A Novel Similarity Measure Model For Multivariate Time Series Based On LMNN And DTW

Multivariable time series is a widely existing data form which relates to the time feature greatly.The knowledge discovery and data mining tasks for time series have attracted a large amount of attention and research efforts in recent years.Most data mining applications on time series are highly dependent on similarity measure.In this paper,a novel model is proposed to measure the similarity of multivariate time series,by combining metric learning method LMNN and dynamic time warping(DTW),which is always applied for univariate time series.Firstly,a modified DTW method is proposed to solve the singularity problem and high time complexity of DTW.DTW is an effective and popular algorithm for univariate time series similarity measure.To solve the singularity problem,the summation dynamic time series warping(SDTW)is proposed by considering both point values and derivatives without extra parameters.Then PLA is applied to reduce the dimensionality of time series,and integrated with SDTW as PLA-SDTW,to reduce the time comsumption.The proposed approach was compared to other techniques and demonstrated its superiority in time complexity and similarity measure.Secondly,DTW method should be extended from univariate time series to multivariable time series.Meanwhile,the relations among the variables of multivariate time series also must be considered.Metric learning is a kind of methods that learns a distance metric which can represent the distance relations among the training data.Large margin nearest neighbor(LMNN)is one of the most popular metric learning methods.In this paper,a novel model is proposed to measure the similarity of multivariate time series by combining LMNN and DTW,called LMNN-DTW.Firstly a Mahalanobis distance-based DTW measure is used for multivariable time series,which considers the relations among variables through the Mahalanobis matrix.Secondly,the LMNN algorithm is applied to learn the Mahalanobis matrix by minimizing a renewed cost function.As the cost function is non-differentiable,the minimization problem is solved from a perspective of k-means by coordinate descent method.Meanwhile,the modified SDTW,which is demonstrated better than DTW,is used to replace DTW as LMNN-SDTW for better performance.The experiments shows that the proposed models LMNN-DTW and LMNN-SDTW perform similar with the state-os-art method LDML-DTW,and much better than other techniques.Meanwhile,LMNN-SDTW performs better than LMNN-DTW,which demonstrate the superiority of LMNN-SDTW in similarity measure for multivariate time series over LMNN-DTW.