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                    Master’s Thesis Defense

Use of Information Theory Measures Extracted
From OBD-II Interface Data for Driver Identification.

Gean da Silva Santos
geans.santos@gmail.com

Advisor:
Dr. André Luiz Lins de Aquino

Maceió
Março, 2024

Gean da Silva Santos

Use of Information Theory Measures Extracted
From OBD-II Interface Data for Driver Identification.

Master’s Thesis presented by Gean da Silva Santos to
the Postgraduate Program in Informatics at the Federal
University of Alagoas as a requirement for obtaining the
Master’s degree in Informatics.

Advisor:

Dr. André Luiz Lins de Aquino

Maceió
Março, 2024

Catalogação na Fonte
Universidade Federal de Alagoas
Biblioteca Central
Divisão de Tratamento Técnico
Bibliotecário: Marcelino de Carvalho Freitas Neto – CRB-4 - 1767
S237u

Santos, Gean da Silva.
Use of information theory measures extracted from OBD-II
interface data for driver identification / Gean da Silva Santos. – 2024.
45 f. : il.
Orientador: André Luiz Lins de Aquino.
Dissertação (mestrado em informática) - Universidade Federal de
Alagoas. Instituto de Computação. Maceió, 2024.
Texto em inglês.
Bibliografia: f. 30-34.
1. Identificação de motorista (Aprendizado do computador). 2. Teoria da
informação. 3. Complexidade estatística. 4. Shannon, Entropia de. 5. Fisher,
informação de. 6. Aprendizado do computador. 7. Dados de veículo. 8.
Sistema de Diagnóstico Embarcado. I. Título.
CDU: 004.85

MINISTÉRIO DA EDUCAÇÃO
UNIVERSIDADE FEDERAL DE ALAGOAS
INSTITUTO DE COMPUTAÇÃO
Av. Lourival Melo Mota, S/N, Tabuleiro do Martins, Maceió - AL, 57.072-970
PRÓ-REITORIA DE PESQUISA E PÓS-GRADUAÇÃO (PROPEP)
PROGRAMA DE PÓS-GRADUAÇÃO EM INFORMÁTICA

Folha de Aprovação
GEAN DA SILVA SANTOS

USO DE MEDIDAS DE TEORIA DA INFORMAÇÃO EXTRAÍDAS DE DADOS DA
INTERFACE OBD-II PARA IDENTIFICAÇÃO DO MOTORISTA
USE OF INFORMATION THEORY MEASURES EXTRACTED FROM OBD-II
INTERFACE DATA FOR DRIVER IDENTIFICATION
Dissertação submetida ao corpo docente do
Programa de Pós-Graduação em Informática
da Universidade Federal de Alagoas e
aprovada em 25 de março de 2024.
Banca Examinadora:

ANDRE LUIZ LINS
Assinado de forma digital
por ANDRE LUIZ LINS DE
DE
AQUINO:03235015400
AQUINO:0323501
Dados: 2024.04.22
20:16:42 -03'00'
5400

________________________________________
Prof. Dr. ANDRE LUIZ LINS DE AQUINO
UFAL – Instituto de Computação
Orientador

________________________________________
Prof. Dr. OSVALDO ANIBAL ROSSO
UFAL – Instituto de Física
Examinador Externo

________________________________________
Profa. Dra. FABIANE DA SILVA QUEIROZ
UFAL – Campus de Engenharia e Ciências Agrárias
Examinador Interno

________________________________________
Prof. Dr. DENIS LIMA DO ROSARIO
UFPA-Universidade Federal do Pará
Examinador Externo

________________________________________
Profa. Dra. RAQUEL DA SILVA CABRAL
UFAL – Campus Arapiraca
Examinador Interno

Abstract
We investigate the use of Machine Learning tools applied to driver identification. We propose using Information Theory measures as features in Machine Learning models. The measures used
are Statistical Complexity, Permutation Entropy, and Fisher Information. We calculate these measures over the raw data of On Board Diagnostics version 2 (OBD-II) sensor values and use them
as new features applying to the following classification models: k-Nearest Neighbors, Support
Vector Machine, Decision Tree, Random Forest, Multi-Layer Perceptron, and Naive Bayes. We
evaluate the driver identification scenario considering sliding windows of 120 samples and an
overlap of 60 samples. In each window, the well-established models are trained and evaluated.
The models are analyzed by accuracy, by the Area Under the Curve of the Receiver Operating
Characteristic Curve (which determines how relevant the classifier is in terms of its sensitivity
and specificity), by precision and by recall. We observed significant gains for all models considered in the scenario. Following the traditional procedure, we obtained the values: 78.5 to 91.1
% of accuracy, 74.5 to 87.8 % of ROC AUC, 62.5 to 84.2 % of precision, and 60.6 to 85.3 % of
recall. While using our proposal, we obtained the values: 94.3 to 99.9 % of accuracy, 91.7 to
99.9 % of ROC AUC, 89.8 to 99.9 % of precision, and 86.4 to 99.9 % of recall.
Keywords: driver identification, information theory, statistical complexity, Shannon entropy,
Fisher information, machine learning, vehicle data, on board diagnostic (OBD).

iii

Resumo
Investigamos o uso de ferramentas de Aprendizado de Máquina aplicadas à identificação de
motoristas. Propomos o uso de medidas de Teoria da Informação como recursos em modelos
de Aprendizado de Máquina. As medidas utilizadas são Complexidade Estatística, Entropia de
Permutação e Informação de Fisher. Calculamos essas medidas sobre os dados brutos dos
valores dos sensores do Sistema de Diagnóstico Embarcado versão 2 (OBD-II) e as utilizamos
como novas características aplicadas aos seguintes modelos de classificação: k-Nearest Neighbors, Support Vector Machine, Decision Tree, Random Forest, Multi-Layer Perceptron e Naive
Bayes. Avaliamos o cenário de identificação de motorista considerando janelas deslizantes de
120 amostras e uma sobreposição de 60 amostras. Em cada janela, os modelos bem estabelecidos são treinados e avaliados. Os modelos são analisados pela acurácia, pela Área Sob a
Curva da Curva Característica de Operação do Receptor (que determina quão relevante o classificador é em termos de sua sensibilidade e especificidade), pela precisão e pela cobertura.
Observamos ganhos significativos para todos os modelos considerados no cenário. Seguindo o
procedimento tradicional, obtivemos os valores: de 78,5 a 91,1% de acurácia, de 74,5 a 87,8%
de ROC AUC, de 62,5 a 84,2% de precisão e de 60,6 a 85,3% de revocação. Enquanto usando
nossa proposta, obtivemos os valores: de 94,3 a 99,9% de acurácia, de 91,7 a 99,9% de ROC
AUC, de 89,8 a 99,9% de precisão e de 86,4 a 99,9% de cobertura.
Palavras-chave: identificação de motorista, teoria da informação, complexidade estatística,
entropia de Shannon, informação de Fisher, aprendizado de máquina, dados de veículo, diagnóstico embarcado (OBD).

