Recognizing Instantaneous Group Patterns in Vessel Trajectory Data: A Snapshot Perspective

Abstract

Recognizing vessel navigation patterns plays a vital role in understanding maritime traffic behaviors, managing and planning vessel activities, spotting outliers, and predicting traffic. However, the growth in trajectory data and the complexity of maritime traffic in recent years presents formidable challenges to this endeavor. Existing approaches predominantly adopt a ‘trajectory perspective’, where the instantaneous behaviors of vessel groups (e.g., the homing of fishing vessels) that occurred at certain times are concealed in the massive trajectories. To bridge this gap and to reveal collective patterns and behaviors, we look at vessel patterns and their dynamics at only individual points in time (snapshots). In particular, we propose a recognition framework from the snapshot perspective, mixing ingredients from group dynamics, computational geometry, graph theory, and visual perception theory. This framework encompasses algorithms for detecting basic types of patterns (e.g., collinear, curvilinear, and flow) and strategies to combine the results. Case studies were carried out using vessel trajectory (AIS) data around the Suez Canal and other areas. We show that the proposed methodology outperformed DBSCAN and clustering by measuring local direction centrality (CDC) in recognizing fine-grained vessel groups that exhibit more cohesive behaviors. Our results find interesting collective behaviors such as convoy, turning, avoidance, mooring (in open water), and berthing (in the dock), and also reveal abnormal behaviors. Such results can be used to better monitor, manage, understand, and predict maritime traffic and/or conditions.

1. Introduction

According to the United Nations, the international seaborne trade volume was 12,027 million tons in 2022 [1], emphasizing the importance of maritime traffic safety. Maritime administrators primarily monitor ship navigation through the real-time information provided by the Automatic Identification System (AIS). Recently, AIS data have been extensively used for, e.g., anomaly detection [2,3,4], behavior analysis [5,6,7], and maritime traffic monitoring [8,9,10]. Nevertheless, the large amount of trajectory data leads to difficulties in analyzing and managing vessel traffic patterns, and complexities in marine traffic environments may increase potential risks and their environmental impact [1]. To address these challenges, new analytical approaches to effectively extract contextual information and patterns from massive trajectory data are in high demand. This endeavor should more effectively improve maritime traffic management (e.g., safety, regulation, and efficiency).

A group of vessels, not necessarily part of a particular fleet, will be governed by specific rules during traffic and their interactions with nearby vessels and the environment. Some organized structures (patterns) thereby emerge spontaneously, much like the flocking and schooling of a swarm of birds or fish [11,12]. Unlike many studies on simulating collective dynamics using the bottom-up approach [13,14,15], we aim to do the opposite: recognizing group-level vessel patterns from real movement data to infer their collective behaviors. Because discernable visual patterns are usually the signatures of a collective behavior of regularity, our clustering approach contributes to the field in the following potential areas:

• Behavior/semantic inference. For example, it can be used to detect anchorage areas (legal or illegal), identify if a vessel group is turning or keeping straight (Figure 1a), reveal the homing of fishing ships back to their port (Figure 1b), etc.
• Maritime safety monitoring. For example, it can be used to predict the future positions of two moving fleets and signal a collision warning. It can also monitor the density of the anchored vessels and detect if individual vessels pass through the anchored group. This is especially useful if the group of vessels are not anchored in a designated area (in this case, the standard geofence technique fails to give warning). It is also able to monitor abnormal behavior in a moving group, like abrupt acceleration, turning, or stopping. Monitors can build on this and combine with domain knowledge (e.g., COLREGS) to make more informed decisions.
• Maritime traffic monitoring. Our approach can help identify whether the main course of a group of vessels matches the designed traffic lane. It is also useful in evaluating real-time traffic over a certain port or channel, comparing traffic in different areas, and then recognizing traffic congestion.

Different from previous approaches, which mostly take a ‘trajectory perspective’ (Figure 2c), our approach takes a ‘snapshot perspective’ (Section 1.1) and aims to recognize instantaneous group patterns that are otherwise concealed by their massive historical trajectories. Our recognition methodology is largely inspired by the recognition of building patterns on topographic maps [16]. Indeed, vessels as seen from a snapshot perspective (Figure 2a) share many properties with building footprints on maps; both form saliant patterns that are visually discernable. Vessels differ from buildings in that the former are moving objects, and hence their pattern-forming processes are governed by collective dynamics similar to those in collective animal behaviors [17]. Therefore, the dynamic properties of vessels are incorporated into our algorithms.

1.1. Spatio-Temporal Views and Related Work

Safety remains a vital topic in maritime transportation. To reduce accident rates, the International Maritime Organization (IMO) released a series of guidelines (e.g., COLREGS [18]). Computational approaches are shown to be useful in outlier detection and early warning. For example, pattern recognition was used identify normal vessel behavior [19], by which dangerous behaviors such as collision risks [20] and abnormal maneuvers [21] can be found more easily.

Methodologically, there are two main views from which the data mining of spatio-temporal traces can be approached, namely, the trajectory versus the snapshot perspective (Figure 2). The trajectory view is a more common one, where the trajectories of moving objects within a time range are ‘flattened’ into linear features laid out on a planar space, also known as traces (Figure 2c). The trajectory points of a moving object are its footprints back in time. Most previous work falls into this category [22,23,24,25]. The second perspective differs from the first one in that it deals only with the footprints of a group of moving objects at a single time point, hence, a snapshot model (Figure 2a) [26,27,28]. Group-level patterns and implied collective behaviors such as the above-mentioned ones (Figure 1) are only visible with this perspective. Although this approach captures instantaneous snapshots of moving objects (i.e., the distribution of points), it contains the dynamical information (e.g., speed) of the objects as well. Hence, groups with different dynamical characteristics can also be distinguished using this approach. We will review the related work following our proposed typology.

Pattern mining approaches, from the trajectory perspective, can be divided into three categories, including methods based on (1) trajectory lines, (2) trajectory points, and (3) origin–destination (OD) pairs. The TRACLUS algorithm by Lee et al. [29] is a typical example of the first approach. In their algorithm, trajectories are partitioned into segments and then grouped to find the common segments of trajectories, which are used to generate representative trajectories for large trajectory datasets. Ma et al. [30] improved the spectral clustering of trajectory lines with a one-way distance similarity model to detect trajectories with common waterways or origins/destinations. For similar purposes, Zhang et al. [31] proposed a clustering algorithm that is adaptive to the dynamic changes of trajectory data. Their line-based measurements are also used for identifying stopping/moving states, maneuvering, and anomalous behaviors [32,33,34]. Willems et al. [35] presented an effective visualization technique, combining kernel density with motion dynamics to visually reveal common navigation lanes/channels, anchorages, and slow-speed areas.

