Abstract: 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.

Key words: Compressed sensing, Data imputation, Correlation data, Orthonormal eigenvector basis, Iterative weighted thresholding algorithm