# A Study of Multi-Step Sparse Vessel Trajectory Restoration Based on Feature Correlation
## 1 Introduction  
With the rapid growth of international trade and global logistics needs, the maritime industry has become an important force driving the global economy. However, the development of the maritime industry has also brought about a series of related issues, such as maritime safety management, marine environmental protection, and other challenges [1; 2; 3]. In this context, a large amount of automatic identification system (AIS) data provides valuable support for related research. AIS is a system that records real-time information about a vessel's position, speed, heading, and other key attributes through satellites and terrestrial base stations. By analyzing AIS data, we can mine the spatial and temporal distribution of ships, route networks, and sailing patterns. These provide decision support for optimizing maritime logistics, improving maritime security, and saving energy [4; 5; 6; 7; 8]. However, AIS data often contain missing data and abnormal data, and these problems mainly stem from factors such as inconsistencies in data collection intervals, limitations in data transmission and storage, and sensor failures. Missing data and abnormal data will cause the acquisition of incomplete vessel trajectory operation information, which triggers the sparsity and abnormality problem of AIS data. It adversely affects the quality of AIS data and brings challenges to vessel feature mining and navigation pattern analysis [9]. Many research efforts have searched for effective methods to control AIS data quality. Such methods mainly reduce sparse and abnormal trajectories by restoring the completeness and accuracy of the trajectory data and also provide a high-quality database for subsequent tasks [10; 11]. Currently, the main approaches to AIS data restoration include traditional mathematical modeling methods and data-driven methods. Traditional mathematical modeling methods achieve trajectory data restoration by building mathematical models from a statistical point of view. However, when facing a large amount of AIS data, traditional methods make it difficult to capture the complex relationship between data dimensions due to the limitations of high data dimensionality and the existence of missing data and abnormal data, and the method is sensitive to abnormal data and missing data. In the process of processing, high computational complexity and serious loss of information will be encountered, thus affecting the accuracy and effect of trajectory restoration. Data-driven methods focus more on automatically learning and extracting key features from the data perspective and capturing the complex relationships between AIS data dimensions by building models. Although these methods are more adaptive, in the case of low data quality, machine learning methods make it difficult to extract complete information and to achieve the expectations for the resulting in trajectory restoration. When the basic neural network method based on deep learning is faced with multi-dimensional data, the problem of input feature redundancy leading to model accuracy degradation occurs. Therefore, to process AIS data more effectively and improve the accuracy of trajectory restoration, it is necessary to process sparse and abnormal vessel trajectory data and then construct a suitable restoration model based on the selection of input features with a high correlation with restoration features to achieve the efficient restoration of sparse vessel trajectories. To achieve this goal, this paper proposes a multi-step sparse vessel trajectory restoration method based on feature correlation, which attempts to solve the challenges brought about by the sparseness and anomaly of AIS data for subsequent trajectory mining. First, trajectory restoration points are identified through sparse and anomalous vessel trajectory data detection, and interpolation restoration methods are utilized to populate these, thus initially ensuring the coherence of the input data.