According to Zhang et al. [36], the approaches making use of trajectory points are more robust to noise, though motional properties and trends (e.g., turning directions) are discarded. For instance, Kabir et al. [5] extracted anchored vessels from their trajectory points using coastline buffers. Lee et al. [37] analyzed maneuvering behavior during arrival and departure in a port using a clustering of trajectory points, which simplifies the computation. OD is a special type of trajectory which contains only the origin and destination of a voyage. This approach helps to generalize from geometric details and yield insight into higher-level interaction patterns [38].

As the detected patterns of common destinations (waterways or lanes) are accumulations of trajectories at different times, this approach does not allow for the detection of vessel group patterns and implied collective behaviors occurring at single times. The snapshot perspective is more suitable for identifying such instantaneous group patterns, but, to our knowledge, there was not much research on movement pattern analysis from this perspective. Examples include the recognition of flock, leadership, convergence, encounter, and convoy patterns [39,40,41,42,43]. Such approaches still require trajectories over a time range to identify the temporal patterns, and hence can be thought of as working in the space–time cube (Figure 2b). Additionally, the rules for identifying groups are limited to proximity and do not lend themselves directly to detecting meaningful vessel groups (e.g., anchoring or turning fleets).

On the other hand, collective vessel behaviors usually cast salient visual patterns that help us to recognize their behaviors. For example, Figure 1a depicts vessels moving across the Akashi Strait in Japan. We have an impression that all the vessels will take a left turn after crossing the bridge. Such a trend can be inferred from the group even without seeing the trajectories (historical footprints). This can be explained by the Gestalt principles of visual perception that dictate the visual recognition of objects that have a common fate/goal [44]. A highly related work is the automated recognition of building alignments on topographic maps proposed by Zhang et al. [16]. By considering features such as proximity, object orientation, shape, and size, their approach produced promising results. We want to extend their framework by incorporating characteristics that are unique to moving vessels, such as dynamic properties and free moving space.

1.2. Vessel Group Patterns in the Snapshot View

Vessels, as mobile objects with dynamic status (e.g., speed, course, draught, etc.), differ from static entities like buildings, meaning that they may exhibit more complex collective patterns and dynamics. From a snapshot perspective, we distinguish vessel groups along two dimensions: spatial and temporal (Figure 3). In each dimension, group members can be homogeneous or non-homogeneous. Although we only deal with a single point in time in the snapshot view, the temporal dimension is approached using the dynamics of the vessels, such as their speed and heading. The term ‘homogeneity’ means that the interesting properties of vessels are highly similar within a group while they are different from other groups, either spatially or temporally. We explain the four basic pattern types in detail below.

• Spatially and temporally homogeneous groups: Vessel groups in this category exhibit both spatial and temporal homogeneity, characterized by a regular spatial arrangement (e.g., similar spacing between objects) and similar motion states (e.g., direction and speed). This is the strongest form of vessel group patterns and such a group can maintain its identity and characteristics (e.g., shape, density, speed) over an extended period of time. The shapes of such groups vary depending on their collective behaviors. Examples include a fleet of moving vessels (convoy) maintaining their linear shape and moving direction, and a bulk of mooring vessels keeping its areal form and the headings of its members (Figure 3b).
• Spatially homogeneous and temporally non-homogeneous groups: Vessels in such a group are uniformly distributed in space but possess different speeds and/or headings. This is a sign of an unstable group that may no longer keep its identity and spatial form in the near future. Figure 3d presents a scenario in which some vessels in an anchorage area are departing to different destinations. Although these vessels remain their positions with the anchored group (highlighted in the dashed circle) in the current snapshot, the group will soon disappear.
• Spatially non-homogeneous and temporally homogeneous groups: Vessels in such a group exhibit similar moving directions and speeds, but do not display apparent spatial regularity. For example, the shuttles in Figure 3a traveling across two mooring areas, with a relatively loose and random spatial distribution. However, they share a common watercourse and perhaps destination (e.g., port).
• Spatially and temporally non-homogeneous groups: Neither spatial nor temporal homogeneity is shown in this group of vessels (Figure 3c). This is just a random group of vessels that are not associated with meaningful collective behaviors.

Homogeneous group patterns are the hallmarks of meaningful collective behaviors. As vessel groups with both spatial and temporal regularity have the most significant and persistent patterns, we mainly focus on this type of pattern. Such patterns can be divided into finer-grained patterns according to their spatial forms and dynamic properties. In general, we classify them as linear (one-dimensional)- and areal (two-dimensional)-shaped patterns, which can be either stationary or moving groups. For example, vessels entering/exiting a port or coming across a narrow waterway usually form a linear (collinear or curvilinear) fleet with similar spacing and speed, while in open water, such regular groups may spread out in areal-shaped patterns (e.g., moving flows or mooring vessels).

The main objective of this paper is to develop a methodology that can recognize the above-mentioned finer-grained (linear and non-linear) groups from a set of vessels spread over a certain region at individual time points. This is essentially a clustering process for vessel groups (stationary or moving). We observe that existing clustering algorithms failed to find meaningful groups with inner cohesion (Section 3.3). To bridge this gap, we propose the algorithms in Section 2 to recognize collinear and curvilinear vessel groups (Section 2.4) and two-dimensional vessel flows (Section 2.5). Complex patterns can be formed by combining basic pattern types (e.g., the fan-shaped pattern in Figure 1b). In Section 3, we test our methodology on real AIS datasets and compare it with competitive clustering algorithms, where we also showcase how vessel group patterns can be used to infer behaviors and spatial context. Implementation details and applications are discussed in Section 4. Finally, we conclude the paper in Section 5.

2. Methodology

2.1. Overall Framework

The framework consists of four steps (Figure 4), which aim at identifying potential clusters from vessel movement data at a given time. The input is a set of points representing the locations of vessels. The steps are outlined as follows:

(1)

Modeling the proximity relationship. We construct a proximity graph ProxG <V, E> based on the input data, so that local neighbors are connected in the graph (Section 2.2). Then, to aid the pattern searching algorithm, we derive a Minimum Spanning Tree (MST) on the proximity graph and further prune the MST to obtain an initial division of the data points (Section 2.3).

(2)

Applying recognition algorithms. We apply searching algorithms on the pruned Minimum Spanning Tree (MST) with rules for linear (Section 2.4) and flow patterns (Section 2.5).

