## 1 Introduction  
Maritime transport is a cornerstone of international trade and the global economy, with over 80% of international cargo trade carried by sea [1]. In most developing countries, this proportion is even higher. As port construction and maritime cargo transport rapidly develop, issues such as complex coastal and port entry and exit routes, increased vessel traffic and density, frequent encounters among various ships, and heightened water traffic safety risks have become increasingly prominent. Maritime traffic safety is crucial to human life, the marine environment, and the material and immaterial assets involved in maritime activities [2]. Moreover, as maritime vessel traffic increases, so do CO\({}_{2}\) emissions, exacerbating environmental pollution [3]. As a critical hub for waterway transportation, port waters are typically busy, especially within fairways where multiple vessels often fail simultaneously. The organization of this traffic affects the frequency of vessel encounters, local vessel density, and waiting times for port entry and exit. These factors directly impact navigation safety within channel waters and port operation efficiency. VTS (Vessel Traffic System) officers need to understand vessel behavior within fairways for effective ship scheduling and risk assessment. This includes knowledge of preferred exit positions, speed variations of different vessel types and sizes, and ship turning behaviors within the channel [4]. Studying vessel behavior within fairways aids in traffic prediction, risk anticipation, anomaly detection, and optimizing the scheduling of port entry and exit. Therefore, research on vessel behavior within fairways is crucial for port traffic management. The Automatic Identification System (AIS) is a modern navigational aid designed to enhance maritime safety. It is widely used in maritime supervision, traffic flow analysis, collision avoidance, and other fields [5]. The AIS system stores extensive historical trajectory data, including vessel positions, speed over ground (SOG), course over ground (COG), vessel length, vessel width, draft, vessel type, and more. This vast AIS data resource supports the extraction of traffic patterns and knowledge mining, further aiding in traffic optimization and safety management. And it contributes to addressing the increasingly complex maritime transportation networks, playing a significant role in enhancing the operational capacity of vessels [6]. The richness of the vessel trajectory data makes traffic pattern exploration and knowledge mining feasible, attracting increasing interest from the research community. Current methods for maritime traffic knowledge mining primarily include grid-based, vector-based, and statistical approaches. The grid-based method divides the study area into indexed grids and places the raw traffic data into these grids. This method effectively reduces the problem size. For instance, analyzing five days of Class A AIS vessel traffic data within the waters east of Bohai, China (117.5\({}^{\circ}\) E 123.5\({}^{\circ}\) E, 37\({}^{\circ}\) N 41\({}^{\circ}\) N), yields 30,325,098 trajectory points. Dividing the study area into grids with 1' latitude and longitude would result in a significant reduction in problem size [7]. However, the grid-based method is more suitable for smaller study areas and often requires predefined grid sizes before the study [8]. An inappropriate grid size or uniform grid setting without considering regional characteristics may affect the study results. The vector-based method effectively identifies route points in vessel trajectories. Most studies only identify entry and exit points, turning points, and stopping points, but do not consider traffic characteristics along the routes. For example, speeds along routes may vary depending on vessel type, size, and region. Ignoring these variations makes it challenging to accurately represent the actual traffic situation in the study area.