iv

Acknowledgement
I extend my heartfelt gratitude to my beloved wife, Jéssika, and our cherished daughters, Abigail,
Noemi, and Debora. Additionally, I wish to express my deepest appreciation to my parents, Gerson and Josenilda, who have always provided me with unwavering support whenever I needed
it.
My aspiration is for my daughters to one day surpass both Jéssika and me. For now, our
focus remains on being the best possible examples for them.
Jéssika has been a steadfast presence by my side, offering unwavering support to both me
and our children. She is a beacon of light, always guiding us in the right direction with her faith,
wisdom and discernment.

v

Contents
Figure List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Table List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii
viii

1

Introduction

1

2

Related Works and Concepts
2.1 Driver Identification Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Driving Data and Application . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Machine Learning Applied to Driver Identification . . . . . . . . . . . . .
2.2 Information Theory Measures . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Ordinal series from Bandt-Pompe . . . . . . . . . . . . . . . . . . . . .
2.2.2 Shannon Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Statistical Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Fisher Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.5 Causal information planes . . . . . . . . . . . . . . . . . . . . . . . . .

3
4
4
4
5
5
7
8
9
9

3

Methodology and Proposal
3.1 Vehicle Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Preprocessing and Calculation of Information Theory measures . . . . . . . . .
3.3 Machine Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 k-Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Support Vector Machine . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Tree algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Multi Layer Perceptron . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Naive Bayes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12
13
13
16
17
18
19
19
20

4

Results and Discussion
4.1 Metrics used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Information Theory measures extraction . . . . . . . . . . . . . . . . . . . . . .
4.3 Proposal evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21
21
22
24

5

Final Considerations

29

vi

List of Figures
1.1
2.1
2.2
3.1
3.2
3.3
3.4
3.5
4.1
4.2
4.3
4.4
4.5
4.6

Car’s sensors and OBD-II interface (1) . . . . . . . . . . . . . . . . . . . . . . .
Position of series in the Complexity-Entropy plane (2). . . . . . . . . . . . . . .
Position of series in the Fisher-Shannon plane (2). . . . . . . . . . . . . . . . .
Proposed process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dataset folders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Correlation among features. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Information Theory computation. . . . . . . . . . . . . . . . . . . . . . . . . . .
Structure of MLP with a single hidden layer (3). . . . . . . . . . . . . . . . . . .
Complexity-Entropy planes for each trip with D = 7. . . . . . . . . . . . . . . . .
Fisher-Shannon planes for each trip with D = 7. . . . . . . . . . . . . . . . . .
Measurements for different parameters in the Complexity and Entropy calculation.
Sliding windows on features. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experiment results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time for preprocessing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vii

1
10
11
12
14
15
16
19
25
26
27
27
28
28

List of Tables
2.1
3.1
3.2
3.3
4.1

Qualitative analysis of related works. . . . . . . . . . . . . . . . . . . . . . . . .
Features removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Features remaining. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameters of the classification algorithms used. . . . . . . . . . . . . . . . . .
Binary Confusion Matrix: True Positives (TP), False Positives (FP), True Negatives
(TN), False Negatives (FN). . . . . . . . . . . . . . . . . . . . . . . . . . . . .

viii

6
16
17
18
21

1
Introduction

Driving is essential in people’s daily lives. Moreover, people relate directly or indirectly to driving.
In other words, even those who do not drive vehicles, for instance, use public transportation,
receive packages, cross busy streets, among other things.
Modern automobiles have several sensors that govern numerous operations, such as safety
features, vehicle control, and infotainment (4). These sensors are connected through an invehicle network called the Controller Area Network (CAN). That is, CAN is an internal vehicle
network where the values of all vehicle sensors are transmitted. To externalize these data, the
On-Board Diagnostic version 2 (OBD-II) interface is used. This interface is usually located near
the driver’s seat and below the steering wheel as shown in Figure 1.1. The OBD standard arose
from the need to reduce the costs of diagnosing cars in workshops and, historically, the need for
pollutant emission control.

Figure 1.1: Car’s sensors and OBD-II interface (1)
The vehicle sensor data, when collected throughout the journey, can represent the driver’s
driving behavior. Studies in the literature utilize this data for various applications, such as:

1

• Driver identification: to offer data to car insurers, to suspect theft, or even to have greater
control over a fleet of vehicles.

• Prediction of polluting gas emissions: for environmental control.
• Identification of road/traffic conditions: to assist in monitoring.
• Identification of driver emotions: for customized ITS applications, or for risk alert.
Studies using vehicle data usually fit into one of these problems: classification problem,
clustering problem, and regression problem. Examples of classification problems are the identification of drivers (1) and the classification of driver behavior. In a classification problem, we
seek to predict the category (or class) of an observation, instance, or input. A regression problem is similar to a classification problem, but it tries to predict a real value in a continuous domain
and not a class (5). Examples of regression problems are predicting fuel consumption, polluting
gas emissions, driver risk, and wear and tear of parts. At the same time, a clustering problem aims to group observations into clusters (6). Examples of clustering problems are grouping
drivers to identify driving profiles (6) or grouping trip data to associate with different road types
or conditions (such as highway, urban area, unpaved road as in (7)).
Many studies aiming for driver identification employ deep learning models to achieve high
accuracy scores. However, the performance in other important metrics such as precision and
recall is often overlooked. Additionally, this type of model requires extensive hyperparameter
optimization and training time.
Moreover, other studies have used Information Theory measures to characterize time series
data. We hypothesize that extracting Information Theory measures from vehicle driving data
can be valuable resources for machine learning models to become more effective. Thus, our
objectives are to describe a method for constructing a new dataset from Information Theory
measures and to compare the models performance using the proposed method and the default
method from literature.
We apply our proposal to driver identification using the dataset "This car is mine!" (8). This
dataset has 51 features, each from a vehicle sensor, with a public parameter ID (PID) regulated
by SAE J1979 (9). We compare our proposal with standard preprocessing method in the literature. We apply the preprocessed data to some classic classification algorithms used in the
literature for driver identification. In our experiments, the classifiers presented better accuracy
using our proposal. This improvement is also evidenced by showing the Area Under the Curve
(AUC) for Receiver Operating Characteristic Curve (ROC), the precision, and the recall results.
The remainder of the work is organized as follows: Chapter 2 contains a discussion of work
related to driver identification and Information Theory; Chapter 3 contains the preprocessing
carried out following the literature and the proposal, and the description of the Machine Learning
model used; Chapter 4 describes the metrics used, how the Information Theory measures were
extracted, and how the models and methods were evaluated; Chapter 5 concludes the work.
2

