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Human Driver Behavior Classification from Partial Trajectory Observation

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As autonomous vehicles are being tested on public roads, they must be able to share the road safely with human-driven vehicles. To ensure safety, autonomous vehicles must be capable of accurately estimating human drivers' intentions and their future trajectories. While there has been extensive research in this area, most of the existing approaches do not take into account the individual drivers' personalities and the patterns these personalities reflect on the trajectories of the vehicles. We tackle this issue by proposing a novel method of extracting high-level features from raw vehicle trajectory data and classifying drivers into behavioral classes based on their level of aggressiveness. We demonstrate how the identification of a driver's behavior improves the accuracy of the short-term trajectory prediction problem by introducing a prior knowledge on their behavior.
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Human Driver Behavior Classification from
Partial Trajectory Observation
Angelos Mavrogiannis
MS Student
Intelligent Control Lab
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Email: angelosm@andrew.cmu.edu
Changliu Liu
Assistant Professor
Intelligent Control Lab
The Robotics Institute
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Email: cliu6@andrew.cmu.edu
As autonomous vehicles are being tested on public roads,
they must be able to share the road safely with human-driven
vehicles. To ensure safety, autonomous vehicles must be
capable of accurately estimating human drivers’ intentions
and their future trajectories. While there has been exten-
sive research in this area, most of the existing approaches
do not take into account the individual drivers’ personali-
ties and the patterns these personalities reflect on the trajec-
tories of the vehicles. We tackle this issue by proposing a
novel method of extracting high-level features from raw ve-
hicle trajectory data and classifying drivers into behavioral
classes based on their level of aggressiveness. We demon-
strate how the identification of a driver’s behavior improves
the accuracy of the short-term trajectory prediction problem
by introducing a prior knowledge on their behavior.
Nomenclature
qi
tState of agent iat time t
QtState of all agents at time t
ξ0tHistorical trajectory information for agent i
Ξ0tMulti-agent historical trajectory information
BBehavioral space
biBehavioral class of agent i
BBehavioral classes of all agents
1 Introduction
Autonomous driving research has drawn a lot of atten-
tion and resources recently, both in the academia and in the
industry. A major challenge impeding the massive deploy-
ment of autonomous vehicles in public roads lies in the un-
certainty introduced by the presence of human drivers in
mixed traffic scenarios. A human driver can be flexible to
the surroundings and accurately infer the future behaviors
of road agents given past experience, but a self-driving car
is not yet capable of emulating this on-the-spot decision-
making process. Furthermore, while autonomous vehicles
might be able to successfully communicate with each other
and plan their motion in a centralized manner in the future,
they will still need to be able to anticipate the future actions
of their human counterparts in order to ensure safety and be-
come valuable members of the society. This is a very chal-
lenging problem due to the stochasticity and heterogeneity
of human drivers, who can often act unexpectedly, leading
to dangerous situations and traffic accidents. Research in
vehicle trajectory prediction has been extensive, constantly
advancing the state-of-the-art with the rise of deep learning
methods. However, there has not been significant focus on
the human personality perspective and its impact on road be-
haviors. While many of the accidents caused in roads can
originate from spontaneous mistakes made by human drivers,
another source is the reckless behavior exhibited by some
drivers in a repetitive manner. For example, some drivers
might often move from one lane to the other without a pri-
ori using a turn signal light or by taking steep turns instead
of smoothly transitioning to the adjacent lane. As a result,
behaviors like this might not always lead to accidents, how-
ever they increase the probability of a crash. Therefore, the
identification of potentially risky drivers is crucial in order to
accurately estimate the future actions of human drivers and
plan the motion of autonomous vehicles ensuring safety.
Our research hypothesis is that leveraging inherent cues
representative of drivers’ personalities can lead to more ac-
curate predictions for their future trajectories. The main con-
tributions of this work can be described as following:
1. We propose a novel data-driven framework of identify-
ing different behavioral classes of drivers and classify-
ing them into these categories.
