Anomaly Detection in Multi-Agent Trajectories for Automated Driving
Authors: Julian Wiederer
Arij Bouazizi
Marco Troina
Ulrich Kressel
Vasileios Belagiannis
Venue: CoRL2021 Poster (2021)
Keywords: Anomaly Detection
Multi-Agent Trajectory
Graph Neural Networks
Automated Driving

Abstract: Human drivers can recognise fast abnormal driving situations to avoid accidents. Similar to humans, automated vehicles are supposed to perform anomaly detection. In this work, we propose the spatio-temporal graph auto-encoder for learning normal driving behaviours. Our innovation is the ability to jointly learn multiple trajectories of a dynamic number of agents. To perform anomaly detection, we first estimate a density function of the learned trajectory feature representation and then detect anomalies in low-density regions. Due to the lack of multi-agent trajectory datasets for anomaly detection in automated driving, we introduce our dataset using a driving simulator for normal and abnormal manoeuvres. Our evaluations show that our approach learns the relation between different agents and delivers promising results compared to the related works. The code, simulation and the dataset are publicly available.

Anomaly Detection in Multi-Agent Trajectories for Automated Driving
Julian Wiederer1.2 Arij Bouazizi Marco Troina'
Urrich Kressel Vasileios Belagiannis
Merredes-Benz AG Ulm University
{julian wiiderer,, arij. bouuzizzaziz, marco. troina, ulrich ihch.... www.eel..eeeeeeeeeeeeeeaecelllee / odaimeer.d vasileios. vasileios.belage annisuuni-ulm
Abstract:
Human drivers can recognise fast abnormal driving situations to avoid accidents. Similar to humans, automated vehicles are supposed to perform anomaly detec- tion. In this work, we propose the spatio-temporal graph auto-encoder for learning normal driving behaviours. Our innovation is the ability to jointly learn multiple trajectories of a dynamic number of agents. To perform anomaly detection, we first estimate a density function of the learned trajectory feature representation and then detect anomalies in low-density regions. Due to the lack of multi-agent trajectory datasets for anomaly detection in automated driving, we introduce our dataset using driving simulator for normal and abnormal manoeuvres. Our eval- uations show that our approach learns the relation between different agents and delivers promising results compared to the related works. The code, simulation and the dataset are publicly available'.
Keywords:
Anomaly Detection, Multi-Agent Trajectory, Graph Neural Net- works, Automated Driving
Introduction
A tired and inattentive driver often breaks the driving regulations by entering, for example, the op- posite lane. This abnormal driving behaviour is usually early detected by the participating human drivers who react early enough prevent harmful situations. Similar humans, autonomous vehi- cles should perform anomaly detection as part of the automated driving modules [1, 2, 3J. Learning, thus, normal driving behaviour is necessary for detecting anomalies.
Anomaly detection is develoeee approach computer vision, for instance, to spot abnormal human behaviour [4, 5] or vehicle motion in traffic [6]. In robotics, the approach detects hardware failures of self-flyin delivery drones [7] or helps a wheeled robot to navigate around unseen obsta- cles [8]. Although these approaches can be transferred to automated driving, they only consider single agent in a static environment. That is barely the case for autonomous vehicles, where multiple agents influence each other through constant interactions. In this work, present approach to detect anomalies of multi-agents based on their trajectories.
We propose spatio-temporal graph auto-encoder (STGAB) for trajectory embedding. Similar to the standard auto-encoder, it learns a latent representation multi-agent trajectories. The main in- novation of STGAE is the ability simultaneously learn multiple trajectories for dynamic number of agents. In a second step, we perform kernel density estimation (KDE) on the latent representation of the STGAE. We empirically observe that KDE captures well the distribution of the normal trajec- tory data. During the test phase, we detect anomalies in low-density regions of the estimated density. introduce
To evaluate approach, for automated driving. The current automotive datasets [9, 10] contain many hours of recordings, but lack anomalies due to the rareness of abnormal driving situations, whereas anomaly detection
dataset for multi-agent trajectory anomaly detection
Project page:
highwyy
5th Conference on Robot Learning (CoRI. 2021), London, UK.