(3)

Post-processing for the recognized linear (Section 2.4.4) and flow patterns (Section 2.5.3) to improve the recognition quality.

(4)

Combining the results from multiple algorithms (Section 2.6). We employ a combination strategy to reconcile and combine conflicting results obtained by individual algorithms.

2.2. Proximity Graph

Delaunay Triangulation (DT) is a widely used spatial partitioning method that generates non-overlapping partitions (i.e., triangles) by connecting a given set of points [45]. This partitioning method provides a more natural way to model proximity relationships between points (vessels) [46,47].

In this study, we adopt DT to model the proximate relationships between vessels. Specifically, vessels are represented as points with two dimensional coordinates, on which a DT is constructed as the proximity graph ProxG <V, E>. Each vertex in ProxG represents a vessel, and adjacent vessels are connected by their edges in E. Then, we compute a MST from the proximity graph. The weight of edges in the DT and MST is defined as the distance between adjacent vertices.

2.3. Graph Pruning

A study on the collective flight behavior of bird flocks [48] demonstrated that the range of interactions among individuals within the group is not determined by a fixed threshold but rather by the relative relationships. We have taken this into consideration when formulating distance-related rules, including the inconsistent edge and the proximity rule in Section 2.4.2, Section 2.4.3, and Section 2.5.1.

A pre-clustering was performed before the pattern recognition algorithm. In this process, we prune inconsistent edges from the MST and divide the dataset into some initial homogeneous groups. Inconsistent edges, originally proposed by Zahn [49] and modified in [16], have a formal definition as follows:

$$S=\mathit{max}\{f\cdot mea{n}_{weight}\hspace{0.33em},\hspace{0.33em}mea{n}_{weight}+n\cdot st{d}_{weight}\}$$

(1)

$$e_i=\left\{\begin{array}{l}inconsistent,\hspace{0.33em}\hspace{0.33em}if\hspace{0.33em}{w}_i>S_l or w_i>S_r\\ consistent,\hspace{0.33em}\hspace{0.33em}otherwise\end{array}\right.$$

(2)

where w_i represents the weight (length) of edge e_i, S denotes the significance of e_i as compared to its neighboring edges to the left or right; mean_weight is the average weight of the neighboring edges (left or right); std_weight denotes the standard deviation of the weights (left or right), and n and f are user-specified parameters.

In Equation (1), we assume that the weights/length within a homogeneous cluster follow normal distribution. If the length of an edge is longer than the mean_weight of its neighboring edges on either side by three times that of std_weight (i.e., n = 3), this means that the edge is longer than 99.7% of the edges that can be drawn from the cluster randomly, thus accounting for an exceptionally/significantly long edge. In practice, it is also possible to encounter cases where the weight distribution is relatively uniform, for which the standard deviation std_weight is close to zero. To fix this issue, we introduce a safeguard threshold f mean_weight to complement the definition of inconsistent (significant) edges. If the weight of e_i is significantly larger than its neighboring edges on either side, we consider it as an inconsistent edge connecting two clusters of different characteristics. In our experiments, we found that f = 2 and n = 3 were the best.

By removing inconsistent edges (red edges in Figure 5c), we obtain initial clusters that are easy to work with in our subsequent processes. Apparently, edges within in each cluster (C1–C3) are of similar lengths, while the lengths (weights) vary among different clusters. This naturally leads to spatially homogeneous groups of vessels (Section 1.2) without further considering their dynamic properties. This is not possible to obtain with a fixed threshold approach.

2.4. Linear Pattern Recognition

In Section 2.4.1, we present a search algorithm for one-dimensional linear patterns. Furthermore, Section 2.4.2 and Section 2.4.3 introduce rules specific to the recognition of collinear and curvilinear vessel groups, which can be parameterized in the search algorithm. Post-processing is needed to finalize the recognition (Section 2.4.4).

2.4.1. Search Algorithm

The search algorithm (Algorithm 1) is performed on each of the subtrees (pruned MSTs) and incorporates specific rules for recognizing collinear and curvilinear patterns. The algorithm starts from a node of degree 1 or 3, and traverses the entire subtree to search for connections (edges) that satisfy specific rules. In general, points of degree 1 are endpoints of linear paths and points of degree 3 are intersections of different linear paths (also endpoints). Searching for each of these two types of points as starting points completes a traversal of the entire MST, and this guarantees that we will discover a full set of patterns. Specifically, given the input node v₀ as the current node, we check each of the adjacent nodes (v₁) of v₀ within the subtree; if edge (v₀, v₁) satisfies the rules described either in Section 2.4.2 or Section 2.4.3, node v₁ is added to the temporary set tempColl and becomes part of the linear structure; v₁ becomes the current node from which to proceed with the search. In cases where multiple edge choices are available, we select the one that best conforms to the rules. If any rule is not satisfied, the algorithm stops and restarts a new search from the next neighbor or with another node of degree 1 or 3 as the current node.

Algorithm 1 Linear Pattern Search Algorithm

Output: Collection of recognized linear-groups

Input: Pruned MST; Rules

for each v0 of degree 1 and degree 3 vertexes do

currentVertex ← v0

tempColl ← empty list

tempColl.append(currentVertex)

while find a v1 adjacent to currentVertex and not visited do

if v1 satisfies rules then

tempColl.append(v1)

currentVertex ← v1

else if v1 not satisfies rules then

add tempColl to ResultColl if ResultColl contains more than 3

currentVertex ← v1

end if

end while

add tempColl to ResultColl if ResultColl contains more than 3

continue;

end for

return ResultColl

2.4.2. Rules for Collinear Patterns

Vessels in a collinear group arrange themselves in a line, keep roughly equal distances from one another, travel at similar speeds, and share common courses (destinations). This is the strictest form of pattern which emerges when a group of vessels sail through a narrow waterway, enter a port, or berth alongside one. To detect this pattern, we first consider the rules of proximity and path angle as suggested in [16]. As vessels are moving objects, we further constrain the pattern searching by incorporating similarities in vessel heading and speed. Path angle is defined as the angle between adjacent edges, while triangle direction indicates the heading of a vessel (Figure 6a).