2. We do not fix the number of driving behaviors a priori,
but we define it based on the available data.
3. The behavior classification framework is computation-
1
ally efficient and scales better with data compared to
similar methods.
2 Related Work
We propose a framework for classifying human driver
behaviors and we apply it to the problem of trajectory pre-
diction. In this section, we discuss about related work both
in the area of human driver classification and in the area of
motion prediction.
2.1 Motion Prediction
Adapting the work of Rudenko et al. [1] in human mo-
tion prediction to vehicle trajectory prediction, we divide
the problem of trajectory prediction into the following three
components.
1. Stimuli, which include the agent’s motion intent as well
as other directly or indirectly observable features en-
coded in the environment. Information related to the
agent’s motion intent usually consists of historical tra-
jectory information about its state, which can include
positional coordinates, velocities or accelerations ac-
quired via on-board sensors or measured from a global
point of view (e.g. a camera-equipped drone from
above). On the other hand, static and dynamic ob-
stacles and constraints, including pedestrians and other
road agents can be considered as environmental features
that implicitly impact an agent’s motion. We can also
consider the different driving scenarios (urban driving,
highway driving) as environmental features which also
affect the behavior of road agents. Both the agent’s mo-
tion intent and the environmental features can be seman-
tic: expressed in a high-level context, like raw vehicle
trajectory data, or auxiliary: constitute of encodings of
various important information with fixed dimensional-
ity and are often hard to interpret, such as data derived
directly from a LiDAR sensor.
2. Prediction, which corresponds to the two major cate-
gories in vehicle motion prediction:
(a) Maneuver prediction, where the output of the pre-
diction consists of discrete states, such as driving
straight, turning right or turning left at an intersec-
tion [2].
(b) Trajectory prediction, where the exact future state
of an agent is predicted. For example, in [3], the
predicted values are the future lateral coordinate
and the longitudinal velocity of a vehicle. Some
other methods [4] propose a multi-modal solu-
tion using Gaussian mixture models over predicted
states or sample from generative models [5].
3. Modeling approach, which addresses the way different
methods represent and solve the motion prediction prob-
lem.
(a) Physics-based methods predict future trajectories
by developing handcrafted dynamical models, as
in [6] and [7]. These methods can be accurate
and reliable for a short prediction horizon, how-
ever they are known to underperform in long-term
prediction problems and therefore they are gradu-
ally replaced by better-performing learning-based
methods. A survey on physics-based methods can
be found in [8].
(b) Data-driven methods learn the motion models of
road agents from observed trajectory data. Tran et
al. [9] construct three-dimensional Gaussian pro-
cess regression models from two-dimensional tra-
jectory patterns and compare the likelihoods of
the observation data for each individual regression
model. Schlechtriemen et al. [10] use a Naive
Bayes approach followed by a Hidden Markov
Model (HMM) where the states of the model cor-
respond to the maneuvers extracted from raw tra-
jectory data and use this framework to detect lane
changes. Liu et al. [11] address the decision mak-
ing problem in highway driving as an optimal con-
trol problem, which is solved through a Hidden
Markov Model formulation, defining the inten-
tion for a set of discrete maneuvers as the states
and predicting future trajectories using an empiri-
cal model which contains adjustable parameters to
accommodate the driver’s time-varying behavior.
However, most of these approaches do not model
the interaction between different road agents in the
future trajectories.
(c) Deep learning methods also constitute data-driven
methods, however they are mentioned separately,
given their wide use and remarkable success in
tackling trajectory prediction problems. More
specifically, recurrent neural networks (RNN) have
been used in vehicle trajectory prediction prob-
lems [12], [2], [4] and especially Long Short-Term
Memory (LSTM) networks, given their ability to
learn long-term dependencies between the inputs.
