Outliers can afect trajectory analysis as they represent errors. There are two outlier detection categories, one focusing on a collection of trajectories, where one whole trajectory can be an outlier and another on points inside individual trajectories. In this paper, we focus on the latter. We benchmark existing open-source libraries and compare their eficiency and accuracy in cleaning outliers. To compare the accuracy, we present a method to build ground truth using the other sensor data in a multi-sensor environment.
Outlier or noise detection is an essential step in trajectory cleaning, as it helps to identify points in the data that deviate significantly from the expected pattern. Moving object trajectory data comes with many outliers due to sensor and connectivity problems. Outliers in trajectory data can lead to misleading analysis results and inaccurate decision-making, which can have significant consequences for businesses, governments, and individuals. This type of data problem afects the accuracy of analytic functions, e.g., trajectory similarity [1, 2]. As such, outlier mining is an essential function in mobility data management systems [3, 4].
There are two outlier detection categories, one focusing on a collection of trajectories, where a trajectory can be an outlier and another on points inside individual trajectories. In this paper, we focus on the latter.
We benchmark open-source libraries and compare their eficiency and accuracy in detecting and cleaning outliers. The main contributions of this work are: • A automated method for generating ground truth in multi-sensor data. • A benchmark of libraries, including movetk [5], movingpandas[6], scikit-mobility[7], Ptrail [8], PyMove [9], Argosfilter[ 10] and Stmove [11] focusing on outlier detection. The benchmark considers the user perspective. That is, the context is to compare the ofering of the existing libraries for end users rather than comparing their algorithms and implementation aspects.
In Section 2 we present essential concepts for outlier detection. Section 3 surveys the state of art. A benchmark using real data is the subject of Section 4. In Section 5, we discuss our findings and we conclude.
Distance-based algorithms compare each point in the trajectory to its neighbors and select the points that are significantly further away than expected. Methods based on the mean or Median Filters replace points compared to the measurements done at preceding points in time. These algorithms are simple and practical for detecting single outliers. Nonetheless, these techniques depend on the number of predecessors compared to the mean. Multiple successive outlier points can afect the accuracy of the outcome trajectory. These algorithms are not always efective at detecting multiple successive outlier points, which can afect the accuracy of the output trajectory. More advanced algorithms or methods may be needed to detect and correct outliers in these cases. authors mention the advantages of the KF and its deriva- is so any subtrajectory. In opposition, it is not necessarily tives is its recursive aspect, which can be used in real- possible to construct a trajectory from the concatenation time. It is also widely used due to its simplicity and of two consistent subtrajectories: the concatenation 〈p1, capability to provide accurate estimations and prediction . . . , pn = q1, . . . , qm〉 of two consistent subsequences T results. = 〈p1, . . . , pn 〉 and U = 〈q1, . . . , qm〉 with pn = q1 is
Particle filters (PF) uses a set of randomly generated not necessarily consistent. Joining these subtrajectories particles to represent the possible states of the system and can reproduce inconsistent points—especially when conupdate the particles based on observed data. In contrast sidering an acceleration-bound model. The speed of two to KF, they are not restricted to Gaussian distribution of points can infer two accelerations for the same position. errors, which makes them applicable in a wider range The model is called concatenable if it is possible to join of noisy data. PF can however be computationally inten- both sub-trajectories respecting the bounds. sive, and thus not commonly implemented in trajectory In the next Session, we relate each of these methods libraries. Additionally, like KF, PF are sensitive to the to state-of-the-art libraries. ifrst measurement in the trajectory, and their accuracy can be reduced if the first point is an anomaly[ 12, 14, 15].
The Hampel Filter (HF) detects and replaces outliers 3. State of Technology in trajectories with estimates via the Hampel identifier.
The HF expresses a conventional heuristic that almost all values lie within three standard deviations of the mean.
For each trajectory, the method calculates the median of a sliding window and adjacent points on each side of the trajectory. The HF estimates the standard deviation of each point about its window median using the median absolute deviation. If a measurement difers from the median by more than the threshold, the filter replaces the sample with the median.
Finally, heuristic-based techniques focus more on detection, rather than correction. For instance, [12] does not replace outlier points with estimated values, but instead removes them from the trajectory. Common heuristics are based on the speed. The idea is that if the speed/speed change rate is significantly higher than a given threshold and a proportion of the points in the entire trajectory, the point is removed. This approach has the advantage of not introducing any estimated values into the trajectory, but it can lead to significant data loss.