Proximity rule implies that the spacing between adjacent vessels in the same group should be more or less the same, similar to the inconsistent edges in Section 2.3. If the weight/length of an edge (v₀, v₁) encountered during the search is significantly different from existing edges in the pattern, we consider it as an outlier and stop searching. The path angle rule (Figure 6b) ensures that the angular deviation between the new edge and all existing edges in the pattern should fall within a specific threshold (PathAngleDev). The heading similarity rule (Figure 6c) requires that the heading direction of a newly added node (vessel) should not deviate from the directions of all existing nodes by a specified threshold (DirectionDev). The speed similarity rule (Figure 6d) requires that a newly added vessel should be similar to the mean velocity of existing vessels in this group within a certain deviation (SpeedDev). The deviation follows the idea of the inconsistent edge in Equation (1), with f = 2, n = 3.

2.4.3. Rules for Curvilinear Patterns

A curvilinear pattern emerges when vessels sail along curved waterways, or maneuver for avoidance. This is more common than the collinear pattern. Unlike straight lines, the heading and connecting paths (Figure 7) between adjacent vessels in a curvilinear pattern keep changing directions, which may lead to a complex curve that is difficult to recognize. However, the human visual system is able to recognize curve shapes from discontinuous stimuli, even with noisy background [50]. This can be explained by the Gestalt theory of visual perception (e.g., good continuity). Field et al. [50] quantified the principle of ‘good continuity’ using local continuity rules, based on which automated recognition becomes possible [16].

The local continuity rule requires that the connection between neighboring vessels is as smooth as possible. The smoothness can be further decomposed into the path angle and the alignment of vessel headings (directions) to the path tangent. Figure 7 illustrates the rules well. Although the path is keeping a constant path angle (turning to the right), the fleets in Figure 7b,c do not appear to have good visual continuity, where the heading direction of v₂ is misaligned, breaking the smooth connecting rule. In Figure 7a, on the other hand, the vessel heading is aligned to the tangential direction of the path, making the fleet a discernable curve.

To formalize this rule, we introduce two parameters: MaxPathAngle and MaxMisAlignment. The former means the maximum allowable deviation for path angles, indicating that paths are considered smooth when the angle is less than the specified value (we used MaxPathAngle ∈ [40°, 60°] as suggested in [50]). The later indicates the maximum tolerable deviation of vessel heading to the path tangent (Figure 7b). The value of MaxMisAlignment depends on the path angle of the current node, which can be formalized into a functional relationship, as depicted in Figure 8. When the path angle is not large (≤15°), MaxMisAlignment is leveled at 15°. MaxMisAlignment gradually reduces to zero when the path angle reaches the MaxPathAngle set by users. If the misalignment angle between the vessel heading and path tangent is less than the MaxMisAlignment, the local connection is considered smooth. Additionally, the proximity rule and speed similarity rule described in Section 2.4.2 are also used in the recognition of curvilinear patterns.

2.4.4. Search for Extension

The search algorithm can sometimes be interrupted due to a discontinuity occurring in the MST (Figure 9), but we can still spot the visual continuous motion of the fleet. For example, the detection of the linear pattern will stop at the green vessel v₁. In such cases, if we resort to the connections in the initial proximity graph, then (v_i−1, v_i+1) is found to be a consistent edge and the search can be extended to recognize a more complete vessel group. This step is applied for both collinear- or curvilinear-pattern search algorithms.

2.5. Flow Pattern Recognition

Flow patterns are frequently observed in congested waterways, open water, or anchorage areas. These patterns are typically formed by a group of vessels with a two-dimensional extended arbitrary shape (e.g., a moving belt or area). We next describe the algorithmic framework (Section 2.5.1) and specific rules for flow patterns (Section 2.5.2) and a division step for finer-grained flows (Section 2.5.3).

2.5.1. Search Algorithm

The above algorithms do not support the discovery of two-dimensional flow patterns, because the MST only allows for the computation of spatial relationships in a linear structure (Figure 10b). We therefore designed a search algorithm for flow patterns on the original proximity graph (Figure 10a).

The flow pattern search algorithm is based on a seed-growing idea (Algorithm 2). This algorithm searches on the proximity graph, taking seeds and flow pattern rules (Section 2.5.2) as input, and finds homogeneous groups. Initially, all vessel points are seeds. Starting from each seed v₀, the algorithm visits the first-order neighbors of v₀, and applies the recognition rules of flow patterns (e.g., proximity and heading similarity) to test the suitability of node v₁ and edge (v₀, v₁). If a vessel v₁ is consistent with the current group (i.e., satisfies all the rules) and is added to the current group, a breadth-first search is performed, starting from this newly added vessel v₁, until the region of growth is stopped. If v₁ is not captured by the current search of a cluster, it will be captured by other seed points in subsequent searches, or it becomes a new seed point on its own. The process continues for all initial seeds (except for the ones that are already in a group).

Algorithm 2 Flow Pattern Search Algorithm

Output: Collection of recognized flow-groups(ResultColl)

Input: ProxG; Seeds; Rules

visited ← empty list

queue ← empty list

tempColl ← empty list

for each vertex v0 of Seeds in ProxG do

if v0 has been absorbed in ResultColl then

continue;

end if

visited.append(v0)

queue.append(v0)

while queue is not empty do

currentVertex ← queue.pop(0)

for each vertex v1 adjacent to currentVertex in ProxG do

if v1 not in visited and satisfies rules then

visited.append(v1)

queue.append(v1)

tempColl.append(v1)

end if

end for

end while

add tempColl to ResultColl if tempColl contains more than 4 vertexes

end for

Return ResultColl

2.5.2. Rules for Flow Patterns

For flow patterns, we consider the proximity rule, heading similarity rule, and speed similarity rule in a local context. For the proximity rule, we employ the statistics of inconsistent edges but define the proximity graph instead of the MST. For heading and speed similarity rules, we only consider the smoothness in a local context. That is, when a vessel belongs to a homogeneous group, it aims to keep its moving direction (heading) and speed as close to its immediate neighbors as possible (Figure 11a). This is in line with the concepts of cohesion and alignment defined in group dynamics to simulate the collective behavior of birds [15]. Here, we define the local smoothness of heading as the maximum deviation from the mean heading of the neighboring nodes (e.g., 20°). The local smoothness of speed is defined in the same way. The local connection and region growth mechanism are able to find vessel groups of complex shapes (e.g., Figure 11b) and to distinguish between mooring vessels and fast-moving fleets.

2.5.3. Division for Finer-Grained Flows

There are cases where the above local smoothness mechanism leads to nonsensical or complex clusters that need to be refined. In Figure 12a, for instance, a group of vessels moving to the east branched into two flows at the junction, visually forming three flows (A, B, and C). The current algorithm recognizes them as one big cluster (Figure 12b). Finer-grained vessel patterns, on the other hand, help us to better understand their behavior or geographic context (e.g., branching into two upper tributaries). To address this issue, we used a progressive strategy where the seed-/region growing algorithm is run twice in the local region, as follows:

The seed-growing algorithm is initially applied with a smaller directional deviation (e.g., 5°) to obtain finer-grained clusters (Figure 12c), each of which consists of more homogeneous vessels in, e.g., spacing, heading, and speed. Smaller thresholds may result in some ungrouped outliers.