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datasets [11. 12] have the required anomaly labels but are not relevant to automotive and automated driving problems. Finally, scenario staging is often applied in behaviour modelling [13], but its prohibitive for driving anomalies since it will put the actors into life danger. For these reasons, we develop a multi-agent simulation and create a dataset with normal and abnormal manoeuvres. Then, we evaluate our method for single- and multi-agent configurations, including comparisons with deep sequential auto-encoder and linear models. Moreover, we rely on the standard metrics for anomaly detection to show that our approach delivers promising results compared to the related methods.
2 Related Work
Multi-Agent Trajectory Modelling. Trajectory prediction is essential for automated driving [14, 15]. Modelling the interaction with the environment and between the participants improves the pre- diction quality [13, 16). The idea of information exchange across agents is actively studied in the literature [17, 18. 19]. For example, Alahi er al. introduced the social-pooling layer into LSTMs to incorporate interaction features between agents [20]. Recently, graph neural networks (GNN) have outperformed traditional sequential models on trajectory prediction benchmarks [21, 22j. GNNs explicitly model the agents as nodes and their connection as edges to represent the social interac- tion graph. Similarly, the social temporall graph convolution neural network (ST-GCNN) [5] extracts spatial and temporal dependencies between agents. Also, we use related architecture to design our spatio-temporal graph auto-encoder for learning the normal data representation.
Anomaly Detection. On image and video data, anomaly detection is a long-standing topic. Hand- crafted and motion features were traditionally employed for anomaly detection based on probabilis- tic PCA [23] or one-class SVM [24]. At the moment, deep neural networks dominate within the anomaly detection approaches [25, 26]. The usual approach is training an auto-encoder with normal data and then measuring the deviation of the test samples from the learned representation. For in- stance, Morais et al. [5] proposed sequential auto-encoder encode skeleton-based human motion and considered the reconstruction error as measure for the detection of irregular motion patterns. Also, the variational auto-encoder (VAB) in [27] can learn the normal data distribution from a set of raw sensor signals in combination with a long short-term memory (LSTM) network. Unlike our work, these approaches assume fixed number of input streams, i.e. sensor signals, instead of a varying number of trajectories, i.c. agents. Here, we formulate the idea of learning the normal data distribution with the temporal graph auto-encoder. Furthermore, we estimate the normal data density function instead of relying on the reconstruction error.
Anomaly Detection in Trajectory Prediction and Control. Anomaly detection has been exten- sively studied in robotics, e.g. model predictive control [28], collaborative robots [29], autonomous drones [7], robot navigation in crowds [30] and uncertain environments [31, 8]. Nevertheless, the prior work only address the problem of single agent anomaly detection. We tackle the problem of
detecting anomalies in multi-agent trajectories.
3 Anomaly Detection in Multi-Agent Trajectories
We study the problem of anomaly detection for multi-agent trajectories. The input to our approach is a scene with N agent trajectorics of length T. where N is dynamic over scenarios. We describe the observed trajectory of the agent with the agent states s' = [s]]T= where sf = (at, vf) denotes the agent location in x- and y-coordinates. Our goal is to estimate the anomaly score ar = [0, 1]. i.c. normal or abnormal, for each time step of an unseen scene during testing, while only showing normal scenes during training.
We present a two-stage approach, where first a spatio-temporal graph convolution network auto- encoder is trained to represent normal trajectories in the feature space (Sec. 3. Second, we use the latent representation to fit probabilistic density to the normal trajectories with kernel density estimation (Sec. 3.2). Finally, we present the anomaly detection score (Sec. 3.3) given the estimated density. The supplementary material provides visualisation of the training and inference process.

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3.1 Spatio-Temporal Graph Auto-Encoder
We define the spatio-temporal graph auto-encoder (STGAE) composition of the auulti-agent tra- jectory encoder (()) and the trajectory decoder (.).. The encoder maps a set of agent trajectories on the latent representation. The decoder transforms the latent representation back trajectories.
spatio-temporal graph convolution neural net- work (ST-GCNN) [32]. Given set of N agent trajectories of length T, we define the spatio-temporal graph 9 = { as a set of directed spatial graphs Ge (V, E.). The spatial graphs model the multiple agents as nodes V. and their connectivity
Trajectory Encoding. The encoder is designed
edges & to compute pairwise influence. The set of graph nodes V. = {vi]== represent the agent states in terms of the relative location vi We define the edges & = {ez N Jij=1 to model how strong the node
(c} 1 11-1. Vt
i influences node j at time step To this end, kernel function ef Kedge (Vi, v²) [33] measures
the similarity between two agents in the same time step defined as
</ 1/llv - villa Iv- v/ + 0
otherwise.
The influence is high for similar agent states and low otherwise. In the rare case of two agents sharing the same location, we set et = O.
We define the weighted adjacency matrix A, E RRNN based on the connectivity parameters e We follow the procedure of Kipf et al. [34] and compute the normalised graph Laplacian A, D A,D, with the graph Laplacian A, = A, + I, where denotes the identity matrix, and the node degree matrix D, with diagonal entries defined as Djr = A. As introduced by Yan et al. [32], we aggregate over neighbouring agents using spatial graph convolutions g=(V, (V,A) A) o (AVe,) with the activation function (-) and the network weights 0,. We denote A and V as the concatenation of the weighted adjacency matrices {Ar) and the node features {V: (2.)zm over all time steps, respectively.
In dynamical systems, spatial features are not expressive enough since they ignore important tempo- ral relationships. To include the time dimension, we connect the same node over consecutive frames using temporal convolutions (-)-) as introduced in [35]. We define the encoder g(-) as composite of spatial graph convolution and temporal convolution layers. As a result the encoder computes the latent representation Z E R 7xNNxF, with the latent feature dimension Fg.
Trajectory Decoding, Given the encoded representation, we define decoder to reconstruct the set of input trajectories. The decoder applics multiple 2D convolution layers on the temporal dimension of the latent features [33]. To include agent interactions, the convolutions aggregate features across agents. We denote the decoder output as V RTXNXF, with output feature dimension Ff.
Training. For the training, we assume that the state of agent i time step comes from bi-variate distribution, given by s, N2 (ni, of pt), where μ4, of R² are the mean and the standard deviation of the location, respectively, and p IR2 is the correlation factor. We estimate the parameters of the bi-variate distribution with the decoder output v = {Ā), oi. pt}- We denote the estimated probability density function q(s)( of, pi) and train the model to minimise the negative lig-likelihood
T
C - Σ log (a (silpi, p1))
(2)
Similar to other sequential models [5], our STGAE requires inputs of fixed temporal length. There- fore we clip each scene the training set into smaller fixed-size segments of length T" using sliding window approach.

