journey, the initial phase of dening the problem, despite its apparent simplicity, assumes elemental importance, serving as an essential foundation for the projects success. At this stage, it is imperative to cultivate a deep understanding not only of the available data but also of the inherent peculiarities within the domain where the model will be applied and the challenges to be faced.
Establishing a specic goal for the project is fundamental. Answering fundamen­tal questions such as What are we seeking to predict or classify?is necessary, delineating the precise task that the model must perform. Additionally, it is necessary to identify the type of problem at hand, whether it is classication, regression, clustering, or anomaly detection.