Altch´
e et al. [3] use an LSTM network, which re-
ceives information regarding an ego vehicle and a
fixed number of surrounding vehicles and outputs
future sequences of coordinates for the ego vehi-
cle. Messaoud et al. [13] use an Encoder-Decoder
RNN architecture with an Attention mechanism
[14] in order to model the spatio-temporal inter-
actions between a road agent and its surrounding
vehicles and predict its future trajectory. In this
work, all agents in the vicinity of the ego vehi-
cle are considered for the prediction task. Other
approaches [15], [16] combine Imitation Learn-
ing with Generative Adversarial Networks (GAN)
under a framework [17] to predict future vehi-
cle trajectories. Furthermore, methods combining
RNN and Convolutional Neural Networks (CNN)
emerged. Deo et al. [18] combined LSTM with
CNN to predict future vehicle trajectories in high-
way driving scenarios. However, these methods
are not considering the human personality factor
and fail to capture underlying traits in the human
2
driver behavior which are responsible for repeat-
ing patterns, such as reckless driving. As a re-
sult, some of these methods only perform well on
specific datasets or even in specific demografic re-
gions. This motivates the study of human driver
behavior classification, which is discussed in the
next subsection.
2.2 Driving Behavior
The term vehicle behavior prediction in literature has
been used in the same context as vehicle motion prediction,
indicating that the predicted values are either future trajec-
tories or discrete maneuvers. However, in this work, we use
the term behavior to indicate the unique personality traits of
human drivers, which influence their actions on the road.
There is a variety of factors that affect human driv-
ing behavior according to studies. Some factors include
the driver’s age, gender, personality, potential disabilities
and other personal characteristics [19], while others include
psychological aspects such as driving under the influence,
drowsy driving and so on [20]. There have been some meth-
ods to classify drivers into categories based on vehicular fac-
tors such as positions, acceleration, speed, throttle responses,
steering wheel measurements, lane changes, and brake pres-
sure. More specifically, Chandra et al. [21] proposed a new
metric to classify driver behaviors based on computational
graph theory concepts and social traffic psychology. In [22],
the inter-agent interactions are represented using unweighted
and undirected traffic graphs, again for the purpose of classi-
fying driver behaviors with an application to trajectory pre-
diction. Similarly, Chandra et al. [23] used a combination of
spectral graph analysis and deep learning to predict both fu-
ture trajectories and road-agent behaviors. Finally, Cheung et
al. [24] identified driver behaviors from vehicle trajectories
via a user study and applied their method on motion plan-
ning. However, some limitations of these methods are that
they are defining a priori the number of different driving be-
haviors, and they can be computationally intractable as the
amount of data increases.
3 Problem Statement
Let qi
tbe the state of an agent i, with qiR2. The state
includes the lateral and longitudinal coordinates (x,y)of an
agent iat time t, measured as shown in Fig. 1.
qi
t= (xi
t,yi
t)(1)
Let Qtbe the state of all nagents of interest at time t:
Qt={(xi
t,yi
t), ..., (xn
t,yn
t)}(2)
Then, let Ξt0t1be the historical trajectory information for
all nvehicles of interest from time t0to time t1. For sim-
plicity we assume t0=0.
Ξ0t1= (Q0,Q1,...,Qt1)(3)
Fig. 1. The coordinates of an agent iare measured from the left-
most edge of the road laterally and from the beginning of the road
segment under consideration, longitudinally, until the front center of
the vehicle (represented by a red dot in the figure).
The solution of the trajectory prediction problem in a multi-
agent setting lies in the estimation of the probability of ob-
serving a future sequence ΞtTgiven a partial observation
in the present Ξ0t1:
P(ΞtT|Ξ0t1)(4)
According to our research hypothesis, an agent’s behav-
ior heavily influences its future trajectory, therefore we can
rewrite the previous probability in the following way:
P(ΞtT|Ξ0t1) =
B
P(ΞtT|Ξ0t1,B)P(B|Ξ0t1)
(5)
where Bis a tuple consisting of all the behavioral classes of
all nagents and Bis a discrete behavioral space that we are
going to define.