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3.2 Kernel Density Estimation for Normal Trajectories
We rely on kernel density estimation (KDE) to approximate the probability density function of the normal trajectories from the latent feature representation of the STGAE. The idea is based on the assumption that normal trajectories fall in high density regions and anomalies occur in regions with lower density.
Given the trained STGAE, encode the training segments and combine all latent representations in the set Zkde. The KDE assumes all samples to be i.i.d. random variables drawn from an unknown true distribution p [36]. We can approximate the true density of new feature vector z by p defined as
1
Zuael
||*||| 2h2
p(z)
Kidd
with the Gaussian Kernel [37] Kide (x) x eap
IZede
h
(3)
The kernel function (x) weights the observations differently based on the similarity to its neigh- bours. The parameter responsible for the weights the points the bandwidth h, which serves as smoothing. To sum-up, Eq. 3 computes the probability density of the agent's 's feature vector
3.3 Abnormal Trajectory Detection
During the inference, we use the same sliding window approach as in the training and get the set of all test segments. For a test segment, the STGAE encoder computes the latent representation and the KDE from Eq. 3 estimates the density for each agent and time step, given the latent feature vector. We take the estimated density measure for anomalies. The feature decoder of the STGAE is not required during testing.
ennddrn
We follow a similar approach as introduced [5] for the anomaly scoring. First, compute N anomaly scores of for all agents included in the same time step, and second compute the anomaly score a to measure if time step t is abnormal. To score for one agent, we average the anomaly scores of all segments where the agent occurs by:
Anomaly Score.
af Loes. p(zi,o)
(4)
[.
where S, the overlapping sliding window segments in which the agent is present and z the resulting feature vectors from the STGAE encoder at time step t. This results in one anomaly score for each agent in specific time step. To identify if time step normal abnormal, compute the anomaly score ae by taking the maximum over all agents:
=
(5)
The max-operation avoids missing anomalies compared the mean. We use a, for the calculation of the metrics in our evaluations.
4 Experimental Results
We present the first dataset for anomaly detection in multi-agent trajectories and evaluate our method in comparison to seven basclines. See supplementary material for more results.
4.1 Dataset Development
To evaluate our algorithm, we propose the MAAD dataset, a dataset for multi-agent anomaly de- tection based on the OpenAl Gym MultiCarRacing-vi environment [38]. Since it was originally released as a multi-agent racing environment for learning visual control policies [39], we adapt it for anomaly simulation. We design the scenario of two-lane highway shared by two vehicles, which

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Figure I: Example sequences from the proposed MAAD dataset. We show the observed trajectory of each agent. The first frame shows save overtaking manoeuvre form the normal set. The other three frames contain abnormal actions: the blue vehicle pushing the red vehicle aside, an aggressive reeving action of the red vehicle and wrong-war way driver who even collides with the upcoming traffic.
naturally leads to interaction, e.g. speed adjustments, lane changes or overtaking actions. The vehi- cles controlled by human players to record multiple expert trajectories. For every sequence, choose random initialisation of the agent starting positions to increase trajectory diversity.
In total, we create dataset with 113 normal and 33 abnormal scenes, Beforehand, 11 different types of anomalies are defined terms of breaking driving rules or careless behaviour". Each abnormal scenario is recorded three times incorporate more variations (see Fig. 1). After all recordings, the sequences are annotated with frame-wise labels by human experts with the ELAN annotation software [40]. We use 80 randomly selected normal sequences for training and the remaining 66 sequences to test. The sequences are sub-sampled to 10 Hz with a segment length of T 15 time steps, which corresponds to 1.5 seconds.
4.2 Baselines
Our baselines include multi-agent agent models as variants of our method, which explicitly model interac- tion, well unngl-agent models, ignoring interaction. The baselines can be further categorised as one-class and reconsiruction methods.
Single-Agent. To examine the effect of interaction, define four interaction-free models, two parameter-free and two neural network approaches. As simple parameter-free reconstruction method, we employ the constant velocity model (CVM) from [41]. Secondly, approximate the trajectory with interpolation between the first and the last time step of the observed trajectory, we denote the model linear temporal interpolation (LTTT.. The linear models succeed in the metrics, the velocity profile of abnormal trajectories highly deviates from the normal trajectories. As a single-agent neural network, first we adapt the Seq2Seq model from [42]. It is composed of an encoder LSTM and decoder LSTM. The encoder computes a feature vector representing one tra- jectory. After the last input is processed, the decoder tries reconstruct the input trajectory from the feature vector. Next, we implement an interaction-free variant of STGAE by setting A, I. apatio-tempora auto-encoder, why we call STAE.
This reduces the model
Multi-Agent.
Based on the proposed STGAE we evaluate three multi-agent baselines. For the first two variants, (STGAE-biv) and a second with classical MSE loss (STGAE-mse) on the trajectory reconstruction task. Similar KDE of our method with a one-class SVM (OC-SVM), which is an adaption of the traditional SVM one-class classification. It takes the encoder features input and finds hyperplane separating the data points from the origin while ensuring that the hyperplane has maximum distance from the origin [43]. The baseline is denoted STGAE+OC-SVM.
STGAE as reconstruction method. We train one STGAE with bi-variate loss
approach, the third variant is one-class classification method. We replace the
4.3 Evaluation Metrics
We quantitatively evaluate approach following the standard evaluation metrics used in the anomaly detection literature [44, 45, 46], namely AUROC, AUPR- Success,,,s, AUPR-Error and FPR at 95% TPR. The AUROC metric integrates over the area under the Receiver Operating Characteristic
We define the 11 anomaly sub- alb-classes as leave road, left spreading, aggressive overtaking, pushing aside, aggressive reeving, right spreading, skidding, staggering, tailating, thwarting and wrong-way- wori-way--riving.
5

