基于压缩感知的相关性数据填补方法

Method for Correlation Data Imputation Based on Compressed Sensing

数据缺失现象在数据的采集和传输过程中经常发生,而对数据集中缺失数据的不当填补,会对后续的数据挖掘工作产生不利的影响。为了更有效地对缺失数据集进行填补,针对相关性数据,提出了一种基于压缩感知的缺失数据填补方法。首先,将缺失数据填补问题转化为压缩感知框架下的稀疏向量恢复问题;其次,针对数据的相关性特点构造了专门的稀疏表示基,从而能够更好地实现数据的稀疏化;最后,提出了一种快速迭代加权阈值算法,在传统的快速迭代收缩阈值算法的基础上引入了一种新的加权因子及重启动策略,提高了算法的收敛性能和数据的重构精度。仿真结果表明,所提算法能够高效地填补缺失数据,与传统的快速迭代收缩阈值算法相比,重构成功率和重构速度都得到了提升。同时,在数据稀疏变换效果较差的情况下,所提算法仍然能够完成对缺失数据集的填补,具有更好的鲁棒性。

The phenomenon of missing data occurs frequently during the acquisition and transfer of data,and improper handling of missing data sets can adversely affect subsequent data mining efforts.In order to fill the missing data set more effectively,a method for data imputation based on compressed sensing is proposed for correlation data.First,the problem of missing data imputation is transformed into a sparse vector recovery problem under the compressed sensing framework.Second,a specialized sparse representation base is constructed for correlation data,so the data sparsity can be better realized.Finally,the fast iterative weighted thresholding algorithm(FIWTA)is proposed,which is refined based on the fast iterative shrinkage-thresholding algorithm(FISTA).The proposed algorithm adopts a new iterative weighted method and introduces a restart strategy,which greatly improves the convergence of the algorithm and the reconstruction accuracy of the data.Simulation results show that the proposed algorithm is able to fill the missing data efficiently,and both the reconstruction success rate and the reconstruction speed are improved compared with the traditional fast iterative shrinkage-thresholding algorithm.Meanwhile,even when the sparse transformation of the data is less effective,imputation of missing data sets can still be accomplished with better robustness.