B= (b1,b2,...,bn)
biB(6)
Expanding the second probability from the right hand size of
equation (5)we get:
P(B|Ξ0t1) = P(b1,b2,...,bn|Ξ0t1) =
in
P(bi|Ξ0t1)
(7)
Therefore, we need to estimate the probability of an agent i
belonging to a specific behavioral class bBgiven a multi-
agent trajectory sequence Ξ0tin the past and expand this
computation for all nagents.
Now we focus on the first probability of the right hand
side of equation (5), and by decomposing the historical
multi-agent information, we can write it as following:
P(ΞtT|Ξ0t1,B) = P(Qt,Qt+1,...,QT|Ξ0t1,B)(8)
3
The basis of our research hypothesis lies on the fact that an
agent’s behavior heavily influences its trajectory, therefore
we can assume that given the knowledge of the behavioral
classes Bof all agents, the future trajectories only depend on
the last element of Ξ0t1. This assumption is then compat-
ible with the following equation:
P(Qt,Qt+1,...,QT|Ξ0t1,B) = P(Qt,Qt+1,...,QT|B)
(9)
Using the chain rule, we get the following equation:
P(Qt,Qt+1,...,QT|B) = P(QT|QT1,QT2,...,Qt,B)·
P(QT1|QT2,QT3, ..., Qt,B). . . P(Q1|Qt,B)
(10)
We now use a Markov assumption, according to which the
state of all agents Qt+1at every timestep only depends on
the value of the state during the previous timestep Qt, but
not on the values of the state before the previous timestep
Qt1,Qt2.. . , Q0.
Qt+1Qt1|Qt(11)
Based on the Markov assumption we can write the final equa-
tion of our model:
P(ΞtT|Ξ0t1) =
T
P(Qt+1|Qt,B) =
T
in
P(qt+1|Qt,B)
(12)
4 Methodology
4.1 Overall Method
The proposed method can be decomposed into the fol-
lowing components:
1. Preprocessing where we prepare the data.
2. Feature Extraction where we compute high-level fea-
tures available from the data.
3. Low-dimensional representation, which is achieved
by applying the Principal Component Analysis (PCA)
[25] algorithm.
4. Behavioral Clustering, where we form the behavioral
clusters by applying the K-means [26] algorithm on the
low-dimensional data distribution.
5. Online Behavior Classification, which is achieved by
comparing the performance of K-Nearest Neighbors
(KNN), Logistic Regression (LR) and a Deep Neural
Network (DNN) on classifying a driver’s behavior given
their descriptive statistics.
6. Trajectory Prediction, where we use a Long Short-
Term Memory (LSTM) [27] neural network in order to
infer the future position of an agent given information
about nearby agents as well as their behavioral labels.
The pipeline is illustrated in Fig. 3.
Fig. 2. Screenshot taken from the simulator we developed on
Python. The red dot represents the ego vehicle and the black dots
represent the reference vehicles which are nearby the ego vehicle for
each timestep.
4.2 Preprocessing
We begin by identifying the active vehicles in our data
for every timestep, and we save their vehicle ID as well as
their trajectory information. Additionally, we develop a sim-
ulator on Python that receives as input the number of lanes
and the coordinates of every vehicle for all timesteps and il-
lustrates the trajectories of the vehicles, so that we can com-
pare the different driving behaviors that emerge from our
model. As seen in Fig. 2, the red dot signifies the ego agent,
while the black dots represent the nearby agents. We pre-
process the data in order to facilitate the performance of the
Principal Component Analysis. For every feature fiof the
data, if µiis its mean and σiis its standard deviation through-
out the entire dataset, we subtract the mean from it and divide
by the standard deviation.
f0
i=fiµi
σi
(13)
In this way, every feature in the data has a mean value µ0
i=0
and standard deviation σ0
i=1.
4.3 Feature Extraction
To define the behavioral space B, we will attempt to un-
cover underlying patterns in the trajectories demonstrated by
drivers, which indicate their aggressiveness on the road. We
believe that there are some descriptive statistics that capture
the entire trajectory sequence of a certain driver and there-
fore accurately describe their behavior on the road. These
are shown in Table 1.