2
Related Works and Concepts

We consider different research sources by the various works that address the classification of
drivers or prediction of polluting gas emissions. One of the most reliable sources of information
about the car’s movement is via simulator (10, 11, 12) or via OBD-II (1, 13), one of the most
prevalent technologies which provide data from the vehicle ECUs (14). Alternatively, we can obtain the information through smartphone sensors (accelerometer, GPS, etc.). Some other works
include data from physiological sensors (15). Finally, works still add other sensors such as cameras and microphones in the vehicles (16, 17). However, we consider only OBD-II data because
they provide information already available in the car, not requiring the addition of sensors.
According to Manderna and Kuma (4), combining vehicle telematics data with relevant Machine Learning algorithms enables the recognition of distinct driving styles, the revelation of
driving behavior and patterns, and even the detection of dangerous driving behaviors. Furthermore, applications for identifying patterns and characterization (18), and prediction (19) can also
be achieved due to the time series characteristic of the data, and path kind identification (i.e., dirt
road, road with bumps, and highway) (7). Finally, some studies aim to cluster the data (20, 6),
which may have the following purposes: identifying driver profiles (aggressive, moderate, calm),
identifying road conditions (motorway, urban area, unpaved) or traffic conditions (slow, moderate,
fast).
Recent works use different models for their applications. In particular, for the case of classification, studies have been using both classic Machine Learning (21, 22, 23, 24) and Deep
Learning models (25, 1, 13, 26). Among the Machine Learning algorithms are kNN, Random
Forest, Decision Tree, SVM, and Naive Bayes. And among the Deep Learning algorithms are
Long Short-Term Memory (LSTM), Generative Adversarial Networks (GAN), and Autoencoder.
In this work, we will use Information Theory measures for training and evaluating Machine
Learning models for driver identification. Section 2.1 discuss the application case of driver identification and Section 2.2 discusss the Information Theory measures.

3

2.1

Driver Identification Case

2.1.1

Driving Data and Application

Different research addressed the drivers’ classification, utilizing various data collection methods. Some of the most reliable sources of information about the car’s movement are simulators
(10, 11, 12), and OBD-II technology (1, 13), which provide data from the vehicle’s ECUs (14).
Alternatively, they obtain the information through smartphone sensors such as accelerometers
or GPS. Additionally, some studies incorporate data from physiological sensors (15), cameras,
and microphones in vehicles (16, 17). However, our research solely considers OBD-II data due
to its availability within the car without requiring additional sensors.
Xun et al. (22) and Uvarov et al. (21) raise a problem with advertising parameters read by the
OBD-II interface. This problem is because manufacturers may not identify all data present on the
CAN bus, keeping them confidential. However, Uvarov et al. deal with this problem using only
some of the public data standardized by SAE J1979 (9), while Xun et al. use all data regardless
of whether they are publicly available. In our work, we use the public data restriction, as we
observed that all 51 sensors present in the (8) dataset are public PIDs.
Combining vehicle telematics data with Machine Learning algorithms enables the recognition
of distinct driving styles, behaviors, and patterns (4). Furthermore, the time-series nature of
the data allows for improvement in the performance of different applications such as pattern
identification, characterization (18), and prediction (19), identifying various types of roads (dirt
roads, roads with bumps, or highways) (7).

2.1.2

Machine Learning Applied to Driver Identification

Most studies follow a preprocessing stage before applying the data to the models. This preprocessing typically involves several standard techniques, including removing missing data, eliminating invariant features or features highly correlated with others, and selecting the best features
through feature selection methods. Other techniques are also employed: value rescaling (normalization) to ensure all features are on the same scale and Principal Component Analysis (PCA)
to reduce the number of features by discarding components with less variation. Furthermore, we
used a sliding window to increase the number of sequences evaluated.
By employing these preprocessing techniques, researchers aim to enhance the quality and
relevance of the data, thus improving the performance of the subsequent classification models in
the driver identification task. Furthermore, Priyadharshini et al. (27) analyze the feature selection
problem for subjective driver identification and then propose using feature selection algorithms
to analyze each feature’s importance. As our proposal, this work presents an improvement in
the data preprocessing stage.
Particularly in the case of classification, they use classic Machine Learning algorithms

4

such as k-Nearest Neighbors (kNN), Random Forest, Decision Trees, Support Vector Machines
(SVM), or Naive Bayes have been employed (21, 22, 23, 24). They also use Deep Learning
models such as Long Short-Term Memory (LSTM), Generative Adversarial Networks (GAN), or
Autoencoders (25, 1, 13, 26). By considering these diverse approaches and models, researchers
have made significant progress in driver identification, behavior analysis, pattern identification,
and predictive modeling, leveraging various data collection methods and Machine Learning algorithms.
The problem of driver identification is a classification one. Considering the characteristics of
the time series data from various sensors, we have a multivariate time series classification problem. To address this problem, we employ Machine Learning models for classification. Several
studies on driver identification propose the use of classic Machine Learning models (21, 22),
while others suggest the utilization of Deep Learning models (25, 1, 4).
Girma et al. (1) and Mekki et al. (25) propose new models based on Deep Learning, seek to
identify different drivers, analyze the model’s accuracy with anomalies in the data, and use other
datasets. Similarly, Manderna et al. (4) propose a new model for driver identification, compare it
with some classic algorithms, and evaluate performance through accuracy, precision, F1-score,
and recall metrics. They measure loss and accuracy over the algorithm’s training epochs. In
contrast, our proposal increments the preprocessing phase of well-established classifiers, analyzing the accuracy, precision, recall, and ROC AUC scores in each data window and at the
preprocessing time. Our proposal improved the performance of non-Deep Learning models for
values very close to the maximum of the metrics used.
Park and Kim (13) raised the problem of having only data from a vehicle owner to train a
model that identifies that driver. They propose using Recursive Generative Adversarial Networks
(RGAN) to stop such issues. This work clearly defines the preprocessing step used in our work.
We use the dataset they made available in this work.
Table 2.1 summarizes the qualitative analysis mentioned Machine Learning methods. However, it is essential to note that many of these previous works propose novel models, introduce
feature constraints, minimize training time, or optimize input size. Only Priyadharshini et al. (27)
analyze approaches to improve data preprocessing.

2.2

Information Theory Measures

2.2.1

Ordinal series from Bandt-Pompe

The quantifiers from Information Theory rely on a probability distribution associated to the time
series. The usual histogram technique is inadequate since the data are treated purely stochastic
and the temporal information is completely lost, in the meantime, Bandt-Pompe methodology
used to take into account time ordering of the time series by comparing neighboring values in a
time series (2).
5

Table 2.1: Qualitative analysis of related works.
Work

Dataset

Preprocessing

Algorithm

Evaluation

(25)

Security Driving
Dataset,
UAH
Driveset, HCILAB
Driveset,
OSF
Dataset

Data
cleaning,
feature selection,
normalization,
slid window: 60s.

