Time series analysis is a key technology for medical diagnosis,weather forecasting and financial prediction systems.However,missing data frequently occur during data recording,posing a great challenge to data mining t...Time series analysis is a key technology for medical diagnosis,weather forecasting and financial prediction systems.However,missing data frequently occur during data recording,posing a great challenge to data mining tasks.In this study,we propose a novel time series data representation-based denoising autoencoder(DAE)for the reconstruction of missing values.Two data representation methods,namely,recurrence plot(RP)and Gramian angular field(GAF),are used to transform the raw time series to a 2D matrix for establishing the temporal correlations between different time intervals and extracting the structural patterns from the time series.Then an improved DAE is proposed to reconstruct the missing values from the 2D representation of time series.A comprehensive comparison is conducted amongst the different representations on standard datasets.Results show that the 2D representations have a lower reconstruction error than the raw time series,and the RP representation provides the best outcome.This work provides useful insights into the better reconstruction of missing values in time series analysis to considerably improve the reliability of timevarying system.展开更多
The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the nec...The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the necessary and sufficient conditions for generators of KerL_M and Ker ad_M and prove that any vector-valued polynomial in Ker ad_M can be constructed from polynomials in KerL_M in a certain way.展开更多
文摘Time series analysis is a key technology for medical diagnosis,weather forecasting and financial prediction systems.However,missing data frequently occur during data recording,posing a great challenge to data mining tasks.In this study,we propose a novel time series data representation-based denoising autoencoder(DAE)for the reconstruction of missing values.Two data representation methods,namely,recurrence plot(RP)and Gramian angular field(GAF),are used to transform the raw time series to a 2D matrix for establishing the temporal correlations between different time intervals and extracting the structural patterns from the time series.Then an improved DAE is proposed to reconstruct the missing values from the 2D representation of time series.A comprehensive comparison is conducted amongst the different representations on standard datasets.Results show that the 2D representations have a lower reconstruction error than the raw time series,and the RP representation provides the best outcome.This work provides useful insights into the better reconstruction of missing values in time series analysis to considerably improve the reliability of timevarying system.
基金Project supported by the National Natural Science Foundation of China.
文摘The key point of the method of calculating the normal form of ordinary differential equations based on the representation theory of sl (2, R) is to find generators of KerL_M and Kerad_M. In this paper, we give the necessary and sufficient conditions for generators of KerL_M and Ker ad_M and prove that any vector-valued polynomial in Ker ad_M can be constructed from polynomials in KerL_M in a certain way.