In [5], a new method category based on physical movement properties is introduced, such as speed (Optimal Speed-bounded) and acceleration (Optimal Accelerationbounded). This method defines limits on the minimum and maximum allowed values for these properties, and uses them to determine whether a point in the trajectory is consistent with the model. The limits are minimum v- and maximum speed v+, minimum a-, and maximum acceleration a+. It follows the definition that from one point to its successor, there should always be inside [v, v+] and [a, a+]. In addition, a trajectory T = 〈p1, . . . , pn 〉 is consistent with the model if and only if there exists at least one point in a path such that the measurement coincides with the point and the speed and acceleration are inside speed and acceleration bounds. The method deifnes a reachable region as a cone, i.e. given the physical boundaries, it is possible to reach the cone from point pi to pi+1. Additionally, If a trajectory T is consistent, then
MovingPandas1 [6] is a Phyton library for trajectories of moving objects. Data can be represented in Pandas [16], GeoPandas [17], HoloViz [18], CSV, GIS file formats, JSON, and geoJSON. MovingPandas implements structures for movement data in Python for interaction and analysis of movement. This library has many trajectory manipulation functions. Focusing on the outlier detection, this library implements KF. For outlier detection, MovingPandas uses the KF algorithm, which is implemented using the Stone Soup software [19].
Scikit-mobility2 [7] is a Python library. It extends Pandas [16]. Scikit-mobility ofers functions for prepossessing and cleaning trajectory and analysis. The library chosen method for outlier detection is heuristic filtering, based on the speed and a given threshold. This approach can be efective for identifying points in the trajectory that deviate significantly from the expected pattern but may not be as accurate as other methods that use estimation to deal with outlier points.
Ptrail 3 [8]is a Python package that uses parallel computation and vectorization, making it suitable for large datasets. It ofers several preprocessing steps, such as feature extraction, filtering, interpolation and outlier detection. Ptrail removes outliers using a Hampel filter [ 20] based on the distance and speed of the ships between consecutive points. For each trajectory, the method calculates the median of a sliding window and adjacent points on each side of the trajectory. The HF also estimates the standard deviation of each point about its window median using the median absolute deviation. If a measurement difers from the median by more than the
2https://github.com/scikit-mobility/scikit-mobility 3https://github.com/YakshHaranwala/PTRAIL threshold multiplied by the standard deviation, the filter described in the paper [22]. This method uses a set of replaces the sample with the median. spatial constraints, such as a minimum distance between
PyMove 4 [9, 21] is a Python library. It ofers a range two points or a maximum distance from a reference point of operations for data preprocessing and pattern mining. to identify and remove outliers from a trajectory. PyMove also provides tools for data visualization, allow- Stmove7 [11] is an R package library. It provides coning users to explore and understand their data through struction functions, filter, and outlier detection functions. various techniques and channels. PyMove detects outlier For the outlier filter, the KF is applied. points considering the distance traveled, minimum and In the next Session, we present experiments performed maximum speed. in the libraries presented above.
Movetk5 [5] is C++ library. It ofers tools for constructing, cleaning and analyzing trajectory data. One of the key features of Movetk is its implementation of the Opti- 4. Experiments mal Speed-bounded and Optimal Acceleration-bounded algorithms for outlier detection. Movetk implements a In this Section, we present our method for constructing series of outlier detection methods based on Optimal ground truth in Subsection 4.1. We present an analysis Speed-bounded algorithm and the Optimal Acceleration- of the benchmark results in Subsection 4.2. bounded algorithm. This can help to identify potential outlier points and can provide a more accurate and reli- 4.1. Constructing Ground-truth able way of detecting anomalies in the data. In addition Constructing a ground-truth for trajectory data analysis to these algorithms, movetk implements a range of other is a task that presents several challenges. The dificulties methods for outlier detection, including greedy and smart include the cost, accuracy, and scale of the ground-truth greedy approaches. These methods build on the basic data that is required. Additionally, cleaning the data to speed and acceleration-bounded algorithms and incor- remove