Measuring trajectory similarity is a fundamental algorithm in trajectory data mining, playing a key role in trajectory clustering, pattern mining, and classification, for instance. However, existing trajectory similarity measures based on vector representation have challenges in achieving both fast and accurate similarity measurements. On one hand, most existing methods have a high computational complexity of O(n × m), resulting in low efficiency. On the other hand, many of them are sensitive to trajectory sampling rates and lack of accuracy. This article proposes QuadGridSIM, a quadrilateral grid-based method for trajectory similarity analysis, which enables high-performance trajectory similarity measure without the cost of low effectiveness. Specifically, we first realize the multiscale coding representation of trajectory data based on quadrilateral discrete grids. Then, a novel trajectory similarity measure is defined to reduce the computational complexity of O(n). Several effectiveness properties of QuadGridSIM are further optimized, including the spatial overlap, directionality, symmetry, and robustness to sampling rate variations. Experimental results based on real-world and simulated taxi trajectory data indicate that QuadGridSIM outperforms most of the other tested algorithms developed previously in terms of effectiveness, particularly in its robustness regarding trajectory sampling rates. Furthermore, QuadGridSIM exhibits superior performance and is approximately one order of magnitude faster than previous methods in the literature. QuadGridSIM provides a solution to the low-efficiency problem of massive trajectory similarity analysis and can be applied in many application scenarios, such as route recommendation and suspect detection.

中文翻译：

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QuadGridSIM：一种基于四边形网格的方法，用于高性能和鲁棒的轨迹相似性分析

测量轨迹相似度是轨迹数据挖掘中的基本算法，在轨迹聚类、模式挖掘和分类等方面发挥着关键作用。然而，现有的基于向量表示的轨迹相似性测量在实现快速和准确的相似性测量方面面临挑战。一方面，大多数现有方法的计算复杂度较高，为O ( n  ×  m )，导致效率低下。另一方面，其中许多对轨迹采样率和准确性缺乏敏感。本文提出了QuadGridSIM，一种基于四边形网格的轨迹相似性分析方法，它能够实现高性能的轨迹相似性测量，而不需要以低效为代价。具体来说，我们首先实现基于四边形离散网格的轨迹数据的多尺度编码表示。然后，定义了一种新的轨迹相似性度量来降低O ( n ) 的计算复杂度。 QuadGridSIM 的几个有效性属性得到了进一步优化，包括空间重叠、方向性、对称性和对采样率变化的鲁棒性。基于真实世界和模拟出租车轨迹数据的实验结果表明，QuadGridSIM 在有效性方面优于之前开发的大多数其他测试算法，特别是在轨迹采样率方面的鲁棒性。此外，QuadGridSIM 表现出卓越的性能，并且比文献中以前的方法快大约一个数量级。 QuadGridSIM为海量轨迹相似度分析的低效率问题提供了解决方案，可应用于路线推荐、嫌疑人检测等多种应用场景。