Uncertainty-aware Visual Analysis For Variable Association

Visualization is an important method for analyzing and understanding big data,aiming at mapping data into graphic representations.Utilizing the high throughput of human eyes,visualization can present the contents intuitively and assist users to find the nuggets hided in the data.As the development of data analysis techniques and the higher requirements of analysis results,uncertainty in the data has been paid more attention by analysts.Uncertainty means that the conditions of objects cannot be understood definitively.The causes include the errors produced in the data collection,the incomplete production model,and so on.Uncertainty exists in the data of many fields inevitably.If we ignore it,the analysis results will be inaccurate and wrong decisions may be made by analysts.Visualization of uncertainty can assist users to catch the uncertainty information during the process of data analysis,which is important for users to make reliabledecisions.In scientific simulations,generating ensemble data is a general way of reducing the influence of uncertainty.As the increase of computing power,ensemble data has been generated for multiple variables.Uncertainty has become a great challenge to the analysis of variable associations for multivariate ensemble data,as the variable associations are very complex and diverse among different ensemble members.In this paper,we propose a novel visualization method to present the uncertain associations between a reference variable and the associated variable for multivariate ensemble data.Considering the huge scale of original ensemble data,Gaussian Mixture Model(GMM)is exploited to quantify the uncertainty and represent the original data compactly.To reveal the spatial uncertainty of the reference variable,a GMM based method for extracting uncertainty isosurface is proposed and shows the accuracy advantage over Gaussian based method.Meanwhile,a data reduction method is proposed to enhance the performance of extracting uncertainty isosurface.By mapping the values of the associated variable onto the uncertainty isosurface of the reference variable,a syncretic rendering method is proposed to show the variable associations intuitively.Besides,the screen space accumulating strategy is introduced to present the uncertainties of the associations.Furthermore,we provide a switchable view for users to obtain the credibility of variable associations.The credible associations can assist users to make reliable decisions.For the regions with not credible associations,the detailed information of the associations in every ensemble member can be explored through animation for further analysis.The effectiveness of our method is demonstrated by synthetic,climate and combustion datasets.