LSTM,
StackedRNN, NoPoolCNN, CNN

Accuracy,
crossvalidation

OCS Lab security

Add features (acceleration, jerk),
normalization,
slid windows:30s.

Random Forest,
Decision
Tree,
kNN,
Gradient
Boosting, SVM

Accuracy,
crossvalidation

LSTM,
FCNN,
Decision
Tree,
Random Forest

Accuracy,
precision,
f1-score,
recall

Own dataset

Normalization,
PCA (to reduce
features)

Naive
Bayes,
kNN,
Naive
Bayes + kNN

Accuracy,
confusionmatrix

(4)

Own dataset

Remove
miss
values, normalization

LSTM, SVM, Decision tree, kNN,
MLP 3 layer

(27)

HCILAB
dataset

Normalization,
dimensionality
reduction
Remove highlycorrelation
and
non-influential
features, sliding
window, normalization
Remove highlycorrelation
and
non-influential
features, sliding
window, normalization, and add
features
(Information
Theory
measures)

KNN, SVM, MLP,
Random Forest,
Decision Tree

(21)

(1)

(22)

(13)

Our

Security Driving
Dataset, Vehicular data trace
Dataset-1, Vehicular data trace
Dataset-2

Driver-

“This
car
mine" (8)

“This
car
mine" (8)

is

is

No preprocessing

6

Accuracy,
precision,
f1-score,
recall
Accuracy,
training
time

RGAN

Accuracy,
precision,
f1-score,
recall, training time

KNN,
Linear
SVM, RBF SVM,
Random
Forest,
Decision
tree, MLP, Naive
Bayes

Accuracy,
precision,
recall, ROC
AUC, crossvalidation

Accuracy (%)

57.2 to 95.1

79 to 99

97.2 to 99.1

28 to 95

99

96.04

88.4

89.4 to 99.9

To extract the time series measures, we used the Bandt-Pompe (BP) method (28) to transform raw data into a histogram. Specifically, the BP symbolization method assigns probability
distributions from the time series under consideration, i.e., the temporal causality of the process. In this sense, given a time series X (t) = {xt : t = 1, . . . , N}, an embedding dimension

D ≥ 2(D ∈ N), and an embedding delay time τ ∈ N, we compute the ordinal patterns of order D
(pattern length) generated by

(s) 7→ xs−(D−1)τ , xs−(D−2)τ , . . . , xs−τ , xs



(2.1)

Afterward, we assign each point in time s with a D-dimensional vector resulting from evaluating the sequence at time s − (D − 1)τ, . . . , s − τ, s. We incorporate more information about the
past into the vector by considering a higher D value. According to the pattern, the meaning of
order D with respect to time s is permutation π = {r0 , r1 , . . . , rD−1 } of {0, 1, . . . , D − 1} is defined
as

x5−rD−1 τ ≤ x5−rD−2 τ ≤ · · · ≤ x5−r1 τ ≤ x5−r0 τ

(2.2)

Thus, we convert the data produced by Eq. 2.1 to the unique symbol π. To get unambiguous
results, we set ri < ri−1 if χs−ri = χs ri−1 . If X(t) follows a slightly continuous distribution, the
probability of equal values is zero. Therefore, we calculate the associated relative frequencies
for all D! and the possible permutations π of order D, which this particular ordered sequence
was found in the time series divided by the total number of sequences. Hence, the histogram

P ≡ {p(π)} is defined as
p(π) =

#{s of type π : s ≤ N − (D − 1)τ}
,
N − (D − 1)τ

(2.3)

where # is the cardinality of the set.

2.2.2

Shannon Entropy

The second concept is Shannon Entropy, a global measure of self-information. Shannon Entropy,
developed by Claude Shannon in 1948 (29), is a measure that quantifies the average uncertainty
in a source of information or dataset. It is calculated as the weighted average of the probabilities
of each event occurring, indicating greater uncertainty when the probabilities are more evenly
distributed. This measure is associated with the concept that the more uncertain the outcome of
a random experiment, the more information is gained by observing its occurrence.



Let X = x j : j = 1, . . . , M be a discrete random variable of length M < ∞ whose distribution features is the probability function P = {pi : i = 1, . . . , M}. pi represents the probability of
state i, and ∑M
i=1 pi = 1, and M is the number of possible states of the checked system. The

7

well-known Shannon entropy is
M

S[P] = − ∑ pi ln pi ,

(2.4)

i=1

Among them, pi ln pi = 0 if pi = 0, it is related to the physical process described by P. Once the
Shannon entropy S[P] = 0, the information (knowledge) of the underlying process described by

P is maximal, and we can predict possible outcomes with complete certainty. On the other hand,
if the physical process follows a uniform probability distribution Pe = {pi = 1/M, ∀i = 1, . . . , M}
then little knowledge is obtained (28).
It is also helpful to define the so-called normalized Shannon entropy to evaluate the selfinformation in a normalized way, denoted by

H [P] =
2.2.3

S[P]
S[P]
S[P]
=
.
=
Smax S[Pe ] ln M

(2.5)

Statistical Complexity

Statistical Complexity is a measure that assesses the structural irregularity of datasets, such
as time series. It aims to capture the diversity and patterns of order within the data. Thus,
López-Ruiz et al. (1995) (30) proposed a definition of complexity based on intuitive notions
from physics and statistics. A system is considered simple when it can be described with little
information, whereas a system is deemed complex when a large amount of information would
be required to describe its state.
We need to find a proper measure of complexity based on classification or information alone.
In this case, Lamberti et al. (2004) (31) proposed a Statistical Complexity (C ) measure CJS[P] ,
which can identify critical dynamic details in the temporal series. López-Ruiz et al. (30) proposed
this complexity measure based on the product of functions,

CJS [P] = H [P] QJS [P, Pe ],

(2.6)

where H [P] ∈ [0, 1] is the normalized Shannon Entropy, and QJS is the disequilibrium based on
the Jensen-Shannon (JS) divergence. In this sense, QJS is expressed by

QJS = Q0 JS [P, Pe ]
 

 
S[P] + S[Pe ]
P + Pe
−
,
= Q0 S
2
2

(2.7)

Where Q0 is a normalizing constant, while JS is the JS divergence to quantify the difference
between probability distributions. The presence of correlation structure is quantified in the SC
(32), which measures time series complexity. In the case where the signal from the dynamical
system is ultimately ordered or completely random, the value of CJS [P] is the same as null,
8

i.e., the signal has no structure. In between these two extremes, dynamic systems can perform
every possible level of physical form. These phases are reflected in the obtained features of the
Probability Density Function (PDF) and quantified by no-null CJS [P]. The global property of
SC is that its value does not change with different PDF layouts. Thus, CJS [P] quantifies disorder
but also the degree of correlated structure.
It has been shown that there are limit curves for complexity: for a given value of H and any
data set, the possible C values vary between a minimum Cmin (H ) and a maximum Cmax (H ),
restricting the possible values of the complexity measure (2, 33)

2.2.4

Fisher Information

We used the Fisher Information (FI) to analyze local aspects of changes in the information content given by a time series. It has different interpretations and calculations; among other things,
the amount of information extracted from a process measures the ability to estimate parameters
or the disordered state of a system or phenomenon (32). We define it as
N−1
√
√
FI[P] = F0 ∑ ( 2 pi+1 − 2 pi )2 ,

(2.8)

i=1

where F0 is a normalization constant defined by

F0 =




1



if pi∗ = 1 for i∗ = 1 or i∗ = N

and pi = 0 ∀i ̸= i∗



1/2 otherwise.