For the lateral direction of motion, we are interested in
the average values of an agent’s velocity and acceleration as
an indication of the deviation of an agent from its current
lane. As the arithmetic mean does not capture all the im-
portant characteristics that we believe are indicative of ag-
gression, we also take into account the maximum values of
4
Fig. 3. The pipeline of the proposed method starts with preprocessing the data and extracting features from it, applying PCA to reach a
low-dimensional representation and forming behavioral clusters with K-means. Finally, K-nearest neighbors, Logistic Regression and a Deep
Neural Network are used for online inference of a behavioral label, which is fed to a Deep Neural Network which predicts future trajectories.
Table 1. Descriptive statistics for every driver used in the Principal
Component Analysis
Statistical Metric Symbol Units
Average lateral velocity |¯
υx|m
s
Maximum lateral velocity |υmax
x|m
s
Standard deviation of lateral velocity σ(υx)m
s
Average longitudinal velocity ¯
υym
s
Maximum longitudinal velocity υmax
ym
s
Standard deviation of longitudinal velocity σ(υy)m
s
Average lateral acceleration |¯ax|m
s2
Average longitudinal acceleration ¯aym
s2
Average speed relative to the traffic flow υf low
ym
s
Average speed relative to the preceding vehicle υprec
ym
s
an agent’s lateral velocity which correspond to potential ag-
gressive lane changes as well as the standard deviation of lat-
eral velocity in order to capture the fluctuation of an agent’s
speed as a metric of irregular behavior.
For the longitudinal direction of motion, we focus on
the average values of an agent’s velocity and acceleration,
as well as the maximum and standard deviation of its veloc-
ity. The intuition behind this lies on the fact that aggression
does not only depend on large values of speed, but also on
other factors, such as patterns of continuous deceleration and
acceleration. We believe that an irregular behavior can be
also identified by comparing an agent’s road behavior with
the behavior of its surrounding agents. As such, we define
a bounded box surrounding an agent for every timestep, and
we measure the average longitudinal velocity for all agents in
the box. Then, we subtract this quantity from our agent’s ve-
locity and we use this difference to quantify the speed differ-
ence between its velocity and the velocity of its neighboring
vehicles. Finally, as an extension to the previous metric, we
also take into account the longitudinal velocity of an agent
relative to the longitudinal velocity of the leading agent (the
preceding vehicle). A large value of an agent’s velocity and
a small value of its leading agent’s velocity corresponds to
an aggressive behavior.
4.4 Low-dimensional representation
After acquiring a set of 10 descriptive statistics for ev-
ery driver in the dataset, we project these statistics to a
low-dimensional space using Principal Component Analysis
(PCA) in order to gain some further insight in determining
the most dominant features that correspond to aggressive be-
haviors. We focus on the two most dominant components,
which capture the largest percentage of the total variance of
the data.
4.5 Behavioral Clustering
Having acquired a low-dimensional space consisted of
the two principal components of the data, we apply the K-
means clustering algorithm in order to define an optimal way
of identifying the different behavioral classes according to
the distribution of the data in the dimensional space defined
by the two dominant principal components. To determine the
optimal number of clusters kfor the K-means algorithm we
5
use two different methods:
1. The elbow method [28]
2. The silhouette method [29]
According to the elbow method, we calculate the Within-
Cluster-Sum of Squared errors (WCSS) [30] for different
values of kand we choose the value of kthat minimizes the
errors. However, the errors keep decreasing as we increase
k, so we need to bound kso that we do not have a large num-
ber of clusters but at the same time we need to maintain a
low value of errors. We believe that a low value of k(e.g.
k=2) is not enough to capture the diversity of the driving
behaviors, as it is possible that the aggressive drivers con-
stitute only a small part of the total number of drivers in the
dataset, however they get classified as outliers and eventually
get merged with other drivers who are not equally aggressive
due to the low value of k. Therefore, we set the following
constraint to the selection of k:
k>2 (14)
As an additional method to validate the optimal number of
clusters k, we use the Silhouette method. The silhouette
method measures how similar a point is to its own cluster
compared to other clusters. A high value is desirable and in-
dicates that the point is placed in the correct cluster. Again,
we calculate the silhouette value for different numbers of k
and we choose the optimal number of clusters.