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Comparison of the proposed method with the baselines on the proposed MAAD dataset using four metrics: AURC, LUPR-Abnormar AUPR-Normal and 1PR-95%-TPP We differentiate between single- and multi-agent and further categorise into reconstruction and one-class classifica- tion methods. Highest scores are written in bold. For the trained models we provide the mean and standard deviation of ten runs. Note, CVM and I.TI are deterministic with zero standard deviation.
Table 1:
Method
One-class vs. Reconstruction
AUROC1
AUPR-Abmormal
AUPR-Normal
FPR-95%-TPK
CVM [41)
reconstruction
83.11 (2:0.00)
54.47 (=0.00)
95.99 (=0000)
74.62 (1:0.00
Single-
Agent
LTT
reconstruction
75.47 (.10.00)
48.89 (_0.00)
92.37 (100000)
95.03 (10.00)
Seq2Seq [42]
recomstraction
56.15 (++0.68)
(-1.00)
89.54 (+-0.13)
84.62 (40.26)
STAE biv [A,=/
reconstruction
57.54
21.77 (-8.48)
89.47 (1.3266
84.42 (12.50)
STGAE-mas
reconstruction
81.53 (1:3.16)
50.76 (=4.47)
95.90 (1:0.93)
67.36 (19.30)
Muta- Agent
STGAE biv
reconstruction
74.82 (:155.10)
37.79 (.16))
94.10 (1.1.31)
77.80 (19.77)
one-class
85.97 (4:2.40)
52.37 (=8.85)
97.11 (40059)
49,90 (16.33)
Ours
one-class
86.28 (::1.73)
55.20 (#7.74)
97.15 (1:0.54)
50.02 (17.977)
curve (ROC) and results in a thresholldindeeeendent evaluation. Note that a classifier with 50 % AUROC is equal to a random classifier, while 100 % is the upper limit and denotes the best possible classifier. We use the Area Under the Precision-Recte (AUPR) curve as our second metric. Other than AUROC, it able adjust for class imbalances, which is always the case in anomaly detection, i.e. the amount of abnormal samples is small compared to normal samples [45]. Here, we show both AUPR metrics, the AUPR-Abnormal, where we treat the abnormal class as positive, and the AUPR- Normal, where we treat the normal class as positive. Additionally we show FPR-95%-TPP False Positive Rate (FPR) at 95% True Positive Rate (TPR). For the one-class methods we directly apply the metrics on the output score and for the reconstruction methods we take the mean squared error (MSE) between the given and the reconstructed trajectory as anomaly score, following [5].
the
4.4 Implementation Details
The CVM approximates the agent trajectories assuming the same velocity for all time steps. The velocity is estimated given the first two time steps of trajectory. For LTI the reconstruction error is defined as the distance between the ground-truth trajectory and equidistantly sampled locations on a straight line between the beginning and the end of the trajectory. Both, the encoder and decoder of the Seq2Seq model, are implemented with 3 stacked LSTM layers and 15 hidden features. We train the network for 1500 epochs using Adam optimiser with learning rate 0.01.
Our STGAE method is implemented as ST-GCNN encoder [33] and TCN decoder [35]. The encoder is composed of one spatial graph convolution layer and one TCN layer, both with five latent features, followed by the decoder consisting of five convolution layers for reconstruction. We train for 250 epochs using Stochastic Gradient Descent and learning rate 0.01, and decay the learning rate to 0.002 after 150 epochs. For evaluating STGAE-biv we sample 20 reconstructed trajectories from the bi-variate Gaussian distribution. STGAE with MSE loss does not require sampling.
Both one-class classification methods (OC-SVM and KDE) are implemented using a Gaussian ker- nel and the best hyperparameters are selected via grid search. Note, that OC-SVM has a minor supervised advantage, since validation of the model takes place on a holdout test set, i.e. 20% ran- domly selected from the test data. Hyperparameter tuning of 7 and y for OC-SVM is performed via grid search with 7 E (2 10 2-9 .... 2-1} and v E (0.01, 0.1}. The bandwidth of KDE is selected from h {2 4.5 2 ...., 26] via f-fold cross- valsddalio with the liglliiel score in [47].
4.5 Results
We present our results in comparison the baselines. Afterwards, we evaluate different anomaly types and finally the performance stability over input sequence length and beyond pairs of agents.
Comparison with the Baselines. The comparison of our method with the baselines is presented in Table 1. Additionally, we show the ROC curves of all approaches Figure 2. Our STGAE- biv+KDE outperforms both the linear and the deep methods in three out of four metrics, namely AUROC, AUPR-Abnormnn and Normal, and is on par with STGGAE-bi++OC-SV for FPR- 35%- The second one-class classification approach STGAE- reaches similar per-