Region growth is then run with the original thresholds (20°), starting from the finer-grained clusters obtained in the first round. Ungrouped outliers are sorted based on their similarity to each of the core clusters, and outliers with higher ranks are given priority for region growth. The core cluster updates itself by attaching compatible vessels until none can be merged (Figure 12d).

2.6. Combination

After performing the recognition algorithms for collinear, curvilinear, and flow patterns, we obtain multiple result sets. The patterns detected by different algorithms may be complementary, overlapping, or even conflicting. For instance, certain elements of a curvilinear pattern may also be identified by the flow pattern. Therefore, a strategy is needed to integrate these potential conflicting patterns for better and more complete results.

2.6.1. Homogeneity

First, we want to measure how homogeneous the detected vessel groups are. In case of conflicting groups, we keep the group with higher homogeneity. The homogeneity measure is decomposed into several aspects: the Proximity Characteristic (PC), heading Direction Characteristic (DC), and Speed Characteristic (SC). Each aspect is computed based on the spatial and dynamic properties of all vessels in the group. We denote a vessel group as VG = {v₁, v₂, …, v_n}, and the characteristic set of all vessels as C_VG, which is defined as follows:

$$\left\{\begin{array}{l}{PC}_{VG}=\left\{\begin{array}{l}\left\{dis\left(v_i,v_{next}\right)|1\le i\le n\right\},if Linear\\ \left\{\frac{1}{n}{\sum }_{j=1}^{NeighborNums}dis\left(v_i,{Neighbors}_j\right)|1\le i\le n\right\},if Areal \end{array}\right.\\ {DC}_{VG}=\left\{directio{n}_{v_i}|1\le i\le n\right\}\\ {SC}_{VG}=\left\{spee{d}_{v_i}|1\le i\le n\right\}\end{array}\right.$$

(3)

where dis denotes the Euclidean distance, while v_next and Neighbors represent the neighboring nodes of the current node in the searching algorithm, respectively. NeighborNums denotes the number of neighboring nodes, and direction and speed are dynamic vessel properties obtained from the AIS.

$$Homo\left(C_i\right)=\frac{std\left(C_i\right)}{mean\left(C_i\right)}$$

(4)

$$Homo=\sum w_i·Homo\left(C_i\right),C_i\in \{{PC}_{VG},{DC}_{VG},{SC}_{VG}\}$$

(5)

The homogeneity of C_VG is calculated as follows. For each aspect (PC, DC, or SC), we follow the reasoning in [16] and compute the coefficient of variance (Equation (4)). Lower values indicate that the group is more homogeneous. Note that the calculation of the variance of heading directions varies among different pattern types. For collinear patterns, the direction is assumed to be constant, thus the mean value is directly used. In flow patterns, significant variations in direction can be expected (see, e.g., Figure 11b), so the deviation from the mean in the local neighborhood is used. Likewise, heading directions in a curvilinear pattern change all the time, thus deviation to the local tangent is chosen. Finally, The total Homo is the weighted sum of all Homo components (Equation (5)). Equal weights were used in our implementation.

2.6.2. Combination Strategies

The strategies are primarily based on the homogeneity (Homo) and the number of vessels (NumOfVessel) in the group. We classify the conflicting situations into Adjacency, Containment, Intersection, and Equality.

• Adjacency is the case in which two groups/clusters have one vessel in common. In this case, the two groups are considered independent.
• Containment refers to the situation in which one group is a subset of another group. We choose the larger group as the final result.
• Intersection is when two groups have two or more points in common. If the two are consistent with each other in, e.g., proximity, path angle, smoothness, etc., we merge the two groups into a larger group; otherwise, we choose the one with smaller Homo/NumOfVessel as the final result.
• Equality refers to the case in which two groups have the same members. Selection is made based on the priority order of the collinear, curvilinear, and flow patterns (flow can be thought of as a superset of the collinear and curvilinear patterns).

2.7. Validation of Recognition Effect

The “Homogeneity” in Section 2.6 is able to reflect whether individual characteristics (distance, direction, speed, etc.) are sufficiently similar for vessels in a detected group. Therefore, we use it to quantitatively validate the effectiveness of the recognition. This can also be used to evaluate the results of other clustering algorithms (e.g., DBSCAN and CDC), where the above-mentioned characteristics are measured between vessel pairs connected by the triangulation nets (Section 2.2) and homogeneity values computed using the same formula.

3. Experiments and Results

We implemented our framework as a web application using Mapbox (https://www.mapbox.com/mapbox-gljs (accessed on 30 July 2023)). Delaunay triangulation was implemented using the Turf.js library (https://turfjs.org/ (accessed on 30 July 2023)). The main steps in our framework were implemented in JavaScript, including pruning, the search algorithm, rules formalization, post-processing, and their combination. In the following, we present the recognition results and case studies using real-world AIS data in the Suez Canal and other areas. A comparison with existing clustering algorithms such as DBSCAN [51] and local direction centrality (CDC) [52] are also presented.

3.1. Study Areas and Data Processing

Case studies were carried out in three areas around the Suez Canal (Figure 13): Port Said to the north, the Gulf of Suez to the south, and the Suez Canal in between. These areas serve as a significant channel for maritime trade between Asia, Europe, and Africa. We chose these areas because they exhibit distinct geographical characteristics and navigation rules, which contribute to the diverse vessel behaviors seen.

The AIS data used for the case studies was downloaded from MarineTraffic (https://www.marinetraffic.com/ (accessed on 25 August 2023)) on the 25 August 2023. Basic vessel information is used for our algorithms, including their position, speed over ground, and heading. In the preprocessing steps, the proximity graph, MST, and pruned MST are calculated (Figure 14).

Data processing is required before applying the algorithm, and the following is our specific strategy:

(1)

The first step is to remove the data with missing information. Errors in data transmission may cause missing attribute fields in some AIS messages, so we delete records that are missing the fields we need (speed, heading, etc.).

(2)

The second step is to delete outdated data. There may be some records in the study area that have not been updated for a long time, but returned with the latest update at the time of our query, with a large time gap (e.g., a few hours) from the time we are interested in, and these data tend to be unreliable and need to be removed.