4.6 Online Behavior Classification
At this point we have defined the behavioral space B,
we know the behavioral labels Bof all agents, and therefore
we can estimate the probability:
P(bi|Ξ0t1)(15)
To this end, we are going to use a set of supervised learning
algorithms to infer the behavioral class of a driver given his
descriptive statistics which were established during the fea-
ture extraction stage. More specifically we train a K-Nearest
Neighbors model, a Logistic Regression model, and a Deep
Neural Network in a multiclass classification setting. The
neural network consists of two hidden layers with 256 hid-
den units on each layer, followed by ReLU activation func-
tions and a so f t max layer in the output layer. The models
receive the descriptive statistics of a training set of drivers
based on partial trajectory observation, as well as their be-
havioral class labels from the K-means algorithm and pre-
dict the behavioral class labels of a number of drivers in a
test set. Finally, we compare these algorithms and discuss
the trade-off between computational complexity and model
accuracy.
4.7 Trajectory Prediction
To test our research hypothesis, we are going to apply
the Vehicle Behavior Classification framework we developed
Table 2. The set of reference vehicles in the vicinity of the ego vehi-
cle for the task of trajectory prediction.
Description Symbol
Preceding vehicle on current lane f
Nearest vehicle on the right lane r
Nearest vehicle on the left lane l
Following vehicle b
Preceding vehicle of f f f
Preceding vehicle of r f r
Preceding vehicle of l f l
Following vehicle of r br
Following vehicle of l bl
to a trajectory prediction problem, estimating the probability
from equation (12):
P(qt+1|Qt,B)(16)
To this end, we are going to use a Long Short-Term Mem-
ory (LSTM) neural network that receives information about
the states of the ego vehicle qego
t, which represents the au-
tonomous vehicle making the prediction, the states of a set
of reference vehicles in the vicinity of the ego vehicle Qt, as
well as the behavioral labels of these vehicles Band predicts
the future state of the ego vehicle qego
t+1at a predefined short-
term time horizon. Following the work in [3], we consider
a set of nine reference vehicles, which form the following
tuple:
(f,r,l,b,f f ,f r,f l,br,bl)(17)
Table 2 describes each of the reference vehicles used. For
every timestep, we extract the states of these reference vehi-
cles and save them during the preprocessing stage, and when
one of these vehicles does not exist at a certain timestep, we
consider the states as zero. A spatial example of an ego ve-
hicle and the reference vehicles is shown in Fig. 4. The mo-
tivation behind the selection of these vehicles is based on the
realistic assumption that the ego vehicle making the predic-
tion can only acquire information regarding the vehicles in
its proximity, due to the limitations of its sensors. The ad-
dition of the vehicle f f in front of the leading vehicle fof
the ego vehicle is an attempt of estimating the traffic flow for
the current lane, as, for example, in a traffic jam situation, f
could be moving very slowly but at the moment f f starts to
move, this indicates fwill also start to move and as a result
the ego vehicle will follow up shortly.
The neural network consists of a layer of 256 LSTM
cells, followed by a fully connected layer of 128 units and
6
Fig. 4. An example illustrating the ego vehicle making predictions
and the reference vehicles considered in its vicinity. Each vehicle
has a number on the upper right part, corresponding to its behavioral
cluster.
ReLU activation and the output layer which results in two
outputs, the lateral and the longitudinal position of the pre-
dicted vehicle in the next timestep.
The neural network predicts the state of the ego vehicle
qego
t+1at the next timestep, but it can also predict its state fur-
ther in the future in the following way: We acquire the pre-
dicted coordinates of the ego vehicle for timestep t+1, and
by inspecting our data, we observe the active reference vehi-
cles in the vicinity of the ego vehicle at timestep t. Therefore,
we use the neural network to predict their coordinates at the
next timestep t+1 and by doing so we have predicted Qt+1.
