Abstract: Similarity measure is a keystone in mining time series data. Numerous methods have been proposed to deal with it over the past decades. This paper summarizes the mainstream similarity measure algorithms so far, points out the defects within each of them. A newly mathematical morphology based similarity measure method is proposed to overcome the low discriminated precision problem. The core part of the mentioned method is dilation and erosion operation, which can strengthen the noise-resistance performance while keeping the difference among different time series at the same time, improving the precision of measurement. The experiment is tested on 8 dataset using KNN classification as evaluation metrics, which turns out that the proposed method improves at most 20% in classification precision, compared with DTW algorithm.

Key words: mathematical morphology, time series, similarity measure

摘要： 时间序列相似性度量在挖掘时间序列模式，提取时间序列关联关系上发挥着重要作用。分析了当前主流的时间序列相似性度量算法，分别指出了各度量算法在度量时序数据相似性时存在的缺陷，并提出了基于数学形态学的时间序列相似性度量算法。通过将归一化的时间序列二值图像化表示，再引入了图像处理领域中的膨胀、腐蚀操作对时序数据进行形态变换分析，提高相似时序数据部分的抗噪性，同时又不降低时序数据非相似部分间的差异度，实现时序数据相似性度量分类精度的提高。在八种时间序列测试数据集合上进行分类实验，实验结果表明提出的基于数学形态学的时间序列相似性度量算法在时间序列分类精度上得到有效改善，相比于DTW相似性度量算法，分类精度平均水平提升了8.74%，最高提升20%。

关键词: 数学形态学, 时间序列, 相似性度量