(2.9)

According to Olivares et al. (32), the local sensitivity of FI to discrete PDFs requires the order
of i of discrete values in P = {pi : i = 1, . . . , N} when summing from Eq. 2.8. It is the distance
between two related probabilities. Therefore, different orders will result in different FI values
and, thus, their local nature.

2.2.5

Causal information planes

To characterize a given dynamical system described by a time series, we are able to use two representation spaces: (a) one with global-global characteristics called causality entropy-complexity
plane (H xC ) and (b) one with global-local characteristics called causality Shannon-Fisher plane
(FxS), respectively (32).
min ,Cmax ], where
The variation range of the causality entropy–complexity plane is [0, 1] × [CLS
LS
min and Cmax are the minimum and maximum values of Statistical Complexity. The values
CLS
LS
min
max can be calculated through a geometric analysis of the probability space and
of CLS and CLS
depend only on the embedded dimension D (34). For causality Shannon-Fisher plane the range

9

is presumably [0, 1] × [0, 1]; no limit curves have been shown to exist so far (2).
As described in (35) and (2), chaotic systems have intermediate entropies H and F (between
0.45 and 0.7), and complexity C close to maximum. For regular processes, H and C have
small values, close to zero, while the Fisher information is close to one. Uncorrelated stochastic
processes (as white noise) have H near one, C near zero and F near zero too, and colored
noises are in the middle, with medium C and medium-high H values, and medium-low F values;
Regular oscillations have low H and C . Figures 2.1 and 2.2 show examples of well-known series
in these planes.

Figure 2.1: Position of series in the Complexity-Entropy plane (2).

10

Figure 2.2: Position of series in the Fisher-Shannon plane (2).

11

3
Methodology and Proposal

As mentioned previously, most of the observed studies seek to train a model for classification
following the steps: data extraction, cleaning and transformation data, training model, and evaluation model. Therefore, we propose to include measures from Information Theory in that process.

Figure 3.1: Proposed process.
First, data from the vehicle’s sensors are obtained and then preprocessed according to the
literature. In this step, we remove some features and instances with missing data. We normalize
the remaining data between zero and one.
Then, we transform the preprocessed data into Information Theory measurements. Each
feature is treated as a time series at this stage and converted into a series of ordinals according
to Bandt-Pome (36). Note that data normalization does not interfere with this transformation,
because the Bandt-Pompe ordinal patterns are calculated based on the relative order of values
12

in a time series, rather than on the absolute magnitude of the values. Based on the series of
ordinals, Information Theory measures are calculated (Shannon Entropy (37), Fisher Information (38), and Complexity Statistic (30)).
Finally, the data is applied to train and execute the machine learning model. A summary of
the steps is listed below. Numbers 1, 2, 4, and 5 are standard in the literature, but we propose
adding step 3.
1. Extraction of driving data from a vehicle via OBD-II.
2. Preprocessing is the process of cleaning and transforming the data before being applied
to training or running the model to improve its performance; therefore, this process varies
depending on the algorithm used in the model.
3. Extracting Information Theory measures from preprocessed data to apply to machine
learning model (our proposal).
4. Training Machine Learning model for classification.
5. Run the trained machine learning model to classify new data.

3.1

Vehicle Data

We obtain vehicle data from the database in (8). This database is composed of the data generated during the driving of four drivers who took the same route and vehicle, extracting 51 features
(each one related to a sensor). For each trip, we have a file with the data, and the files of each
driver were separated into a folder as shown in the Figure 3.2.
Although there are few drivers in this dataset, it does not contain missing values and has a
relatively large amount of data for each driver. Drivers A and B made eight trips, C made five,
and D made nine. Each trip generated a data file, and each file contains between 1444 and 2296
lines of data.

3.2

Preprocessing and Calculation of Information Theory
measures

To allow a fair comparison with the proposed technique, we consider the preprocessing commonly used in the literature (13), such as: remove feature invariant, highly correlated features
and normalization. Our proposal adds a new step to generate a new dataset containing information theory measures.
The dataset samples comprised the data from the first trip of each driver. Subsequent feature
selection steps were then performed on this sample. The preprocessing steps performed in this
work were as follows:
13

Figure 3.2: Dataset folders
1. Get data from dataset raw: there are a total of 51 features.
2. Preprocessing from literature
(a) Feature indifferent: Analyzing the data, we observe that the value of some characteristics did not change for each driver. We identify a set of features whose value did
not vary over time for each driver. At this stage, 11 features were eliminated and 40
remained.
(b) Feature invariant: These are features whose value remains unchanged in all instances, that is, they have zero variance. At this stage, 3 features were eliminated
and 37 remained.
(c) Exclusion of highly correlated Features: After removing invariant features, we observe that, among the remaining features, some are similar. They have a high level
of correlation. Figure 3.3 visualizes the correlation matrix of the 37 features. Most
researchers agree that a coefficient below 0.1 indicates an insignificant relationship,
while above 0.9 indicates a very strong relationship (39, 40). Thus, features with a
correlation greater than 0.9 were removed, and 25 features remained.
(d) Normalization: To cancel out the effect of different sensor measurement scales, we
standardize the dataset using (1)

Xnew =

X − Xmin
.
Xmax − Xmin

(3.1)

The normalization step will transform data to be ranged between 0 and 1 and thus
treated equally by the classification algorithms (25). We use the minimum and maximum, considering all data from all drivers.
14

Figure 3.3: Correlation among features.
3. Information theory measures
(a) From each preprocessed series, several subseries are generated using sliding windows that slide to each sample (Figure 3.4). To obtain the maximum amount of data,
we make the maximum overlap between the windows, that is, we move the window
by one sample. Each subseries applies the Bandt and Pompe symbolization approach to obtain a sequence of ordinal patterns (41). Then, for each sequence of
ordinals, the Information Theory measures are calculated, namely Shannon Entropy,
Statistical Complexity, and Fisher Information.
(b) We remove duplicate sequences from each subseries, and if the remaining sequence
is smaller than the embedding dimension D, the information measures take on a null
value (NaN). The size of the embedding dimension D is explained in Section 4.2.
(c) We remove features that contain any null values; 10 features were removed, as seen
in Table 3.1.
Table 3.2 shows the obtained, generated and remaining features at each step, while the Table
3.1 shows the features removed in each step. Step 2 reduces the number of features to 31, and
from these features, Shannon Entropy, Statistical Complexity, and Fisher Information measures
are calculated. However, please note that not all features from Step 2 are used to get Information
Theory measures. This is because after Step 3b, some features have missing values and these
features were removed in Step 3c.
15

Figure 3.4: Information Theory computation.
Table 3.1: Features removed.

