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[Page no. 6] "in different regions and time periods. Our method has improved the accuracy by more than 20% than other methods. C. Results on Vessel Motion Dataset We perform two tasks on this dataset. The ﬁrst one is the standard trajectory clustering task. In this task, we utilize our framework to generate clusters that have similar moving behavior, and then analyze the meaning of trajectories in them. The second one is vessel type analysis. After clustering, we examine whether the vessels having the same type are grouped into the same cluster or not and measure the accuracies. Trajectory Clustering Task: Utilizing our framework, trajectory moving behavior vectors are generated. Most of the parameters used in this procedure are the same as synthetic dataset except the number of iterations and hidden states. Because real trajectories are usually much longer, we set the number of iterations to 3000 and the size of the hidden layer to 300. We use K-means to generate the clusters for the Z set. As we do not know the number of ground-truth clusters on the real data, we describe how we choose the value of K as follows. We increase the number of K from 3 to 100 with step-size 5. For each K, we calculate the sum of distances from samples to their nearest centroid and denoted it as Ek. The result is shown in Figure 9. The K value corresponding to the elbow point can be found in Figure 9. As shown in Figure 9, we choose K = 33, extracting 33 clusters for the 4700 trajectories. Some of the cluster results are shown in Figure 10 and Figure 11. The blue lines stand for the trajectories, the yellow points stand for the start point and the red points stand for the end point. The ﬁrst cluster"

[Page no. 2] "strategy that considers each trajectory as a sequence of three-dimensional records (time, latitude, longitude) leads to dramatically oscillating parameters and non-convergence in the optimization process of RNNs. In light of the above issue, we ﬁrst extract a set of movement features for each trajectory. Our feature extraction module is based on a ﬁxed-length sliding window, which scans through the input trajectory and extracts space- and time- invariant features of the trajectories. After feature extraction, we con- vert each trajectory into a feature sequence to describe the movements of the object and employ a sequence to sequence auto-encoder to learn ﬁxed-length deep representations of the objects. The learnt low-dimensional representations robustly encode different movement characteristics of the objects and thus lead to high-quality clusters. In summary, we make the following contributions: • We study the problem of detecting space- and time- invariant trajectory clusters. Such a task differs from previous works in that it can group trajectories collected in different regions with varying lengths and sampling rates. • We employ a sliding-window-based approach to extract a set of robust movement features, and then apply se- 978-1-5090-6182-2/17/$31.00 ©2017 IEEE 3880  quence to sequence auto-encoders to learn ﬁxed-length representations for the trajectories. To the best of our knowledge, this is the ﬁrst study that leverages recurrent neural networks for the trajectory clustering task. • We evaluate our method on both synthetic and real-life data. We ﬁnd that our method can generate high-quality clusters on both data sets and largely outperforms existing methods quantitatively. The rest of this paper is organized as follows. In Section II, we review related work. We overview of our method in Section III and then detail the main steps in Section IV. We empirically evaluate the proposed method in Section V and ﬁnally conclude in Section VI. II."

[Page no. 1] "characteristics of the moving objects, but also support a wide spectrum of high-level applications, such as travel intention inference, mo- bility pattern mining [1], [2], location prediction and anomaly detection [3]. A plethora of trajectory clustering techniques have been proposed [4]. They typically use certain measures to quan- tify trajectory similarities, and then apply classic clustering algorithms (e.g., K-means, DBSCAN, spectral clustering). Popular trajectory similarity measures[5] include DTW (Dy- namic Time Warping), EDR (Edit Distance on Real sequence) and LCSS (Longest Common Subsequences). Although these measures can group trajectories that are similar in a ﬁxed geographical region and time period, many practical appli- cations involve trajectories that distribute in different regions with different lengths and sampling rates. In such applications, one is often required to ﬁnd clusters where the within-cluster similarity appears in different time and space. For example, the taxis in trafﬁc jams can have similar moving behaviors, but the trafﬁc jams usually occur in different areas in the city with different durations. Such spatio-temporal shifts [6] are common in many scenarios and render current trajectory clustering algorithms ineffective. In this work, we revisit the trajectory clustering problem by developing a method that can detect space- and time- invariant trajectory clusters. Our method is inspired by the recent success of recurrent neural networks (RNNs) for handling sequential data in Speech Recognition and Neural Language Processing. Given the input trajectories, our goal is to convert each trajectory into a ﬁxed-length representation that well encodes the object’s moving behaviors. Once the high-quality trajectory representations are learnt, one can easily apply any classic clustering algorithms according to practical needs. Nevertheless, it is nontrivial to directly apply RNN to the input trajectories to obtain quality representations because of the varying qualities and sampling frequencies of the given trajectories. We ﬁnd that a naive"

