Extension Of Generalized Low Rank Approximation For Applications To Multivariate Time Series With Different Time Lengths

Multivariate time series classification get a lot of attention all the time.However,in the process of data collection,the length of time is not well controlled,resulting in different time lengths of collected data.There are many limitations in classification,resulting in poor classification results.Based on the basic theory of generalized low-rank approximation,this paper takes the minimization of the reconstruction error as the objective function for the characteristics of multivariate time series data with different lengths of time dimension.Three convergence algorithms are proposed in the case of no mean and mean:algorithm 1(G1-Xm,MG1-Xm)considers multivariate time samples of different lengths as missing;algorithm 2(G2-Xm Z,MG2-Xm Z)introduces latent variables and regards both data and latent variables as missing;algorithm three(G3-Z,MG3-Z)only regards latent variables as missing; from the difference between algorithms,algorithm 1 is suitable for low data dimensions,algorithm 2 performs better when data dimensions are high,and algorithm 3 has an advantage in time,but when the proportion of missing data is large,a regular term needs to be added.Algorithms G1-Xm and MG1-Xm get a good classification error rate on real data compared to truncated data,and the algorithm can also get an estimate of missing values,which can fill the data into a complete dataset.The mean squared error obtained by filling with a mean in low-dimensional filling is smaller than that without the mean,and the classification error rate is lower.Using the algorithm MG1-Xm to fill the bidirectional two-dimensional principal component analysis(BPCA)classification method improves the classification effect of BPCA on data sets with different time dimensions.The algorithm proposed in this paper can not only directly perform dimensionality reduction classification for data sets of different lengths,but also fill the data set into a complete data set,break the classification limitations of other classification methods,and improve the classification effect of other classification methods.