errors and noise can be time-consuming and may porate additional strategies and techniques to improve not always produce reliable results. their performance and accuracy. For the greedy approach, We present a method that can be applied to the data movetk greedily builds a consistent subsequence by test- originating from multi-sensor tracking technologies. Our ing if the new mesurament is consistent with the last in proposed method ofers a diferent approach to tradithe subsequence under the speed-bounded model (GSB) tional methods for constructing ground-truth, such as or acceleration-bounded model (GAB). In addition, the manual annotation or data cleaning techniques like those authors implement a Smart Greedy Speed/Acceleration- described in [23, 24, 25]. It also allows for data integrabounded methods (SGSB/SGAB). With SGSB and SGAB, tion from multiple sensors, increasing the overall accumultiple subsequences are tracked simultaneously. The racy of the ground-truth. The Algorithm compares the next mesurament is added to all subsequeces that end in a calculated speed and bearing with the recorded values consistent measurement; if there is no such subsequence, present in the data. The input consist of speed and heada new subsequence starting with the measurement is ing thresholds (tS and tH) and the file path. In line 6, created. In the end, the longest subsequence is returned. for each point in the file, firstly, we check if the IDs are Also, as a baseline, the library implements their interpre- the same, i.e. the points belong to the same trajectory. tation of the method described in [12] as Local Greedy Secondly, we calculate speed and bearing between the Speed-bounded (LGSB). In LGSB, a graph is constructed point and its successor. Later, we compare the newly with a vertex per measurement. Two vertices are con- calculate speed and bearing with the files’ input in line nected if their timestamps are successive in the original 11. If the diference in speed or heading are bigger than trajectory and they are consistent to the speed-bound. the inputted thresholds, the point is considered an outlier A measurement is added to the output, if and only if its and added to the output array. vertex is in a connected component of a given size. LGSB Our method involves cross-referencing the data from does not guarantee that the complete output is consistent multiple sensors in order to generate a more accurate repaccording to the speed bound [12]. resentation of the true trajectory. We apply this method
Argosfilter 6 [10] is an R package that ofers a set of in data from modern multi-sensor trackings, such as GPS, functions for working with trajectory data. The outlier AIS, ADS-B, Mode S, TCAS and FLARM sensors. By comdetection in Argosfilter uses two diferent methods: one bining the data from multiple sources, we can increase based on speed and the other based on location. The the overall accuracy of the ground-truth in the presence speed-based method is similar to the one provided in [12], of errors or noise in individual sensors. When comparing but the location-based method is based on the algorithm data from diferent sources, we can diferentiate the data to see if there are any discrepancies or inconsistencies
5https://github.com/movetk/movetk 6https://cran.r-project.org/web/packages/argosfilter/argosfilter.pdf
between multiple sources, such as diferent sensors or instruments. In addition, statistical tests can determine whether the data is consistent with a particular hypothesis or model. For example, we can check the calculated speed with the speed given in the data.
Our datasets for this benchmark consist of multisensor trajectory data. The first source is AIS data 8: AIS is the location tracking system for sea vessels. Additionally, the AIS data is collected from a variety of diferent ships, providing a diverse set of trajectories to work with. This can be useful for testing the robustness of diferent algorithms and methods, and for evaluating their performance on diferent types of data. In this paper, we utilize total of 4.3 GB. The Fig. 1 shows the raw data and Fig. 2 shows filtering of outliers.
The raw data collected in the OpenSky Network 9 is stored in a historical database and used by researchers to study and improve air trafic control technologies and processes. The Fig. 3 shows the raw data.
We utilize two datasets from [26] 10 consists of GPS trajectory datasets of Southeast Asia from Singapore and Jakarta. Grab-Posisi covers over 1 million kilometers and contains more than 88 million points. The Images 4 and 5 show the raw data.
Table 1 shows the total number of records, as well as the number of outliers detected in the cross-check, the correct points, i.e., points that are not considered outliers, and the percentage of outliers over total points. The cross-check method was used to detect the outliers.