[Page no. 7] "types have different behavior patterns[26][27]. In this task, we try to recognize the vessel type by utilizing the trajectory clustering. We took the trajectory moving behavior vectors of an vessel as the input of encoder and minimized the mean squared error between encoder input and decoder output. Subsequently, we obtained the moving behavior vector of the vessel. Based on these vessel moving behavior vectors, we utilized our clustering algorithm to get the vessel clusters. Ideally, the vessels in different clusters should have different vessel types. The clustering accuracy results are shown in Table 2. Although our approach is totally unsupervised, we still observe quite good vessel typing accuracies. The overall accuracy for vessel type recognition is about 78%. Especially, the precision / and recall for the oil ship and the passenger ship are 0.67/1.0 and 0.91/0.88, respectively. However, the result of cargo ship is only 0.7/0.52. We consulted the experts in the shipping ﬁeld for this phenomenon. The reason is that cargo ships contain many subtypes such as dry cargo ship, TABLE II VESSEL TYPE CLUSTERING RESULTS Passenger Fishing Cargo Oil Total Number 50 50 50 50 Precision 44/48=0.91 35/41=0.85 26/37=0.7 50/74=0.67 Recall 44/50=0.88 35/50=0.7 26/50=0.52 50/50=1.0 Overall Accuracy: (44+35+26+50)/200 = 0.78 wet cargo ship, and roll-on-roll-off ship. These different types make a great difference in the moving behavior patterns. However, if such subtype information is available in the training process, the cluster performance is expected to have better improvements. In general, this set of experiments show that different vessel types have different moving behavior patterns, and our framework is good at capturing such patterns. VI. CONCLUSION In this paper, we proposed a novel framework for trajectory clustering with similar movement patterns. A moving behavior feature extraction algorithm was proposed to extract moving behavior features that captured space- and time-"

[Page no. 1] "Trajectory Clustering via Deep Representation Learning Di Yao1,3, Chao Zhang2, Zhihua Zhu1,3, Jianhui Huang1,3, Jingping Bi1,3 1Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China 2Dept. of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, USA 3University of Chinese Academy of Sciences, Beijing, China Email: 1,3{yaodi, zhuzhihua, huangjianhui, <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>, <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS> Abstract—Trajectory clustering, which aims at discovering groups of similar trajectories, has long been considered as a corner stone task for revealing movement patterns as well as facilitating higher-level applications like location prediction. While a plethora of trajectory clustering techniques have been proposed, they often rely on spatiotemporal similarity measures that are not space- and time- invariant. As a result, they cannot detect trajectory clusters where the within-cluster similarity occurs in different regions and time periods. In this paper, we revisit the trajectory clustering problem by learning quality low- dimensional representations of the trajectories. We ﬁrst use a sliding window to extract a set of moving behavior features that capture space- and time- invariant characteristics of the trajectories. With the feature extraction module, we transform each trajectory into a feature sequence to describe object movements, and further employ a sequence to sequence auto- encoder to learn ﬁxed-length deep representations. The learnt representations robustly encode the movement characteristics of the objects and thus lead to space- and time- invariant clusters. We evaluate the proposed method on both synthetic and real data, and observe signiﬁcant performance improvements over existing methods. I. INTRODUCTION Owing to the rapid growth of GPS-equipped devices and location-based services, enormous amounts of spatial trajec- tory data are being collected in different scenarios. Among various trajectory analysis tasks, trajectory clustering — which aims at discovering groups of similar trajectories — has been recognized as one of the most important. Discovering trajectory clusters can not only reveal the latent"

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