If we repeat this procedure by feeding the predicted state in-
formation to the network, we can predict for more timesteps,
however, it is evident that if we attempt to predict for too
many timesteps, the error will propagate and the accuracy
will drop significantly as time flows.
5 Experiments and Results
The dataset we are using to evaluate the proposed
method is the Interstate 80 (I-80) freeway dataset from the
Next Generation SIMulation (NGSIM) [31] program. The
dataset consists of 2355 trajectories corresponding to unique
drivers, which were obtained from video analysis. The video
was recorded on eastbound I-80 in the San Francisco Bay
area in Emeryville, CA, on April 13, 2005. The road seg-
ment under consideration is approximately 500 meters in
length and consists of six freeway lanes including a high-
occupancy vehicle (HOV) lane. The dataset provides a total
of 45 minutes of raw vehicle trajectory data, segmented into
three 15-minute periods: 4:00 p.m. to 4:15 p.m., 5:00 p.m.
to 5:15 p.m., and 5:15 p.m. to 5:30 p.m. Some of the ad-
vantages of this dataset are that it has been widely studied in
literature, and, except for the coordinates of the vehicles, it
also provides information about the preceding and following
vehicles of each vehicle, as well as lane identifiers. Finally,
it offers the coordinates of the vehicles in the format we de-
scribed during the problem statement, therefore it is suitable
for evaluating our method.
After preprocessing the data and performing feature ex-
traction, we apply the PCA algorithm on the extracted de-
Fig. 5. First and second principal components of the PCA algorithm,
capturing 54% of the total variance of the data.
Fig. 6. Within-Cluster Sum of Squared errors for different values of
kaccording to the elbow method.
scriptive statistics. We retain the two first principal compo-
nents, as they capture 54% of the total variance of the data.
The low-level representation we get from the PCA algorithm
is shown in Fig. 5, where we observe a pattern of linearity be-
tween Principal Components 1 and 2. As we can see in Fig. 6
the recommended optimal number of clusters is k=2, since
an elbow at the curve usually represents the point at which
we start to have diminishing returns. However, according to
our constraint, the number of clusters should satisfy the con-
dition:
k>2 (18)
Therefore, we use the Silhouette method as an additional tool
to define the optimal number of clusters. Respecting the con-
straint we set on kand ignoring the first peak at k=2, we can
see in Fig. 7 that the optimal number of clusters is the second
largest silhouette value:
k=4 (19)
7
Fig. 7. Silhouette values for different number of clusters k.
Fig. 8. The four behavioral clusters formed using K-means. The
black dots represent the center of each cluster, respectively.
Proceeding with k=4 as the number of clusters, we apply the
K-means clustering algorithm on the low-dimensional space
and we get the four clusters shown in Fig. 8. To evaluate
the defined behavioral classes, we compare the ten statistics
used in the Principal Component Analysis and examine how
these values differ throughout the four clusters. We show the
results from the comparison for three representative statis-
tics (υmax
y,|υmax
x|,υf low
y) which we believe are the most in-
dicative of the differences between the four behaviors. Ob-
serving Fig. 9, we can see that the maximum longitudinal
velocity as well as the relative velocity to the traffic flow in-
creases from cluster 1 to cluster 4, however the maximum
lateral velocity is showing a decreasing trend. We can cor-
relate these results with the distribution we saw in the di-
mensional space defined by principal components 1 and 2.
It is clear that the most dominant feature is the longitudinal
velocity, which corresponds to Principal Component 1 and
increases throughout the cluster, whereas the lateral velocity
corresponds to Principal Component 2, and shows a slightly
decreasing tendency. This can be explained rationally, con-
sidering that drivers who move very fast on the road in the
Table 3. The set of reference vehicles in the vicinity of the ego vehi-
cle for the task of trajectory prediction.
