Missing data imputation in multivariable time series data

Multivariate time series data are found in a variety of fields such as bioinformatics, biology, genetics, astronomy, geography and finance. Many time series datasets contain missing data. Multivariate time series missing data imputation is a challenging topic and needs to be carefully considered before learning or predicting time series. Frequent researches have been done on the use of different techniques for time series missing data imputation, which usually include simple analytic methods and modeling in specific applications or univariate time series. In this paper, a hybrid approach to obtain missing data is proposed. An improved version of inverse distance weighting (IDW) interpolation is used to missing data imputation. The IDW interpolation method has two major limitations: 1) finding closest points to missing data 2) Choosing the optimal effect power for missing data neighbors. Clustering has been used to remove the first constraint and find closest points to the missing data. Therefore, most similar data to the missing data are found. In this paper, the k-maens clustering method is used to find similar data. This method has been more accurate than other clustering methods in multivariate time series. Evolutionary algorithms are used to find the optimal effect power of each data point to remove the second constraint. Among evolutionary algorithms, evolutionary cuckoo search algorithm is used due to high convergence speed, much less probability of being trapped in local optimal points, and ability to quickly solve high dimensional optimization problems in multivariate time series problems. To evaluate the performance of the proposed method, RMS, MAE,   , MSE and MAPE criteria are used. Experimental results are investigated on four UCI datasets with different percentages of missingness and in general, the proposed algorithm performs better than the other three comparative methods with an average RMSE error of 0.05, MAE error of 0.04, MSE error of 0.003, and MAPE error of 5. The correlation between the actual data and the estimated value in the proposed method is about 99%.