3.3

Step

Name of removed features

#

2a

Latitude acceleration, glow plug limit request, brake cylinder, fuel pressure, flywheel torque revised, accelerator position filtered, clutch check,
flywheel torque, longitude acceleration, torque transform coefficient, and
fire angle delay tcu.

11

2b

Engine pressure maintenance time, target engine velocity lockup, and
compressor activation

3

2c

Wheel velocity back right, throttle position, wheel velocity front right, engine torque max, wheel velocity front left, engine torque, engine torque
revised, accelerator position, torque converter turbine speed, calculation
overhead, car speed, and throttle position abs

12

3c

Reduce block fuel, gear choice, engine velocity increase tcu, mission oil
temp, block fuel, and standard torque ratio.

6

Machine Learning

We used seven different classification models to compare our proposal with the literature. These
are non-Deep Learning classifiers commonly used in the literature. In each of them, we apply
preprocessed data according to the literature and then the preprocessed data according to our
proposal. We describe the classification algorithms used in the following subsections.
Table 3.3 shows the parameters of each algorithm. We do not intend to optimize the parameters for these algorithms. Thus, we use the default values from the library (42), except for

√

Nearest Neighbors (kNN). In this case, we use k = f loor( N) (where the floor function returns
the largest integer less than or equal). N is the window size and is 120. This neighbor’s value
is commonly used and linked to the sample size. For Multi-Layer Perceptron (MLP), we use the
iteration limiter equal to 1000 to guarantee an acceptable training time for the solution.

16

Table 3.2: Features remaining.
Step

Name of remaining features

#

1

Fuel usage, accelerator position, throttle position, short fuel bank, inhale
pressure, accelerator position filtered, throttle position abs, engine pressure maintenance time, reduce block fuel, block fuel, fuel pressure, long
fuel bank, engine speed, engine torque revised, friction torque, flywheel
torque revised, current fire timing, cooling temperature, engine idle slippage, engine torque, calculation overhead, engine torque min, engine
torque max, flywheel torque, torque transform coeff, standard torque ratio, fire angle delay tcu, engine torque limit tcu, engine velocity increase
tcu, target engine velocity lockup, glow plug limit request, compressor
activation, torque converter speed, current gear, mission oil temp, wheel
velo front left, wheel velo backright, wheel velo frontright, wheel velo
backleft, torque converter turbin speed, clutch check, converter clutch,
gear choice, car speed, logitude acceleration, brake switch, brake sylinder, road slope, latitude acceleration, steering wheel acceleration, and
steering wheel angle.

51

2

Long fuel bank, torque converter speed, reduce block fuel, short fuel
bank, steering wheel angle, cooling temperature, engine torque limit tcu,
fuel usage, brake switch, engine speed, standard torque ratio, engine
torque min, mission oil temp, road slope, steering wheel acceleration,
engine idle slippage, wheel velocity back left, inhale pressure, block
fuel, gear choice, current fire timing, engine velocity increase tcu, friction torque, current gear, and converter clutch

25

3

Statistical Complexity, Shannon Entropy, and Fisher Information of :
Long fuel bank, short fuel bank, steering wheel angle, cooling temperature, engine torque limit tcu, friction torque, fuel usage, brake switch, engine speed, engine torque min, road slope, steering wheel acceleration,
engine idle slippage, wheel velocity back left, inhale pressure, current
fire timing, torque converter speed, current gear, and converter clutch

57

3.3.1

k-Nearest Neighbors

K-Nearest Neighbors (kNN) can be considered a voting system, where the majority class label
determines the class label of a new data point among its nearest k (where k is an integer)
neighbors in the feature space (43). Neighbors-based classification is instance-based or nongeneralizing learning: it does not attempt to construct a general internal model, but simply stores
training data instances (42).
The number of neighbors (k) is a parameter of this algorithm. Adjusting to a higher value of
k can suppress noise effects. However, it makes the classification limits less distinct. That is, the
classifier is more susceptible to errors at the boundaries between the classes.
We can adjust the classifier regarding the weights assigned to each instance. With uniform
weights, each of the k nearest neighbors has the same contribution. With weighted weights, the

17

Table 3.3: Parameters of the classification algorithms used.
Classifier

Parameter

K-Neighbors

n_neighbors= f loor(sqrt(120)), weights=’uniform’,
leaf_size=30, p=2, metric=’minkowski’

SVC linear

C=1.0, kernel=’linear’, degree=3, gamma=’scale’, coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, verbose=False,
max_iter=-1, decision_function_shape=’ovr’, break_ties=False

SVC

C=1.0, kernel=’rbf’, degree=3, gamma=’scale’, coef0=0.0, shrinking=True, probability=False, tol=0.001, cache_size=200, verbose=False,
max_iter=-1, decision_function_shape=’ovr’, break_ties=False

Decision Tree

criterion=’gini’, splitter=’best’, max_depth=None, min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
min_impurity_decrease=0.0, ccp_alpha=0.0

Random Forest

n_estimators=100,
criterion=’gini’,
min_samples_split=2,
min_samples_leaf=1,
min_weight_fraction_leaf=0.0,
max_features=’sqrt’,
min_impurity_decrease=0.0,
bootstrap=True,
oob_score=False, verbose=0, warm_start=False, ccp_alpha=0.0

MLP

hidden_layer_sizes=100, activation=’relu’, *, solver=’adam’, alpha=0.0001, batch_size=’auto’, learning_rate=’constant’, learning_rate_init=0.001,
power_t=0.5,
max_iter=200,
shuffle=True,
tol=0.0001, verbose=False, warm_start=False, momentum=0.9, nesterovs_momentum=True, early_stopping=False, validation_fraction=0.1,
beta_1=0.9, beta_2=0.999, epsilon=1e-08, n_iter_no_change=10,
max_fun=15000

Gaussian NB

var_smoothing=1e-09

algorithm=’auto’,

closest neighbors contribute more to the adjustment. The weights are proportional to the inverse
of the distance from the query point.