Algorithm KNN Logistic Regression DNN
Runtime (s) 0.025 0.06 1.4
Accuracy (%) 87 86 97
longitudinal direction of motion tend to stay in the current
lanes and avoid lane changes more than the drivers who move
in a slower speed. Overall, the driving behavior from cluster
1 to cluster 4 ranges from timid to aggressive.
At this point we know the behavioral classes of all
drivers in the dataset based on our previous analysis, and
we want to train a model that learns to map the descriptive
statistics of an agent to its behavioral class. We split the de-
scriptive statistical data in a training and test set, keeping
80% of the drivers for training and 20% of them for testing.
We train a Logistic Regression model, a K-Nearest Neigh-
bors model with k-fold cross validation, and a neural net-
work consisting of two hidden layers with ReLU activation
functions and a so f t max layer in the output layer. The learn-
ing rate is η=0.001, the objective function is the Cross En-
tropy Loss and the network is trained for 200 epochs with
the Adam optimizer. Simulating a realistic scenario, an ego
vehicle navigating in public roads will need to obtain infor-
mation through its sensors and perform the behavior classifi-
cation in an online setting, therefore except for the accuracy
of the model, we also care about the computational complex-
ity. Therefore, after conducting several experiments training
all models and testing multiple times, we present the results
in Table 3. As we can see in the table, as well as in Fig. 10
and Fig. 11, KNN and Logistic Regression are very fast to
train and demonstrate good results in the classification prob-
lem (Accuracy: 87% and 86% respectively), while the DNN
has a larger runtime (1.4s) but achieves almost perfect accu-
racy (97%). The final choice of the classification algorithm
depends on the trade-off between the accuracy and the com-
putational complexity, since the runtime will increase as the
amount of data increases. For the purpose of our study, we
will continue with the DNN and prioritize accuracy over time
complexity.
Now that we have defined the behavioral space and de-
veloped a mechanism for human driver behavior classifica-
tion, we can use the behavioral classes of the agents to pre-
dict their future trajectories. We train our LSTM network
on 80% of the data for 30 epochs using the Adam optimizer
and a learning rate of η=0.0005. The duration of the se-
quences considered is 20 seconds and the prediction hori-
zon is 1 second in the future. During the first experiment,
the network receives as input the states of the ego vehicle
and its 9 surrounding vehicles, while during the second ex-
periment, the network additionally receives the behavioral
classes of the respective agents. Testing on the remaining
20% of the data, we observe that the addition of the behav-
8
Fig. 9. Bar charts illustrating the distribution of three important descriptive statistics of drivers throughout the four different behavioral clusters.
Fig. 10. Accuracy of the algorithms used for the online behavior
classification.
Fig. 11. Runtime of the algorithms used for the online behavior clas-
sification.
ioral classes increases the accuracy of the prediction by 56%
longitudinally and 22% laterally. The Root Mean Squared
Error (RMSE) per vehicle is used as the comparison metric,
as shown in Table 4.
Table 4. Root mean squared error values per vehicle for 1 second
prediction horizon
Without Behavioral Classes With Behavioral Classes
Longitudinal RMSE (m)5.60 2.44
Lateral RMSE (m)0.92 0.71
6 Conclusion and Future Work
We proposed a framework for identifying human driver
behaviors in behavioral classes, classifying drivers in them,
and using them to predict their future trajectories. We
demonstrated that the addition of the behavioral classes to
our LSTM predictor improves the accuracy of the short-term
future predictions both in the longitudinal and in the lateral
direction of motion. However, our method has some limi-
tations. There is an implied linearity assumption behind the
use of PCA for projecting the descriptive statistics to a low-
dimensional space. In the future, we could try to use a Varia-
tional Autoencoder (VAE) to project the descriptive statistics
to a latent space and consider non-linearities as well. Fur-
thermore, our model has only been evaluated on the NGSIM
I-80 dataset, so we need to apply it on other publicly avail-
able datasets as well in order to generalize its validity. Fi-
nally, as part of future work, we could improve the prediction
part of our framework, using a more advanced neural archi-
tecture, such as an Encoder-Decoder model, and extend the
prediction horizon.
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