Time Series Similarity Research Based On Low Rank And Sparse Representation

With the development of data era,there are large amount of time series data in many fields.Time series similarity studies how to classify time series according to these data feature attributes,and then applies to classification and clustering.Under the influence of high dimension and correlation among variables,and other factors,which is a great challenge to time series data mining and time series similarity research.And how to extract features and represent time series effectively has become the main research problem of time series similarity.Feature representation of time series reduces dimension by extracting significant features of time series.At present,feature selection has gradually been used to reduce dimension in this direction.The method is to reduce the dimension of high-dimensional time series phase space data and comply norm constraint with projection matrix to guide feature selection.However,these methods fail to measure the loss of information and lack of preserving structure of time series.The similarity measurement of time series data is realized by calculating distance according to specific measurement methods between time series.Recently,dynamic time warping has become a research hotspot.When dynamic time warping measures multivariate time series,however,forcing the alignment of first to first and last to last series causes the time series to be overstretched or compressed.As a result,the illconditioned matching and the loss of important feature information between data affect the classification accuracy.Therefore,this paper studies the feature representation and similarity measurement of time series,and proposes corresponding solutions,and compares and verifies the proposed methods on some public data sets.The main work of this paper is as follows:1.In order to solve the problem that DTW neglects the consideration of keeping structure of univariate time series,this paper proposes LRSE-DTW algorithm which fusing dynamic time warping with embedding feature selection of low rank sparse representation to univariate time series.The model selects feature of the embedded projection matrix according to learn low rank sparse representation of phase space of univariate time series,and comprehensively considers information difference measurement,structure preserving and sparse regular term of projection matrix so that improve efficiency of pattern representation of time series.2.To solve the defect of dynamic time warping ill-conditioned alignment,this paper proposes adaptive cost dynamic time warping(ACM-DTW)for multivariate time series.For dynamic time warping,we give a weight coefficient which is counting the used times of one point between multivariate time series to constrain this point be used again,so that change the cost ratio of the current step to control distortion degree of multivariate time series.