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ROC curves
AUROC over Sogment Length
1.0
Trio Postive Rate [-]
0.8
CVM
0.6
SeggSeg
AUROC
70
STARI-bX AAr
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.6
1.0
0.5
1.0
1.5
2.0
2.5
3,0
3.5
4.0
False Postive Rate |-1
Segment Length [s]
Figure The ROC curves of the single-agent models (dashed lines) and the multi-agent mod- els (solid lines).
Figure 3: AUROC metric over the segment length. Our method is more stable for various segment lengths.
Table 2: AUROC different types of anomalies. We differentiate between non-interactive and interactive anomalies. The multi-agent models reach high-scores in both interaction and non- interaction anomalies. Highest scores written in bold.
Non-interactive
STAE-biv
STGAE -mse
STGAE -biv
STGAE-biv +SVM
Abnormal
Interactive
Seq2Seq
A
leave
non interactive
88.66
99.24
94.32
99.57
98.22
left spreading
interactive
90.88
96.90
47.06
55.06
91.92
52.76
94.16
96.56
aggressiive overtaking
interactive
91.78
78.30
91.80
93.24
pushing aside
interactive
91.54
79.98
75.55
82.02
98.73
72.51
89.84
90.44
aggnessive reeving
interactive
96.67
92.31
right spreading
interactive
87.66
89.83
45.22
61.75
96.33
53.57
95.55
96.24
skidding
non non-interactive
96.90
94.69
98.
staggering
non internctive
86.87
85.30
$7.83
72.64
90.58
66.53
94.91
96.01
tailgating
interactive
77.18
70.20
$8.71
83.55
84,87
thwarting
interactive
98.08
90.75
88.34
92.56
92,68
96.58
81,95
81,59
wrong-way driving
interactive
63.16
64.63
61.46
57.88
73.11
overall
83.11
75.47
58.06
70.01
87.70
72.67
87.38
88.34
formance and is the best for FPR-95%-TPP -PRR, but cannot reach the high-score the remaining met- rics. Considering the ROC curves, both one-class methods have similar course with slight advan- tages for our method using KDE for anomaly detection. general, the one-class methods are more stable over multiple runs. Our approach has practical advantage superior even in consideration the standard deviation of all other models.
the baselines it remains
Overall, besides STGAE-biv, the multi-agent models show higher accuracy compared to methods considering each agent individually. This indicates that some manoeuvres are only anomalous in the context of other traffic participants and could be considered as normal if the agent is alone on the street. This also the reason for the performance drop for STGAE-biv, matrix A, is reduced to the identity matrix, i.e. no feature aggregation over neighbours. The linear models perform competitively, which gives rise to the difference between normal and abnormal lying in the degree of linearity of the trajectories. We empirically observe that Seq2Seq can not differentiate between normal and abnormal trajectories for most experiments, because it fails to learn approach can detect most of the anomalies compared to
the adjacency
the sequential dependencies. Overall, the baselines. practice, high detection rates directly support the decision making process. Once an anomaly is detected the automated vehicle can react pass the control to the human driver.
Detection Score on Anomaly Types. Table shows the evaluation of the eleven anomaly types. To compute the ROC curve for an anomaly type, we consider this anomaly as positive and ignore all frames labelled with another anomaly category. Our method outperforms the others in four of the eleven classes and is competitive for the remaining ones. In particular, we significantly out- perform the single-agent baselines on the aggressive overtaking category. We argue that it requires interaction modelling to distinguish the aggressive from a normal manoeuvre. Overall, the wrong- way-driving category leaves space for improvement. Including absolute coordinates in addition to velocity could help to learn more meaningful interaction features. Some abnormal trajectories can be detected without caring about interaction. This is when the linear models show their benefits, see left spreading or thwarting for L.T and CVM, respectively. The left spreading action is highly non-
7

