基于压缩感知的时间序列缺失数据预测算法

Missing Data Prediction Based on Compressive Sensing in Time Series

数据缺失在时间序列采集过程中频繁发生,已经严重阻碍了精确的数据分析.然而,现有的缺失数据预测算法多是从采集到的数据中发现某种规律,从而预测缺失的数据,并不适用于缺失数据较多的情况.基于此,提出了一种基于压缩感知的缺失数据预测算法.首先,该算法利用时间序列的时域平滑特性设计稀疏表示基,从而将缺失数据预测问题转化成稀疏向量恢复问题.其次,根据未缺失数据的位置特点设计了与稀疏表示基相关性低的观测矩阵,从而保证了算法的重构性能.仿真结果表明,即使数据缺失率高达90%,所提方法依然可以非常有效地预测出缺失数据.

The frequent occurrence of data loss in time series acquisition process has seriously hindered the accurate data analysis.However,most of the existing methods mainly find a certain pattern from the collected data to predict the missing data,which are only feasible to be applied to the case where only a low ratio of collected data are missing.In view of the problem above,this paper proposed an algorithm of missing data prediction based on compressive sensing.The missing data prediction problem is formulated as the multiple sparse vectors recovery problem.Firstly,the sparse representation basis is designed by making use of the temporal smoothness of time series,thus transforming the missing data prediction problem into the problem of the sparse vector recovery.Secondly,the observation matrix is designed based on the location characteristics of the data that are not missing,which is lowly coherent with the designed representation bases,thus ensuring the reconstruction performance of the proposed algorithm.The simulation results show that the proposed algorithm can predict the missing data very effectively even if the ratio of data loss is as high as 90%.