(3)

The third step is dynamics interpolation. Since each ship’s AIS message information is not sent at the same time, the timing will be misaligned and there may be a short period of error from the point in time we are interested in. We assume that this time period is one of a uniform motion with constant speed and direction for the ships. Here the velocity and direction of the most recent updated AIS messages are interpolated to obtain the predicted values at a particular time slice. The linear interpolation method is used.

3.2. Results from the Case Studies

To demonstrate our framework, the following parameters were used for all datasets: PathAngleDev = 15°, DirectionDev = 10° for collinear patterns, MaxPathAngle = 60° for curvilinear patterns, and DirectionDev = 20° for flow patterns. “This optimal set of parameter values is suggested by Field et al.’s study [50] of visual continuity and confirmed in our study empirically”. A total of 27 collinear clusters, 28 curvilinear clusters, and 24 flow clusters were detected for the study areas, which were then combined into 33 final groups using the steps described in Section 2.6.2. Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20 demonstrate our recognition results for the three areas, where the recognized clusters are visualized in color (random), while unrecognized elements are in light gray. The paths of the linear patterns are depicted as bold colored polylines. At larger scales, the vessels are symbolized by triangles to indicate their heading directions. Triangles with bars on the front indicate vessels with speeds greater than 0 knots.

A general observation is that despite significant differences in the spatial distribution of vessels in different study areas, group patterns can reliably be recognized. Moreover, different collective behaviors, such as convoys, turning, mooring (in open water), and berthing groups (in the dock), can be distinguished via the different types of patterns detected and their dynamic properties (e.g., velocity). Detailed results are presented in Section 3.2.1, Section 3.2.2 and Section 3.2.3.

From another perspective, recognizing homogeneous groups provides us with a means of categorizing normal individuals, making it easier to uncover potential “anomalies” in the data. These anomalies can manifest either in the form of group deviations or individual cases.

3.2.1. Port Said

Figure 15 presents an overview of the group patterns recognized by the collinear, curvilinear, flow, and combined algorithms near Port Said. Apparently, the combined results give more complete and better recognition than the individual algorithms. A close-up view of the combined results (Figure 16b) reveals that mooring and moving groups are intertwined in these areas. Three significant turning groups (linear patterns) are accurately identified. Two of them (in pink and purple) were leaving the canal, while the smaller group (in orange) was turning towards the canal and intending to sail cross the anchorage area (the green rectangle in Figure 16b-2). A fleet of moving vessels was moving straight along the wide Mediterranean shipping route (Figure 16a). Light gray vessels are outliers/noise from the groups.

Interestingly, the two mooring groups highlighted by the green rectangle in Figure 16b-2 are reasonably separated, as the pink group is moving (at 0.68 knots) and the purple group is stationary. They are located exactly in the designated anchorage area, as shown in the nautical chart (Figure 16b-3). This implies that the vessels in the pink group might be approaching the anchorage area, or starting to depart from it. Likewise, berthing behavior can be inferred by the recognition of vessels aligned in a straight line (a collinear pattern) that have zero speed (Figure 16b-1).

3.2.2. The Suez Canal

Figure 17 is an overview of the recognized vessel groups in the Suez Canal, with the highlighted areas displayed in Figure 18. The most salient feature in this case is the long linear structure detected by the curvilinear algorithm among the presence of moderate noise (Figure 17b,d and Figure 18c). This pattern depicts a fleet of vessels sailing southward along the long canal down to the Gulf area. Our approach recognized at least three anchored groups south of the canal, which are waiting for the northward route to open again (Figure 18c,c-2). No vessels were traveling in the opposite direction in the canal. This implies that only one-way traffic is allowed in this canal portion and the northward and southward traffic may be alternated over time. Figure 18b shows some of the anchored vessels in the Great Bitter Lake, which is located in the middle section of the canal and may serve as an exchange area between northward and southward traffic (Figure 17d). A berthing pattern is recognized near Ein El Sokhna Port (Figure 18d). Additionally, the algorithm recognizes homogeneous vessel groups, which in turn helps us to detect crucial “anomalous” behaviors from unrecognized vessels. For instance, Figure 18c-1 reveals that v₁, with comparable speeds to v₂ and v₃, is included in the group of curves instead of v₀. This implies that v₁ may be moving more consistently and regularly in the channel, whereas v₀ might be abnormal during the encounter. As per Rule 17 of the COLREGs [18], v₁ must maintain its course and speed as a stand-on vessel, while v₀ is obligated to take evasive action in the event of a potential collision. Our approach is able to detect suspicious violations to the regulations in COLREGs by identifying outlier vessels, which could be of great value in decision making at a regional level (by broadcasting warning messages) or operational level (by directing the vessel to make an appropriate maneuver). For example, v₀ could be directed to actively avoid the risky areas, maintain a safe distance from v₁, and to be on high alert for the approaching v₂. If, at any point, v₁ deviates from its group, it will be simple for traffic managers to identify and investigate the reason for the deviation.

3.2.3. The Gulf of Suez

Figure 19 gives an overview of the recognitions made, using our four algorithms, in the Gulf of Suez, with additional details in Figure 20. In contrast to the situations in the Suez Canal, the open Gulf of Suez imposes less restrictions on vessel movement, allowing vessels to move relatively freely in open water. As a result, flow patterns dominate the detected groups in this area (Figure 20b–d). Vessel groups traveling in opposite directions were accurately separated in our approach (Figure 20b–d), suggesting there is two-way traffic in the Gulf. Additionally, some small-scale anchored groups on the side of the Gulf were detected (Figure 20a,c).

3.3. Comparison with Existing Approaches

To evaluate the performance of the proposed algorithms, we compared our results to those obtained by DBSCAN and CDC. DBSCAN is a density-based clustering algorithm. Two parameters, namely the neighborhood radius (Eps) and the minimum number of points in a neighborhood (MinPts), are used to control the output. DBSCAN1 with {Eps = 2 km, MinPts = 3} and DBSCAN2 with {Eps = 6 km, MinPts = 3} were used in our comparison. In general, our results show that a smaller Eps better captures finer-grained clusters but misses many meaningful clusters with larger intra-group distances (e.g., Area 4 in Figure 21b). A larger Eps finds more complete sets of clusters, but fails to separate finer groups with different behaviors from the coarser cluster (e.g., Area 1 in Figure 21c). The CDC algorithm is designed to separate weakly connected clusters, which includes two parameters: the number of nearest neighbors (K) and a parameter used to determine the partitioning of the core and boundary points (TDCM). The combination {K = 3, TDCM = 0.1} was used to produce reasonable results for the whole area (Figure 21d).