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Table Comparison of STGAE-biv and our method on test sets with two, three, and four agents on the highway. Other than the reconstruction method, our one-class approach remains more stable in all metries with increasing traffic density.
Test Agents
Model
AUROCT
AUPR-Abnormal t
AUPR-Normal f FPR-95%-TPK !
=2
STGAE-biv
69.08
39.28
90.07
92.19
N 2 Ours
92.34
66.75
98.48
35.20
N 3
STGAE-biv
78.20
42.52
94.73
78.23
N
3
91.26
63.57
98.36
35.38
N 4
STGAE-biv
52.42
17.95
88.03
88.19
N
Ours
89.41
60.52
97.87
42.55
linear, such that the LTI model fails to approximate correctly what results in high anomaly scores. Similar, thwarting results through strong braking, which is not following the constant velocity sumption of CVM. Again, STGAE-mse is the best reconstruction method and outperforms three sub-classes, however with the downside of a computational expensive trajectory decoder.
Ablation Study on Observed Sequence Length. Figure 3 shows the influence of different segment length T' {4, 8, 10, 15, 20, 30, 40} the recognition performance. For the comparison train all models on different segment length. Although we see correlation between STGAE-biv and our method, best performance for 7" = 15. The performance of the linear models decreases for higher input length, which means that linear models good trajectory approximators only for short sequences. In general, the reconstruction methods drop in performance for longer sequences. Both, CVM and LTT have peaks at 0.8 seconds, however method remains the best overall with 88.34 % AUROC.
results remain stable for large interval. As reported before, reach the
Ablation Study on Scalability Beyond Pairs of Agents. The proposed MAAD dataset includes diverse interactive anomalies between pairs of agents. However, the proposed model is flexible to the number of agents in a scene and can process more than two agents without adaption. We evaluate the recognition performance for highway with higher traffic density two models. In detail, compare Our approach with the performance of STGAE-biv. Both models are trained on the original MAAD training set with two agents in each scene. For testing create three ablation test sets with N = 2, = 3 and N = agents, see details in the supplementary material. The results are shown in Table 3. As before, Interestingly, the metrics of the reconstruction method vary intensively with the number of agents. This indicates that once trained on two agents the reconstruction is confused by the features from the additional agents. It looks different for our method. Even though we see small performance decrease with an increasing number of agents, method is more stable and reliably detect anomalies even on highways with higher traffic density.
approach reaches higher scores compared the reconstruction method.
Conclusion
We presented the spatio-temporal graph auto-encoder for trajectory representation learning. Our main contribution is the ability to simultaneously learn multiple trajectories for a dynamic number of agents. Our model learns normal driving behaviour for performing afterwards anomaly detection. To this end, we performed kernel density estimation on the latent representation of the model. During testing, we detect anomalies in low-density regions of the estimated density. Due to the lack of datasets for multi-agent trajectory anomaly detection for automated driving, we presented synthetic multi-agent dataset with normal and abnormal manoeuvres. our evaluations, we compared our approach with several baselines to show superior performance. Although study is driving trajectories, our approach can Iearn joint feature spaces in other multi-agent domains like verbal and nen-verbal communication, sports human-robot interaction. This would be future work direction.

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Acknowledgments
The research leading to these results is funded by the German Federal Ministry for Economic Affairs and Energy within the project "KI Delta Learning" (project number: 19A19013A). The authors would like to thank the consortium for the successful cooperation.
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11


