Abstract: The value of uncertain time series at each timeslot is derived from a set with possible values, it is hard to judge which one is the determined value. This uncertainty is a huge challenge for dimensionality reduction and similarity match. Existing time series dimensionality reduction and similarity match methods have been unable to apply. To solve this problem, this paper models uncertain time series with descriptive statistics, reduces an uncertain time series to three certain time series which dimensionality is reduced by DFT (discrete Fourier transform), DCT (discrete cosine transform) and DWT (discrete wavelet transform). This paper also presents the similarity match algorithm based on observations interval and central tendency. After the trial validation, under the descriptive statistics model, DCT and DWT perform well in dimensionality reduction, the similarity match algorithm proposed in this paper is superior to others existed.

Key words: uncertain time series, dimensionality reduction, similarity match, discrete Fourier transform (DFT), discrete cosine transform (DCT), discrete wavelet transform (DWT)

摘要： 不确定时间序列的每个时间点上对应一个可能取值的集合，无法给出其确定值，这种不确定性给时间序列降维处理和相似性匹配带来巨大挑战，现有的时间序列降维方法和相似性匹配算法已经无法适用。针对此问题，提出了描述统计模型，将不确定时间序列归约为3条确定时间序列，通过离散傅里叶变换（discrete Fourier transform，DFT）、离散余弦变换（discrete cosine transform，DCT）、离散小波变换（discrete wavelet transform，DWT）对模型下不确定时间序列降维；根据模型特点，提出了以观察值区间和区间集中趋势为核心的相似性匹配算法。经过实验验证，描述统计模型下DCT和DWT有良好的降维效果，提出的相似匹配算法与现有算法相比提高了匹配准确率。

关键词: 不确定时间序列, 降维, 相似性匹配, 离散傅里叶变换（DFT）, 离散余弦变换（DCT）, 离散小波变换（DWT）