3.3.2

Support Vector Machine

In 1992, Vapnik and coworkers proposed a supervised algorithm for classification that has since
evolved into what is now known as Support Vector Machines (SVMs) (44). Its difference is that
the algorithm seeks to separate the classes by a hyperplane, maximizing its margin and the
distance between the hyperplane and the data.
We use two kernels in this work: linear and radial. SVM with the linear kernel separate data
points using a linear hyperplane with the most significant margin (45). SVM with Radial Basis
Function kernel (RBF SVM) separates data points using a higher dimensional space. A higher
value of the gamma parameter will perfectly fit the training dataset, which causes over-fitting.

18

3.3.3

Tree algorithms

Decision Tree (DT) is a non-parametric supervised learning method. The goal is to create a
model that predicts the value of a target variable by learning simple decision rules inferred from
the data features. The deeper the tree, the more complex the decision rules and the fitter the
model (46). In other words, A decision tree is a predictor, h : X → Y , that predicts the label
associated with an instance x by traveling from a root node of a tree to a leaf, that is, the nodes
contain the decision rules and the leaves contain the classes of interest (47).
The advantages of this classifier are that it can work with both numerical and categorical data
and is easy to understand and interpret. Trees can be visualized. Decision tree-based classifiers
may need to generalize classifications better depending on the problem and data, in addition to
dealing with the imbalance in the amount of data in each class.
Decision trees are built by adding nodes with rules to separate the data. The rules that most
clearly separate the data are chosen; we try to make rules that best separate the classes.
Random Forest (RF) is a meta-estimator that fits several decision tree classifiers on various
sub-samples of the dataset and then takes the most popular result (48).

3.3.4

Multi Layer Perceptron

A Multi-Layer Perceptron (MLP) is based on Perceptron, also called a neuron, and it can have
one or more layers of neurons between the input and output layers (3) as shown in figure 3.5.
The layers are entirely connected, and learning occurs when the weights of these connections
change.

Figure 3.5: Structure of MLP with a single hidden layer (3).
Given a set of features and a target, an MLP can retain a non-linear function approximator
for either classification or regression (49).

19

3.3.5

Naive Bayes

Widely discussed in (50), this method uses a probabilistic approach based on Bayes’ Theorem.
The "naive" assumption of conditional independence between every pair of features given the
value of the class variable (51).
Given an element x = x1 , x2 , . . . , xn with n attributes, Naive Bayes predicts the class Ck for x
using the probability calculated by Bayes’ Theorem,

p(Ck |x) =

p(x|Ck )p(Ck ) p(x1 , x2 , . . . , xn |Ck )p(Ck )
=
p(x)
p(x1 , x2 , . . . , xn )

(3.2)

where C is the set of k possible classes. After calculating the probabilities, the Ck class with the
highest probability is assigned to element x.

20

4
Results and Discussion

This chapter is organized as follows: Section 4.1 describes the metrics used, Section 4.2 outlines
how the Information Theory measures employed in this work were extracted and organized, and
Section 4.3 details how the models were evaluated and presents the results comparing the
methods.

4.1

Metrics used

We also use accuracy, precision, and recall measures. To understand these measures, we
suppose a binary classification task with a positive class C+ and a negative class C− , the confusion matrix or contingency table counts correctly and incorrectly classified samples in a decided
manner, see Table 4.1.
So we define the precision as the fraction of predicted positives to be actual positives (52).
This metric shows the correct proportion of identifications, also called True Positive (TP). Considering our case of owner-driver identification, we want to know what proportion of data is actually
from the owner-driver out of all the data that the model labeled as owner-driver data.

Precision =

TP
.
(T P + FP)

(4.1)

Table 4.1: Binary Confusion Matrix: True Positives (TP), False Positives (FP), True Negatives
(TN), False Negatives (FN).
True class
Predicted

C+
C−

21

C+

C−

TP
FN

FP
TN

The accuracy used in the experiments is as follows:

Accuracy =

TP+TN
correct classi f ication
=
.
T P + T N + FP + FN
all classi f ication

(4.2)

where TP is number of true positives (correctly identified owner driver data), TN is the number of true negatives (correctly identified thief driver data), FP is the number of false positives
(incorrectly identified owner driver data), and FN is the number of false negatives (incorrectly
identified thief driver data) (25). Considering our case, recall correctly identifies the owner-driver
data among all the owner-driver data.

Recall =

TP
.
(T P + FN)

(4.3)

We also used the Area Under Curve (AUC) value of the Receiver Operating Characteristic
(ROC) Curve. This metric evaluates both the sensitivity (recall) and specificity. Specificity refers
to the test’s ability to correctly reject data that does not belong to the target driver (owner):

Speci f icity =

4.2

TN
.
(T N + FP)

(4.4)

Information Theory measures extraction

To obtain Information Theory measures that improve the performance of a classifier, we vary two
parameters: the series size and the value of D. The value of D is the embedding dimension on
the horizontal axis. It means the number of ordinals that form each symbol. For example, for

D equal to 3, we have the ordinals 1, 2, and 3. With these ordinals, we can form six symbols:
(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). Thus, the larger the D, the more
information we can obtain from the series; however, if the number of symbols is huge for the size
of the series, it may be that many symbols do not appear in the series. Therefore, we choose
the smallest value for D so that D! equals or exceeds the series size.
First, we carried out a visual analysis of some features in the Complexity-Entropy and FisherShannon planes to provide evidence of the feasibility of using these measures. We then evaluate
the best parameters to calculate the measurements. Finally, we use the measurements to train
the models and compare them with models trained with preprocessed data according to the
literature.
We observed the positioning of Information Theory measures of some characteristics in the
Complexity-Entropy planes and in the Fisher-Shannon plane, so we sought to see if these measures could help in training machine learning models. We use each driver trip to generate a point
in the plane, drivers A, B, C, and D. In this scenario, the length of the series corresponds to the
22