Reviews:
[{"review_id": "npIVJ88qMZB", "reviewer": "Reviewer_BxGJ", "summary": "This paper proposes a method for anomaly detection for the autonomous driving domain, by learning a representation for joint trajectories of normal driving behaviors, then performing density estimation on the latent representation of the joint trajectory auto-encoder.  At test time, anomalies are detected by test trajectories occurring in low density regions of the learned latent space.  In particular, the proposed method consists of first training a spatio-temporal graph CNN auto-encoder (STGAE) to both represent individual “normal” trajectories in a latent feature space (autoencoder) and model agent (car) interactions over time by computing pairwise agent influences (spatio-temporal graph).  Secondly, it uses kernel density estimation on the latent feature representation of the STGAE to approximate the distribution of the normal trajectories.  The proposed method is evaluated against single-agent and multi-agent baselines, on standard metrics for anomaly detection.  The paper also contributes a new simulated dataset for multi-agent driving trajectories, with both normal and abnormal driving maneuvers.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Identified strengths of paper:\n+  Addresses an interesting and under-explored problem in multi-robot systems, anomaly detection given joint continuous trajectories; thus it explores the detection/recognition of anomalous behaviors for multi-robot systems, intended for the autonomous driving domain.  I also wonder how well this approach would generalize to other MA problem domains with continuous action spaces?  E.g. multi-agent nonverbal communication or coordination in a shared environment.  If the authors have insights about this, some discussion of it at the end of the paper would be interesting and potentially useful.\n+  Provides extensive empirical analysis, which is important for extracting meaningful insights.  Good that the work evaluates methods using several metrics from the Anomaly Detection literature; provides a stronger basis for hypothesis testing.  Qualitative analysis from Table 2 is useful for providing additional insight into aggregate results and also seems like good evidence for differentiating between the value of single-agent versus multi-agent methods on this problem.\n+  Contributes a simulated driving dataset to the MA community, with 146 scenes and 11 different types of driving anomalies, which can be a really useful tool for the community in a problem domain of interest to many.\n\n\nI would suggest that the authors improve their submission, including the following:\n-  For all results reported: Would be extremely useful (and provide more compelling evidence) if some measure of statistical dispersion was included (e.g. standard deviation or standard error), so as to assess statistical significance when comparing the different methods.  Currently, this is not shown at all, only mean data.  So it is difficult to assess the reliability of the findings.  Also, how many seeds/runs are these curves averaged over?\n-  The paper briefly explains each of the evaluation metrics used, which is really helpful as context.  However, even with that, it's not entirely obvious to me how to interpret each of the result columns in Table 1.  I understand for certain columns, lower/higher is better, but what do the differences in performance imply?  How much of a difference is significant?  Overall, it would be helpful to provide additional explanation/intuition as to how to interpret the findings, particularly for readers not from the Anomaly Detection community.  Also, still unclear as to *why* all baselines are not shown in Figure 3.\n-  From a qualitative analysis perspective, it could be insightful to show an example of where the same trajectory for agent i is normal in the single-agent case but can be anomalous in the multi-agent case (dependent upon the behavior by another agent j).  Would also serve as additional compelling motivation for modeling of joint continuous trajectories, which I’m wondering how much more computationally expensive it is than modeling only individual trajectories? Some discussion about computational complexity would be useful.\n-  Minor Clarification:  In Equation 5, remember to define p^i_t\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "This paper makes a novel methodological contribution to the space of multi-agent robotic or dynamical systems, by applying spatio-temporal GNNs for anomaly detection.  While the work is intended for a specific application domain (autonomous driving), which serves to limit the generality of its findings, the method considers learning in continuous joint trajectory spaces, which contributes to an under-explored part of the multi-agent reinforcement learning (MARL) problem space.  The application domain itself is of high relevance and interest to the MARL and Robotics communities, particularly as the former is moving toward developing methods for more complex domains.  And in the application domain of interest, the paper is able to show that the proposed method benefits from modeling the interactive (multi-agent) nature of the driving problem, not just considering the single-agent problem.  It also provides insights on the types of driving anomalies where the method performs well.  Finally, it contributes a simulated driving dataset, which is a nice contribution to the community.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "2: Unsure, difficult to assess.", "issues": "Listed above as suggestions for improvement.", "reviewer_expertise": "Good: General knowledge of the area"}, "extra_text": {}}, {"review_id": "fhL5mCmytjh", "reviewer": "Reviewer_tMsu", "summary": "This paper makes two contributions: (1) it proposes a spatio-temporal graph auto-encoder for learning nominal driving behaviors, after which kernel density estimation is performed on the latent state to quantify unlikely (i.e., “anomalous”) latent states, and (2) develops a dataset of nominal and anomalous driving behavior with associated human labels. ", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The contribution of a novel dataset of two-agents driving on a highway with associated human anomaly labels is interesting and relevant to the autonomous vehicle community. \n- The problem domain of anomaly detection in multi-agent trajectories is highly relevant for modern autonomous vehicle systems.\n\nWeaknesses:\n- The core contribution in this work is “the ability to simultaneously learn multiple trajectories for a dynamic number of agents” and then “perform kernel density estimation on the latent representation of the [proposed approach].” However, this has been extensively studied in the behavior prediction domain, it is not immediately clear why the proposed approach is a better paradigm since there is no discussion or comparison to state-of-the-art approaches which meet both these criteria. Further explanation is described in the detailed comments. \n\nDetailed comments:\n\nSection 1:\n- “...e.g., recognizing a ghost driver…”, please clarify / define what a ghost driver is, as this is not standard terminology. \n- “the main innovation of STGAE is the ability to simultaneously learn multiple trajectories for a dynamic number of agents'' and  then “perform kernel density estimation on the latent representation of the [proposed approach].” This idea has been studied in various ways by industry behavior prediction teams [1, 2] and academia [3]. In the proposed method, kernel density estimation is performed on the latent representation, and the density estimates are then utilized to detect anomalies. In the aforementioned cited approaches, the distribution over the latent state is often directly estimated, and then coupled with the trajectory forecasting method as a means to quantify likely and unlikely behaviors. For this reason, the novelty of the proposed approach should be discussed / compared to the aforementioned methods which capture similar distributions over latent states as well as produce trajectory predictions for a dynamic number of agents. \n[1] Chai, Yuning, et al. \"Multipath: Multiple probabilistic anchor trajectory hypotheses for behavior prediction.