To gain more insight, we compare the recognition results in four areas in greater detail (Figure 22). In Port Said (Area 1, Figure 22), all approaches except for DBSCAN2 (with larger Eps) were able to identify the fine-grained vessel groups. Our approach was superior to the others in detecting vessel groups that are more homogeneous in semantics/behaviors, e.g., the three linear moving fleets cutting across the several areal anchored groups, and a berthing group (Figure 16 and Figure 22a). Although DBSCAN2 seemed to identify the linear structure in the Suez Canal (Area 2, Figure 22j), it failed to distinguish the linear structure from the noise in Area 3 (Figure 22k). This salient moving structure was successfully separated from the anchored vessels only when using our approach (the orange curve in Figure 22b,c). CDC also did not provide a satisfactory separation in this case (Figure 22n,o). In the Gulf of Suez (Areas 3 and 4 in Figure 22), our algorithm was better than the others in distinguishing between homogeneous fleets of different mean headings and velocities.

Note that in our study areas, homogeneous vessel groups usually exhibit different intra-group distances (spacing). For instance, a fleet moving faster may be sparser (lower density) than a slow-moving fleet. This makes it harder for the density-based clustering algorithms like DBSCAN to adapt. With decreased Eps values, DBSCAN fails to find clusters with large intra-group distances (e.g., Figure 22g,h). However, by increasing Eps, DBSCAN fails to separate the behaviorally finer-grained clusters (e.g., Figure 22k). Our approach is more adaptive in this respect, as proximity is modeled via Delaunay triangulation, which is parameter-free (Figure 14).

CDC does not have a distance-related parameter and hence is also free from the problem. The strong point of the algorithm lies in that it effectively separates weakly connected clusters. For example, CDC seemed to find the several anchored groups to the south of the Suez Canal (Figure 22o), but it failed to isolate the linear moving fleet from the anchorage area. Our approach produced a better-separated and more accurate grouping of vessels that exhibit cohesive semantics and clearly defined behaviors.

Meanwhile, based on our proposed validation framework in Section 2.7, we performed a quantitative evaluation of the clustering effect. Figure 23 shows the homogeneity value score as well as the distribution of each cluster for different algorithms. The closer the homogeneity value is to 0, the better the homogeneity of the cluster is represented. Obviously, the homogeneity values of our algorithm are centrally distributed with smaller values [0, 0.4], which proves that the members of the clusters we identified are more similar in each attribute. The other three algorithms, on the other hand, more or less contain some clusters that are non-homogeneous (larger homogeneity values).

3.4. Computational Efficiency

AIS datasets (time slices) of different sizes were selected in four regions to test the efficiency of our algorithms. Among them, Dataset 1 (Suez) is the same as that mentioned in Section 3.1; Dataset 2 is a part of the Malacca; Dataset 3 is a part of Yangtze Estuary, China; and Dataset 4 is the Seto Inland Sea in Japan. We calculated the average time for 100 executions of our approach. The results are shown in Figure 24.

Overall, the efficiency of our approach meets practical requirements. Even though Dataset 4 contains almost all ships in the Seto Inland Sea of Japan at a single time slice (the area is about 58,014.78 km²), the algorithm took about 283ms on average to compute them. As our approach is designed to use in interactive visual exploration, one usually analyzes a much smaller region per frame, e.g., less than the area of Suez (Dataset 1); areas larger than this would be less meaningful for visual exploration. Even so, our approach scales far beyond such a designed data size. Our approach scaled linearly with data sizes (Figure 24). The largest dataset in our test can be processed 3~4 times per second (still usable for interactive analysis). For even larger datasets, real-time interactive analysis is not possible; offline processing is required.

Note that as we analyze data once for a time point, the data to be processed by our algorithms are much smaller than the massive trajectory data points (Figure 24). Therefore, the proposed algorithms are realistic. One can further improve their performance via data-level parallelism. For example, we found that the processing time of Dataset 4 can be reduced by half with a divide-and-conquer strategy. The JavaScript implementation of our algorithms, which is for prototyping purposes, can be further improved.

4. Discussion

4.1. Individual vs. Multiple Algorithms

After carefully inspecting the results from the individual algorithms and the results combined from multiple algorithms in Figure 15, Figure 16, Figure 17, Figure 18, Figure 19 and Figure 20, we find that each algorithm has its own unique strengths and limitations. First, the groups detected by the linear (collinear and curvilinear) algorithms more strongly imply collective behaviors and semantics compared with those detected by the flow algorithm. Together with heading, velocity, and their relation to other groups, one can infer the intention, spatial context, and geographic characteristics related to a group (e.g., the turning fleet in Figure 16). For berthing vessels that are typically anchored along the coastal line of a port, linear algorithms are more suitable (e.g., Figure 16b-1 and Figure 18d). The flow algorithm is more flexible and both linear structures and areal patterns can be detected, without knowing which is which. Together with the vessel speed, flow patterns can be used to recognize anchored groups and moving fleets (e.g., Figure 16 and Figure 20). The recognition results also help us to infer geographic characteristics. For example, for vessels moving within the confined space of a canal, the recognized linear pattern (Figure 18) also characterizes the geographical meandering of the narrow waterway. However, results from collinear and curvilinear algorithms do not always contain a complete set of meaningful groups, especially in open water; whereas the flow algorithm yielded better results (Figure 15, Figure 17 and Figure 19).

The best results were obtained by merging the results from multiple algorithms. We identified a total of 64 conflicting pairs with four conflict types (adjacency, containment, equality, intersection) for the whole study area (Figure 25). For example, a collinear pattern can be covered by a curvilinear group, or by a flow pattern. More specifically, a collinear pattern is sometimes a special case of a curvilinear pattern, or it can be part of a curvilinear pattern (c.f. purple rectangles in Figure 15a,b). However, the curvilinear algorithm cannot detect all straight-line patterns due to the different recognition rules used (Section 2.4), especially when there is a significant difference between vessel directions and the path direction (c.f. red boxes in Figure 19a,b). On the other hand, a two-dimensional (flow) pattern is, most of the time, a superset of one or more one-dimensional pattern(s). However, not all linear patterns can be recognized as flow patterns. For example, the flow algorithm can only recognize vessels with small angle changes in the southern section of the canal (the a in Figure 17c), while the curvilinear algorithm can detect the entire canal segment (c.f. Figure 17b).

