【摘要】 由于改进波段深度（modified band depth,MBD）和改进上镜图深度（modified epigraph index,MEI）主要度量曲线数据的平均波动情况及深度变化，所以基于这两个深度设计的函数型数据异常值检测算法无法有效识别出仅在小范围内异常的曲线。针对这个问题，本文提出了形变异常度，主要用于度量曲线数据集中每一条曲线对应整个曲线集的形状变化异常度，并结合形变异常度对原异常值检测算法进行改进。先对函数型数据导数曲线计算统计深度，剔除深度值较小的外围曲线后求取平均曲线，再计算导数曲线的形变异常度，最后结合形变异常度对异常值检测算法进行修改，补充函数型数据的形变异常信息。模拟结果表明，本文改进的异常值检测算法可以有效识别出仅在小范围异常的曲线，同时提高了对形状异常值的识别准确率。更多还原

【Abstract】 Since the modified band depth(MBD) and the modified epigraph index(MEI) are used to measure the average fluctuation and depth change of the curve data, the functional data outlier detection algorithm designed based on these two depth is fail to detect the curves which are just abnormal in a small range. In order to solve this problem, we propose a new shape-outlyingness which is used to measure the deviation degree of each curve in the curve data set corresponding to the whole curve set, and to improve the outlier detection algorithm based on the shape-outlyingness. Firstly, we calculate the data depth of the functional data’s derivative, eliminate the abnormal curve whose depth value is smaller, and compute the mean curve. Then we calculate the shape-outlyingness of the derivative curve. Finally, we modify the outlier detection algorithm combined with the shape-outlyingness, which supply the functional data’s shape information. The simulation results show that the improved outlier detection algorithm in this paper can effectively identify the curve whose anomaly range is small, and it also improves the shape outliers’ detection rates.更多还原