Non-parametric Similarity Measure Algorithms For Uncertain Time Series

Time series data is a set of time-ordered sequence of observations,widely found in various application areas,such as stock data,weather and ecological data.Time sequence characteristics make the data with the information collection time interval different with the continuous or decentralized form and other characteristics;In addition,with the continuous development of information technology,due to data acquisition equipment accuracy,data collection granularity conversion,for privacy protection or other special purpose or data integration and so on,so that the time series data at each point in time observations may be fuzzy or uncertain,this contains the uncertainty of the time series data is also widespread in such as location-based services and wireless Sensor networks and many other applications.The existence of uncertainty also brings further complexity to the mining of time series data.In this paper,the similarity measure of uncertain time series data is taken as the starting point,and the method of analyzing the uncertain time series data is studied.There are some problems in the existing research on the uncertainty of the time series similarity measure: the model representation of the uncertain object and the research of the distance measurement method.Such as constructing an uncertain data model that reflects the uncertainty probability density distribution based on the parameter estimation method,and the parameter estimation method relies on the assumption that some of the theoretical distributions that makes it difficult to work well to the real complex data for the unknown density distribution,thus affecting the accuracy of the construction model.Considering that the nonparametric estimation method does not need to presuppose the data distribution,the density distribution of the model is closer to the true density distribution of the data,and it has high flexibility without any accuracy.So it can be applied to different Determine the object type.Therefore,aiming at the main problems in the construction of uncertain time series data model and similarity measure method,this paper firstly construct the basic research of object uncertainty model based on the histogram density estimation method.Then,based on the uncertainty of Gaussian kernel density estimation modeling method and the uncertainty approximation modeling method based on Gaussian transformation,the core accuracy of nonparametric density estimation model and high-dimensional complexity are studied.And for intensive study,we applied the analysis and prediction of moving trajectory behavior by the application of uncertain time series similarity measure based on nonparametric density estimation from.The research work mainly includes the following aspects.(1)Considering the discrete feature of time series data,the modeling of uncertain time series and the similarity measure method are studied based on the non-kernel density estimation method-histogram estimation method in nonparametric estimation.Including the probability density function of the object uncertainty in the uncertain time series;the representation of the uncertain time series,that is,the frequent pattern of the probability density function is obtained and abstracted as a semantic representation.Determining the data sequence and the time series similarity measure method.(2)In order to solve the problem that the histogram estimation method is influenced by the interval width and make full use of the original features of the data and improve the flexibility of the uncertain time series modeling and similarity measure method,we study the uncertainty of time series similarity measure method.Including constructing a model of the uncertain time series based on the kernel density estimation method in the non-parametric estimator to describe the time series data characteristics including the uncertainty;and the probability density function of the object uncertainty distribution based on the random simulation metric the absolute difference,as the basis for the similarity measure between the uncertain time series and the similarity measure.(3)In order to improve the accuracy and performance of high-dimensional uncertain object analysis,we study the similarity measure method of uncertain object based on fast Gaussian transform.Firstly,the data model conforming to the uncertainty distribution feature is constructed without assuming the data distribution.When the data model dimension is high,the Gaussian kernel density function of the uncertain object is transformed by fast Gaussian transformation,and the distance of high dimensional model is calculated fast.Based on this,an uncertain data clustering algorithm is proposed,which lays the foundation for the similarity measure of uncertain objects.(4)We study the uncertain trajectory end point prediction method based on nonparametric density estimation for the application of uncertain time series similarity measure method.Including the modeling method of the moving trajectory expressed in timeseries,that is,using the nonparametric estimation to construct the end-to-end uncertain trajectory model based on the density distribution with the same trajectory as the starting point and the end point;The method of matching the trajectory model based on the historical trajectory is used to predict the trajectory with the same starting point by KS hypothesis test.Finally,this paper summarizes the work and puts forward the further research focus.