Therefore, combining the patterns detected by different algorithms (Section 2.6) gave more complete and accurate results than any individual algorithm. One reason is that we differentiated the recognition of specific patterns during the design phase. Furthermore, the combination strategy compares different patterns and selects higher-quality patterns, thereby improving the quality of the results.

4.2. Effectiveness of the Post-Processing

4.2.1. Extension Strategy

Figure 26 demonstrates how extending the search space from MST (solid edges) to the original Delaunay triangulation (dashed edges) helped to improve the pattern recognition process. The MST structure provides an easy way to start the search (e.g., a vertex of degree 1) and accelerates the whole process. However, the structure interrupts connections necessary for recognizing a more complete linear pattern (Figure 26b). Changing the starting point and search direction does not help, as, regardless of the direction, the search algorithm must follow the constrained path (Figure 26a). This extension step is only performed when our algorithm stops the search. In Figure 26c, a more complete set of curvilinear patterns were identified using the extension trick.

4.2.2. Subdivision Strategy

Due to the issue of weak connectivity [52], some finer-grained clusters may have been recognized as one whole group (Area 3, Figure 22). Here, we show how our subdivision strategy is effective in dividing coarser flow patterns into finer-grained ones. In the anchorage area to the south of the Suez Canal (Figure 27a), two groups with significant differences in mean headings are recognized as a contiguous cluster (brown). This is because the two vessels highlighted by the dashed circle have intermediate headings and hence ‘weakly’ connect the two groups. To overcome this problem, we first perform the flow algorithm using a stricter angular deviation (e.g., DirectionDev = 5°). This yields two core clusters as the initial cores/seeds (Figure 27b). Then, we perform the region growth starting from the two cores with the initial threshold (e.g., DirectionDev = 20°), which gives the expected clustering (Figure 27c). The result can be validated by looking at the designated anchorages in this area on a nautical chart (https://map.openseamap.org/ (accessed on 30 July 2023)). Figure 27d shows that the two anchorages, separated by a port entrance lane, correspond well with our detected vessel groups with different headings.

4.3. Potential Applications

With our visual analytical approach, several applications can be explored:

(1)

Vessel management and monitoring. Our approach makes it easy to know the occupation rate, anchorage spacing, and mooring headings of vessels, which are useful for management and anomaly detection. By comparing the detected group with the planned anchorage areas (e.g., the box in Figure 28a), it is obvious that the anchorage is fully occupied and thus many vessels are forced to anchor outside. “Besides, our approach can be applied to isolate vessel fleets traveling in opposite directions (e.g., Figure 28c) in response to the traffic separation schemes of COLREGs [18] are practiced. This helps to detect vessels with anomalous course directions so as to avoid potential collisions”.

(2)

Characterization of geographic context. As vessels exhibit specific behaviors under different geographic conditions, vessel patterns can be used to characterize the geographic context. For example, ships berthing in a port must be aligned to the shape of the dock. The detected linear patterns along the dock (Figure 28b) characterize the shape and distribution of the so-called ‘dockable’ areas in the port. The accumulation of ‘dockable’ areas over a period would provide a more comprehensive view of how the dock was used.

(3)

Higher-level collective behavior. It is possible to recognize complex vessel group patterns by combining basic (e.g., collinear, curvilinear, and flow) patterns, such as converging and diverging movement patterns. For example, the homing of fishing vessels can be recognized as multiple streams of linear and flow patterns heading towards the harbor (Figure 28d), which, when combined, form a larger pan-shaped pattern of convergence movement.

(4)

Security Assessment. The by-products of our recognition algorithms (individual vessels not belonging to any group) can help us to quickly identify potential threats. Combined with the regulations that must be adhered to avoid collisions between vessels as outlined by COLREGS [18], such risky behaviors can be better understood and evaluated. Figure 28e-1 illustrates an overtaking scenario in which the overtaking vessel is travelling at a higher speed and is therefore not within the group’s range. Figure 28e-2 illustrates a head-on situation where the general trend of the curvilinear group adheres to COLREGS Rule 14 [18], which requires head-on vessels to give way to the port side of the ship. Figure 28e-1 depicts a crossing scenario where individual vessels must yield and not pass early, as per COLREGS Rule 15 [18]. These are typical situations that assist traffic managers in spotting potentially risky areas. Our next step will be to demonstrate more powerful capabilities in dynamic scenarios”.

5. Conclusions

This study aims to recognize vessel group patterns and their collective behaviors from a snapshot perspective. We distinguish between the one-dimensional (collinear, curvilinear) and two-dimensional (flow) patterns of vessel groups, and propose a framework that includes recognition algorithms and rules specific to collinear, curvilinear, and flow patterns; the clusters found by the different algorithms are combined into the final result. We tested our approach on real AIS data in the Suez Canal and other areas, and compared our approach to existing methods (DBSCAN and CDC).

Empirical results show that, compared with the existing methods, our approach obtained a more complete set of vessel groups with finer-grained and more homogeneous semantics or behaviors, due to the combination of multiple algorithms. We also show that the detected group patterns can be used for understanding group behaviors, detecting “anomalous” vessels, and characterizing geographic contexts. Therefore, our approach can facilitate the efficient management and monitoring of maritime traffic, early warnings, and collision avoidance. For example, it can be used to detect a vessel overtaking or sailing across a moving fleet, predict the future course of a vessel fleet, and evaluate real-time traffic and potential congestion to ensure maritime safety.

The proposed approach has the following technical merits. First, it recognizes meaningful groups using only the spatial context and dynamic properties of vessels, without relying on historical trajectories. Second, the algorithms incorporate visual perception and require parameters only relevant to vision, which are free from variations in vessel spacing and density and are hence more adaptive in their wider application. Third, multiple algorithms and a combination strategy are employed to ensure more complete and accurate results in complex situations. Last but not least, the algorithms are practically realistic, as we show that they run reasonably fast and can be used in an interactive data mining scenario.

However, we find that with different parameter values in terms of directional deviation (Section 2.5), different levels of clustering can be detected. This suggests that patterns can exist at various scales. Additionally, it would be more interesting to verify our approach by comparing the results with actual maritime traffic patterns. Currently, this is partially completed for mooring/berthing behaviors as well as linear fleets approaching or leaving a port. In the future, interactive visualization can be used to facilitate end users’ better exploration of vessel group patterns by tuning parameters interactively, and recognized vessel groups can be color-coded in terms of their implied behaviors or semantics to help users better interpret the patterns. In addition, our static approach (a snapshot model) can be extended over time to analyze the dynamics of the vessel groups found.