Manifold Learning Based Time Series Feature Extraction And Multi-task Modeling

Multivariate time series can represent the evolving state of complex systems,and time se-ries modeling is widely used in meteorological forecasting,environmental monitoring and other fields.Analyzing the interaction mechanism among multivariate variables and predicting their evolution trends is of great significance for understanding the evolving mechanism of complex systems.Taking multi-task learning as the modeling idea,the thesis studies the feature extraction and prediction methods in the multi-task time series modeling process.The manifold features with important contributions to multi-task prediction are extracted and the role of shared-private features on prediction results is analyzed.Ultimately,the modeling accuracy is improved.The research results can be used for information processing,modeling and prediction of complex systems.The research content includes the following three aspects:(1)Aiming at the problem of phase space reconstruction and common feature fusion of time series multi-task modeling,a non-uniform delay embedding method for heterogeneous time se-ries based on manifold alignment is proposed.The proposed method transforms the phase space reconstruction problem of heterogeneous time series into the combined problem of manifold feature fusion and input feature selection in over-complete delay embedding space.The joint sparsification of input features can filter out redundant information in high-dimensional vari-ables,which obtains the effect of non-uniform embedding and reduce the complexity of multi-task modeling.The manifold alignment could effectively fuse high-dimensional input features of heterogeneous time series,and extract the main information of heterogeneous time series for multi-task prediction.The obtained low-dimensional manifold representation can reflect the dy-namics of the original system,which facilitates input feature analysis for multi-task modeling of high-dimensional heterogeneous time series.Furthermore,the prediction accuracy is improved.(2)Aiming at the robustness of intermediate manifold feature fusion in time series multi-task modeling,a regularization method based on random manifold perturbation is proposed.The method firstly performs manifold embedding on multivariate time series to extract the common low-dimensional manifold features of multiple tasks.Then,the low-dimensional manifold fea-tures are randomly perturbed during the training process to improve the generalization perfor-mance of the model.In addition,the thesis theoretically analyzes and proves the robustness of the model after perturbation.An explanation of the robustness of the model after perturbation is provided by analyzing the relationship between stochastic manifold perturbation and Tikhonov regularization.The proposed method can improve the quality of time series manifold feature extraction and improve the accuracy of noisy time series prediction.(3)Aiming at the problem of feature component analysis of the output in time series multi-task modeling,a common-private feature separation method for time series multi-task modeling is proposed.The proposed method divides the intermediate features of the prediction model into linear low-rank common features and nonlinear random private features under the framework of structural multi-task learning.The prediction of each task is decomposed into a weighted sum of common features and private features.The common low-frequency features could be separated from private high-frequency features by using the inductive bias of multi-task learning and the frequency principle when training the model.The proposed method can extract the common prediction trend of multiple tasks,which could promote the latent variable analysis ability of the time series prediction process.Furthermore,the prediction accuracy of the multi-task model is improved.