OpenSky data does not have a significant amount of outliers. One possible reason for the low number of outliers in the OpenSky data could be the accuracy of the sensors used to collect the data. If the sensors are highly accurate, there may be fewer errors or discrepancies in the data, resulting in fewer outliers. Additionally, it is pos
sible that the data has been adjusted or corrected in some way to account for any errors or noise, further reducing the number of outliers. It is also worth considering the nature of the data itself. to use 3D data or incorporate altitude data in some cases to analyze flight patterns accurately. 4.2. Benchmark Fig. 6 relates the run time of libraries. The top left The benchmark was run in seven libraries composed by graph corresponds to Jakarta datasets, divided by each Ptrail, MovingPandas, Scikit-Mobility,Pymove, Stmove, file part 0, 1, 2, and 3. The top right graph represents Argosfilter and MoveTk. These were described in Session the Singapore dataset and corresponding files. OpenSky 3. Fig. 6. The data used in the benchmark was decribed in dataset run time is at the bottom left and AIS is at the botSession 4.1. The benchmark code is publicly available11. tom right. It is possible to see that the first four libraries,
The European aviation industry [27] developed meth- i.e., Ptrail, Moving Pandas, Scikit Mobility and Pymove ods to reduce carbon emissions to meet climate targets. takes the longest to finish as they are implemented in An aircraft can fly an optimal flight path and use var- Python. For Jakarta and Singapore datasets, Pymove ious technologies and infrastructure to minimize fuel presents the highest run time in the biggest datasets. consumption and carbon emissions. This might include Both R libraries have similar performance. Also, C++ has using modern flight planning software and meteorolog- a similar performance to the R libraries. ical data to plan for a minimal amount of fuel, using For the OpenSky dataset, Pymove and Moving Pandas green energy at the airport to power the aircraft on the have similar performance in terms of run time, while ground, and using electric taxi solutions to minimize MoveTk is slightly faster but has similar performance to ground-based emissions. The aircraft would also fly an Stmove and argosfilter. optimal climb phase, follow a fuel-eficient cruising level, The AIS data exhibits an exception in the run time of and use idle thrust descent to minimize fuel consumption MoveTk, which may be due to the implemented process during descent, i.e., the aircraft should change its altitude of reading the data. Its performance is comparable to that as rarely as possible. Due to this standard, we consider of Pymove. The run time of the various libraries varies the OpenSky dataset with only 2D rather than 3D data. depending on the dataset being used and the specific However, it is important to note that the assumption may implementation of the library. It is important to consider not hold true in all circumstances. It may be necessary the run time of the diferent options when selecting a library for detecting and erasing trajectory data. 11https://github.com/marianaGarcez/OutlierDetectionLibraries Fig. 8 and 9 illustrate the run time for the Python and Pandas, Stmove, argosfilters, and MoveTk have a consistent amount of removal. For the AIS dataset, all libraries seem consistent in the number of points removed, with the exception of Pymove, which removes a larger number of points. It is important to note that the number of removed points does not necessarily imply accuracy or precision. It is necessary to compare the actual outlier and normal points with the resulting trajectories in order to fully assess the accuracy and reliability of the trajectories cleaned by each library.
In order to analyze results, we utilize scores to compare the performance of the diferent libraries. Fig. 10, 11, 12, Figure 8: Run time for Python Libraries 13 show the Accuracy, precision, recall and F-1 scores of each library, respectively. The scores are based on comparison to the cross-check data and libraries output.
Fig. 10 shows the accuracy of each library. It is possible to observe that over all datasets, Movetk has the highest accuracy. For Jakarta dataset, Moving Pandas accuracy is comparable to MoveTk. As second, we observe Ptrail, argosfilter and Pymove. Scikit Mobility, has the lowest accurarcy in this dataset. For the Singapore dataset, Moving Pandas also has comparable accuracy to MoveTk. Libraries Scikit Mobility, Pymove, StMove, argosfilter have a comparable performance. Ptrail has the Figure 9: Run time for R libraries lowest accurarcy in this dataset. For OpenSky data, both argosfilter and Movetk have the highest accuracy. All other libraries have a comparable performance. With the R programming languages, respectively. For the Jakarta exception of Ptrail which presents a low accuracy in the and Singapore datasets, the python libraries Ptrail, Mov- file ’2020-02-25-00’. A high accuracy score means that ing Pandas and Scikit Mobility have a similar perfor- the library is able to correctly identify a large proportion mance. It is possible to see a higher processing time for of the true outliers and normal points in these datasets. the Pymove library. For the OpenSky and AIS datasets, A high accuracy score indicates that the trajectory is Ptrail and Scikit Mobility present a better performance. likely to be accurate and useful for identifying patterns In contrast, Moving Pandas exhibit a higher processing or anomalies in the data. While Ptrail and Scikit Mobility time for both datasets. Pymove run time is comparable tend to have lower accuracy. with Ptrail and Scikit Mobility only with AIS dataset. Precision measures the proportion of true positives Overall, Pymove has a higher processing time compared among all positive predictions made by the library. A to the other libraries. Both R libraries have a similar high precision score indicates that the library can corrun time for the Jakarta and AIS datasets. Although, Ar- rectly identify a large proportion of the true outliers. In gosfilter run time is consistently lower throughout all contrast, a low precision score indicates that the library datasets. It is possible to see a considerable diference in is prone to false positives. Looking at Fig. 11, we can see performance for Singapore and OpenSky datasets. that the libraries Ptrail, Moving Pandas, Scikit Mobility,