number of instances in the file representing each trip. With the files containing between 1444
and 2296 lines of data, we selected an embedded dimension value of 7 (D = 7). This choice
ensures that the factorial of 7 is greater than the maximum number of lines in the files.
Figures 4.1 and 4.2 are examples of the observed planes, showing only the sensors: accelerator position, steering wheel angle, car speed, and cooling temperature. In Figures 4.1, the
solid lines from the Complexity-Entropy planes are the upper and lower limits of the Complexity
value. The closer to the maximum limit, the more information is required to describe the series.
In other words, the further it is from a uniform distribution. Figure 4.2 shows that the FisherShannon planes, as the Complexity-Entropy planes, can reveal the particularities of each driver.
Nevertheless Fisher Information unveils local characteristics, indicating the frequency of abrupt
changes within the series, while also assessing the data’s ordering.
Figures 4.1a and 4.1c have greater Entropy, indicating that the drivers’ behavior considering accelerator position and steering wheel angle represents a chaotic system with a mediumhigh entropy and an high complexity. The accelerator position behavior highlights driver D. The
steering wheel angle behavior can distinguish the drivers. These measure values can change
immediately with the driver’s action.
However, Figures 4.1e and 4.1g show values with slightly medium-lower Entropy, as they
come from sensors that are more indirectly affected by the driver’s action. Thus, it is not easy to
distinguish among the drivers evaluated. This behavior suggests that it is feasible to use a set of
Information Theory measures from each sensor as new features for classification algorithms to
distinguish between drivers.
To obtain several Information Theory (H C ) points, we take several subsequences from the
series that represent each driver’s trip. Then, we vary the size of this subsequence: 20, 120, 300,
720, 900. The sequence length is the number of instances and the time in seconds. We consider
values below 20 instances with little information to be obtained and values above 900 seconds
as a very long time to start generating data in an application and would possibly generate little
information measurement data; for example, the files used have between 1444 and 2296 rows
of data which is between 1444 and 2296 seconds.
Our previous studies suggest that tree-based algorithms outperformed other methods for
classifying drivers. Therefore, we employed a Random Forest classifier to investigate the parameter variation for Bandt-Pompe symbolization. Our aim is to determine the optimal number
of samples required to achieve information measure values that enhance classifier performance.
Figure 4.3 depicts a more pronounced increase between 300 and 540, followed by a smaller
increase between 540 and 840. It’s noteworthy that the four largest sizes (720, 780, 840, and
900) exhibit the highest values but are statistically indistinguishable. In Figure 4.6, the preprocessing time of both the proposed method and the standard method from the literature is
illustrated. It’s evident that the computational cost significantly escalates beyond size 780. This
escalation is attributed to the increase in the embedded dimension (D) from 6 to 7, given that
the number of possible symbols for each D follows a factorial relationship. Finally, we used the
23

amount of 720 samples (equivalent to 720 seconds) in our evaluation.

4.3

Proposal evaluation

Driver C has five trips and makes the fewest trips, so we use the first 5 trips for each driver.
Just as done by Girma et al. (1), we divided each driver’s dataset into 120-second windows
(120 samples) with a shift of 60 seconds, as shown in Figure 4.4. The overlapping window is
important to smooth the flow of sequence, capture sequential information, and increase training
data size for better generalization (1). So we formed a new dataset with each driver’s windows.
We apply a cross-validation with five folds in this dataset to analyze each classifier. We also
made a binary distinction for each driver with the others.
Figure 4.5a shows the accuracy of each classifier in each method using the literature method
and the proposed. We note that our approach improved the accuracy of all evaluated classifiers.
The improvement may be because the algorithms evaluated in this work do not intrinsically consider the temporal characteristics of the data. Bandt-Pompe symbolization and the values of
Information Theory used in this work add global, local and temporal information to the input of
these algorithms.
Due to the construction of the dataset, we have a minority of the data as being in the true
class (owner-driver - 25%) and a majority in the false class (theft - 75%). To evaluate the sensitivity and specificity of the classifier, we observed Figure 4.5b that shows the value of the ROC
AUC. The AUC value varies from 0.5 to 1.0. The closer to 1.0, the better the classifier. However,
closer to 0.5 means it is effectively not classifying, as it is similar to a random classification. The
AUC values show that in our proposal, the classifiers perform better in finding true cases (owner)
and false ones (theft).
We further assessed the classifiers based on precision and recall to obtain a more comprehensive qualitative perspective. Our observations revealed that incorporating Information Theory
measures significantly enhanced the performance of all classifiers across the four metrics employed. Notably, the KNN, RBF SVM, and Random Forest models achieved scores very close to
the maximum across all evaluated metrics.
According to the literature, another metric we look at is that the total time for calculating Information Theory measures and training is longer in the proposed method than in preprocessing.
Figure 4.6 shows that to generate the Bandt-Pompe symbolization and calculate the information measures (Statistical Complexity, Shannon Entropy and Fisher Information) the time was
significantly longer than using the standard preprocessing in the literature. However, the time
to maximum for the sample size we used (720 samples) does not exceed 30 milliseconds. The
high difference is because the other strategies are high-speed. However, based on the requirements of driver detection applications, this execution time still preserves the effectiveness of our
proposal.

24

(a) Accelerator position

(b) Zoom of Accelerator position

(c) Steering wheel angle

(d) Zoom of Steering wheel angle

(e) Car speed

(f) Zoom of Car speed

(g) Cooling temperature

(h) Zoom of Cooling temperature

Figure 4.1: Complexity-Entropy planes for each trip with D = 7.

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(a) Accelerator position

(b) Zoom of Accelerator position

(c) Steering wheel angle

(d) Zoom of Steering wheel angle

(e) Car speed

(f) Zoom of Car speed

(g) Cooling temperature

(h) Zoom of Cooling temperature

Figure 4.2: Fisher-Shannon planes for each trip with D = 7.

26

Figure 4.3: Measurements for different parameters in the Complexity and Entropy calculation.

Figure 4.4: Sliding windows on features.
The working environment of the experiment was as follows:

• CPU 11th Gen Intel Core i7-1165G7 @ 2.80GHz × 4.
• GPU Intel Corporation TigerLake-LP GT2 [Iris Xe Graphics].
• RAM 16GB.

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(a) Accuracy score

(b) ROC AUC

(c) Precision score

(d) Recall score

Figure 4.5: Experiment results.

Figure 4.6: Time for preprocessing.

28

5
Final Considerations

This work aims to improve the performance of machine learning models by adding measures
from Information Theory to time series data in the particular case of automotive driving data.
It was possible to compare the preprocessing described in the literature with a method that
extracts measures from Information Theory for driver identification. We have shown that the
proposal improved the performance of all classifiers analyzed for the parameters considered to
calculate the Statistical Complexity, Permutation Entropy, and Fisher Information measures.
We observed that, with Information Theory measures, the models can identify a driver with
an accuracy above 94.5% for the classifiers used, and some classifiers getting scores very close
to maximum. In addition, some algorithms also achieved scores very close to the maximum for
presicion, recal and ROC AUC metrics.
It is essential to consider that the total time for calculating Information Theory measures and
training is longer in the proposed method, but the case of greater processing considered in this
work is equivalent to a maximum of 30 ms for the environment used. We also intend to apply
the proposed method to other datasets for driver identification and use it in other classification
applications.
Additionally, we aim to assess the models using datasets featuring various class balances,
incorporate additional public datasets, and evaluate deep learning algorithms. Finally, as future
work, we may include the following topics: optimization of classifier hyperparameters, utilization
of feature selection techniques, and incorporation of other measures: False Acceptance Rate
(FAR) and False Rejection Rate (FRR).

29

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