摘要：

航海领域现有的轨迹相似性度量方法多以传统方法为主, 计算复杂度较高, 尽管已经提出了一些基于深度学习的方法, 但存在时空联合建模不足的问题, 导致相似性度量的准确性和鲁棒性有待提升。针对上述问题, 提出MDU-Net(Marine Density U-Net)模型。该模型能够自动提取船舶轨迹的低维特征, 从而高效可靠地检索与指定目标相似的轨迹。首先, 对轨迹数据进行等时间间隔插值, 再采用核密度估计(KDE)生成融合空间与速度信息的核密度灰度图, 实现轨迹像素化。然后, 采用基于U-Net结构的神经网络进行无监督学习, 获得轨迹的低维表示。最后, 通过计算低维特征向量间的余弦距离构建相似矩阵, 量化轨迹间的相似性。实验结果表明, MDU-Net模型在评估指标上显著优于传统模型与主流深度学习模型, 与经典动态时间规整(DTW)、Hausdorff距离、卷积自编码器(CAE)模型相比, MDU-Net模型前10条轨迹命中率提升了7.691、14.741、25.191百分点, 充分验证了MDU-Net模型在船舶轨迹相似性度量任务中的优越效果。

关键词: 轨迹相似性, 自编码器, 时空数据挖掘, 深度学习, 自动识别系统, U-Net神经网络

Abstract:

Most existing trajectory similarity measurement methods in the maritime domain rely on traditional algorithms that often suffer from high computational complexity. Although several deep learning-based approaches have been proposed, they cannot jointly model spatial and temporal features. Therefore, the accuracy and robustness of similarity measurements must be improved. To address these issues, this paper proposes a novel model named Marine Density U-Net (MDU-Net), which automatically extracts low-dimensional features from ship trajectories, enabling efficient and reliable retrieval of trajectories similarly to a specified target. Specifically, trajectory data are first interpolated at equal time intervals, and then Kernel Density Estimation (KDE) is applied to generate grayscale maps that integrate spatial and velocity information, thereby achieving trajectory pixelization. Subsequently, an unsupervised U-Net-based neural network is employed to learn low-dimensional representations of the trajectories. Finally, the cosine distance between the resulting feature vectors is then calculated to construct a similarity matrix and quantify trajectory similarities. Experimental results demonstrate that MDU-Net significantly outperforms traditional methods and mainstream deep learning models across multiple evaluation metrics. Compared to that of the classical Dynamic Time Warping (DTW) method, MDU-Net improves HR@10 by 7.691 percentage points, and by 14.741 percentage points over the Hausdorff distance. Furthermore, compared with those of deep learning models, the proposed model achieves a 25.191 percentage point improvement in HR@10 over the Convolutional Auto-Encoder (CAE), validating its superior effectiveness in ship trajectory similarity measurement tasks.

Key words: trajectory similarity, Auto-Encoder (AE), spatio-temporal data mining, deep learning, Automatic Identification System (AIS), U-Net neural network