As shown in Fig. 7, the number of outliers removed Pymove, and StMoe have a consistent level of precision by each library varies depending on the dataset being across the diferent datasets. Except for StMove in the AIS used. These points consist of total points, i.e., outliers dataset, the precision is the lowest among all libraries. and normal points. The amount of points corresponds Argos filter and MoveTk have lower precision scores to the correct points detected by each library. For the throughout all datasets. Overall, these results suggest Jakarta dataset, there is a consistent quantity of removed that Ptrail, Moving Pandas, Scikit Mobility, Pymove, and points, with Pymove removing the most points followed StMoe are relatively reliable in precision, with a low rate by Ptrail. The Singapore dataset is consistent between of false positives. On the other hand, Argos filter and Stmove, argosfilter, MoveTk, and Moving Pandas, with MoveTk tend to have lower precision scores, indicating Pymove, Ptrail, and Scikit Mobility removing points in that they may be prone to false positives. increasing order. For the OpenSky dataset, Scikit Mo- Recall is a measure of the proportion of true positives bility and Ptrail remove the most points, while Moving correctly identified by the library. A high recall score indicates that the library is able to correctly identify a large proportion of the true outliers in the dataset, while The F-1 score is a metric used for comparing the overa low recall score indicates that the library is prone to all performance of the diferent libraries. The final metric false negatives. The Fig. 12 shows the recall. Movetk we consider is the F-1 score, a combination of precision have the highest recall for almost all datasets and files. and recall, shown in Fig. 13. The MoveTk library has For the Jakarta dataset, Moving Pandas has the second the biggest rate for the F1-score in all datasets. Followed highest recall, followed by Ptrail, argosfilter and Pymove. by argosfilter library. In the Jakarta dataset, Moving Scikit Mobility presents the lowest recall. The libraries Pandas has the second highest F-1 score. Followed by MoveTk and argosfilter in Singapore dataset have the argosfilter and Pymove. In contrast, Stmove and Scikit highest recall. Followed by Moving Pandas. Also, StMove Mobility have a low rate for the F-1 score. For the Singaand Scikit Mobility have comparable performance and, pore dataset, Moving Pandas has the third highest rate, Ptrail presents the lowest performance. For the OpenSky followed by StMove. Ptrail has the lowest rate in this dataset, the libraries have a similar performance. Still, dataset. The OpenSky dataset, has a similar performance MoveTk presents the highest recall and Ptrail the lowest. in all libraries. With the exception of Ptrail which has The AIS dataset has MoveTk as the highest recall. Ptrail, the lowest score in the first file. In AIS dataset, Movetk, Moving pandas, Scikit Mobility, Pymove and Stmove have Ptrail, Moving Pandas, argosfilter have the highest score. the lowest recall rate. These results suggest that MoveTk In contrast, Pymove and StMove have the lowest rate. is the most reliable library regarding recall, with a low These results suggest that MoveTk [5] is the most rerate of false negatives. On the other hand, Ptrail, Moving liable library for trajectory outlier removal, with a high pandas, Scikit Mobility, Pymove, and Stmove tend to have level of accuracy, precision, and recall. Moving Pandas lower recall scores, indicating that they may be prone [6] also performs well in terms of F-1 score, particularly to false negatives. These results suggest that MoveTk is for the Jakarta and Singapore datasets. On the other hand, the most reliable library regarding the recall, with a low Ptrail, argosfilter, Pymove, Scikit Mobility, and Stmove rate of missed true outliers. On the other hand, Ptrail, tend to have lower F-1 scores, indicating that they may Moving Pandas, Scikit Mobility, Pymove, and Stmove not be as reliable for removing outliers in these datasets. tend to have lower recall scores, indicating that they may It is also important to consider the specific requirements be prone to missing true outliers. of the application and the trade-ofs between precision, recall and run time. Also, it is important to note that [10] C. Freitas, C. Lydersen, M. A. Fedak, K. M. Kovacs, the libraries’ performance varies based on the dataset. In A simple new algorithm to filter marine mammal addition, the ground-truth method can be applied in all argos locations, Marine Mammal Science (2008). of these datasets to assist in outlier detection. [11] D. P. Seidel, E. R. Dougherty, W. M. Getz, Exploratory movement analysis and report building with r package stmove, bioRxiv (2019). 5. Conclusion [12] Y. Zheng, Trajectory data mining: An overview, ACM Trans. Intell. Syst. Technol. 6 (2015).
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