\" arXiv preprint arXiv:1910.05449 (2019).\n[2] Tolstaya, Ekaterina, et al. \"Identifying driver interactions via conditional behavior prediction.\" arXiv preprint arXiv:2104.09959 (2021).\n[3] Ivanovic, Boris, et al. \"Multimodal deep generative models for trajectory prediction: A conditional variational autoencoder approach.\" IEEE Robotics and Automation Letters 6.2 (2020): 295-302.\n- The paper does not upfront define what is meant by “anomaly” in this work. Anomalies can take many different forms in multi-agent trajectory forecasting (e.g., is an agent’s true latent state in the hypothesis space of the model? Is the distribution over states well-calibrated? Assuming the probabilistic model is well-calibrated, is an agent performing a sufficiently unlikely maneuver deemed “anomalous”? What constitutes “sufficiently unlikely”?). It is only in Section 3.2 where the idea of anomalies being samples taken from low-density regions of the latent feature space is described. Being upfront about what anomaly means in this work would strengthen and clarify the narrative. Additionally, a discussion on why this notion of anomaly is valuable compared to alternative notions would also be valuable.  \n\nSection 3:\n- Conditional variational autoencoder approaches (CVAE) seem well-suited for the proposed approach, as they both produce a conditional probability distribution given a dataset of driving trajectories but also project the inputs into a lower latent space and a distribution over the latent variable. It would be valuable to discuss why the proposed approach -- which performs kernel density estimation on the latent representation of the STGAE -- is different / more beneficial for autonomous vehicle trajectory modelling compared to the CVAE approaches. \n- “To identify if a frame is normal or abnormal we compute the frame anomaly score… max-pooling avoids missing anomalies compared to the mean, which is not justifiable in automated driving.” While it is true that anomalies compared to the mean are not justifiable, looking at the mean when detecting anomalies may not be sufficient, as anomalies are often tail-events. This section would be strengthened with a further discussion on why looking at the mean during anomaly detection is a good measure of an anomaly. For example, why not detect the most-anomalous agent and latent state?\n- At the end of this section, it would be valuable to describe what should be done (from an AV design and/or decision-making perspective) once an anomaly is detected. This would improve the impact of this work for the broader AV community that would have to integrate an anomaly detection framework into the vehicle perception/prediction/planning/control stack. \n\nSection 4.3:\n- Please define AUROC, FPR, and TPR prior to using the abbreviation. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "I recommended weak rejection because although the domain of anomaly detection for autonomous driving prediction is highly relevant, the proposed method is not clearly described and evaluated compared to state-of-the-art trajectory forecasting methods which both predict multi-agent trajectories but also learn distributions over latent states. This paper would have been stronger with a focus on the design and collection of a novel anomaly-centric dataset, since this is something thoroughly lacking in the autonomous vehicle safety community. \n\n====================\nAfter the rebuttal phase, I have increased my recommendation to \"weak accept\".\n", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed.", "reviewer_expertise": "Good: General knowledge of the area"}, "extra_text": {"issues": "- Clarify how the proposed approach differs from state-of-the-art trajectory predictors (cited in the detailed comments). \n- Clarify why the measure of anomaly studied in this work is a sufficient metric \n"}}, {"review_id": "UtK3jjUWSEg", "reviewer": "Reviewer_McLa", "summary": "The authors develop a system for anomaly detection in driver interactions using a novel spatio-temporal graph neural network architecture combined with a Kernel Density Estimator. \n", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The definition of a spatio-temporal graph and its use in a GNN architecture is a very interesting contribution of the work. \nThe authors provide relevant baselines for comparison, and perform several ablation studies. \nThe results clearly demonstrate that considering multi-agent interactions in anomaly detection is essential. The characterization of the performance of the system over various segment lengths is also important. \n\nOne shortcoming of the approach is that the kernel density estimator must use all of the training samples. Many of the most popular autonomous driving datasets have millions of examples, and it is unclear how the KDE methodology would scale to larger datasets. \nI would like to see a discussion of how this approach could scale beyond pairs of agents, since the most challenging and interactive scenarios occur in dense urban traffic. \n\nThe current pipeline for anomaly detection could be used for data mining in a larger dataset to find interesting long-tail cases for training or testing components of autonomous cars. I think this system could also be useful for anomaly prediction, or early detection of situations that may become anomalous in the near future. The use of the max-pooling operation in Eq. 8 may allow for this, especially considering the consistent performance across segment lengths in Fig. 3. If this approach shows promise for this task, then the anomaly detection system could be used on-board an autonomous vehicle to detect when the car would need to revert to a human fall-back driver. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "The paper describes a novel architecture for processing interactive trajectories and detecting anomalies, but the applicability of it to large modern datasets is limited by the use of KDE.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed.", "reviewer_expertise": "Very good: Comprehensive knowledge of the area"}, "extra_text": {"issues": "In Table 2, it would be helpful to indicate which are the single agent anomalies, and which describe interaction between agents. \n\nIt would be good to discuss the possible uses & applications of anomaly detection in autonomous driving to further motivate the work. "}}]

Author rebuttal:

Meta-review: The paper introduces a novel anomaly detection mechanism for the multi-agent, autonomous driving domain. All reviewers agree that the paper addresses an important and timely problem for autonomous vehicles. The reviewers expressed concerns about the performed
evaluation that should be addressed in the revised version:
- Clarify the results and the inconsistencies represented in the tables and Fig. 3. It seems that the statistical spread in the performance of the proposed method and other baselines is missing. A more detailed discussion of the presented results will strengthen the paper significantly (see reviewers' suggestions).
- Clarify how the approach scales in terms of multi-agent interactions (as opposed to a pairwise interaction) and as the number of data samples increase.
- Discuss how the proposed approach differs from some of the related multi-agent trajectory prediction efforts pointed out by the reviewers. 
- Address the suggested language improvements.

===== Post rebuttal =====

The authors have sufficiently addressed reviewers' concerns; specifically, ablation studies with multi-agent interactions were particularly interesting. For the final version, I recommend the authors to add some of these studies in the main paper. I would also suggest doing a more thorough statistical analysis (3 trials are not that significant to compute the mean/variance of the performance).
Decision: Accept (Poster)