基于时空特性的交通数据补偿算法对比

李月标++李力++张毅

摘 要：數据缺失问题是交通领域中的主要难题之一。为了解决这一问题，国内外的学者在近年来提出了大量的数据补偿算法，这些算法虽然都能在一定程度上提高交通数据的准确性，但其精度和运算速度均有所区别。从已有算法中选取精度高、运算速度快的算法对提高交通系统的性能具有重要的意义。该研究以目前的主流预测算法为对象，分析了各类算法的优缺点，并选取典型的预测类补偿算法、插值类补偿算法和统计类补偿算法对PeMS线圈数据进行补偿，几种算法的准确性和运算速度的结果表明主成份分析法PPCA具有最好的补偿效果。进一步分析PPCA算法与其改进算法KPPCA和MPPCA对单点数据补偿的效果，结果表明，改进算法的补偿精度稍优于PPCA算法，但其计算时间也明显高于PPCA算法。在此基础上，分析PPCA算法和KPPCA算法对多点数据进行补偿的效果，结果表明考虑多点数据的空间关联性可以使PPCA算法和KPPCA算法的补偿精度得到明显提高。同时考虑多点数据的时间关联性和空间关联性时，KPPCA算法精度优于PPCA算法，但其运算效率明显低于PPCA算法。因此，对单点数据进行补偿或多点数据间的时间关联性不强时，选用PPCA算法进行补偿能同时获得较高的补偿精度和运算速度。在不考虑运算时间成本时，KPPCA算法可以获得更高的补偿精度。

关键词：数据补偿 主成份分析法 基于Kernel的主成份分析法 时空特征

Comparison of Traffic Imputation Methods Based on Spatial and Temporal Characteristics

Li Yuebiao Li Li Zhang Yi

（Tsinghua University）

Abstract：Data Missing is one of the major problems in the traffic area. In order to solve this problem， numerous data imputing algorithms have been proposed in recent years. All these algorithms can improve the accuracy of the collected data to some extent， but the precision and calculating speed can vary greatly. Selecting the algorithm with high accuracy and calculating speed is significant to improve the performance of the traffic systems. This research analyzes the typical algorithms of prediction methods， interpolation methods and statistical learning methods. And the advantages and disadvantages of these methods are compared. Using these typical algorithms to imputing the data from PeMS， the results show PPCA algorithm has optimal imputing effect. By further comparing the imputing effects of PPCA algorithm and improved PPCA algorithms - KPPCA algorithm and MPPCA algorithm for single detector data， we find that improved algorithms show higher accuracy but long calculating time. On this basis， this study analyzes the performances of PPCA and KPPCA algorithms for multiple detector data imputation. It turns out that considering data spatial characteristics can reduce imputing errors for both PPCA and KPPCA algorithms. While the imputing accuracy will improve for KPPCA but reduce for PPCA when taking time lag of data into account. Therefore， for single detector data or multiple detectors data whose time correlation is not obvious， PPCA is a best data imputation choice which has both high accuracy and calculating efficiency. KPPCA will show high performance on accuracy when not considering calculating time cost.

Key Words：Data Imputation； PPCA； KPPCA； Temporal and spatial characteristics