Learning In The Model Space For Time Series Classification And Its Application For Imbalanced Data

Time series is a series of sequential observations of a dynamical system.It is usu-ally characterized by high dimension,heterogeneous and noise.Time series often ex-emplify long or short-term temporal dependencies,which govern the specific dynamical patterns.This makes time series data different from typical vectorial data.For struc-tured objects such as time series,the key problems are(1)how to obtain parsimonious low dimensional representations that are aware of the dynamical patterns.This would facilitate the learning algorithms to leverage the dynamical behaviours of sequential data.(2)how to define a discriminative distance metric,which makes the data in the same class stay closely while data in different classes stay apart.This paper proposes a time series classification approach based on learning in the model space.The key idea is to learn a model for each time series and measure the distance of the original data by calculating the distance between the function models in the model-spanned space.Finally,classification algorithms are performed in the model space.We study the generating mechanism of the model space and its application in imbalanced time series classification.We propose to optimize the representation ability,separation ability of models and a complexity regularization term to generate the model space.We also analyze the relationship among multiple objectives empirically.Due to the inconsistency among the objectives and the difficulties in optimizing multiple objectives,we propose to exploit a multi-objective non-dominated sorting evolutionary algorithm to simultaneously optimize the three objectives.For imbalanced time series classification,we propose to perform oversampling in the kernel feature space based on kernel learning.The main contributions of this paper include:1.This paper proposes a multi-objective learning approach to optimize the represen-tation ability,separation ability,and the complexity regularization term simulta-neously for time series.The learned representations demonstrate better classi-fication performance and prediction performance than that of optimizing each individual objective.2.As one of the most important solutions to imbalanced data classification,over-sampling approaches are not suitable to time series data that have temporal de-pendencies,multi-variable,and possibly variable lengths.This paper proposes to formulate the nonlinear distance measurement between time series based on ker-nel learning and perform oversampling in the centered kernel feature space.The data are more likely to be linearly separable in the kernel feature space,which satisfies the usually ignored linear separability assumption of most oversampling algorithms.Therefore,the generated synthetic samples have more respect for the minority class distribution and are less likely to overfit.3.Experiments on the benchmark datasets and the artificial datasets demonstrate the effectiveness and robustness of the proposed approaches.