LINEAR REGRESSION OF INTERVAL-VALUED DATA BASED ON COMPLETE INFORMATION IN HYPERCUBES

Recent years have witnessed an increasing interest in interval-valued data analysis.As one of the core topics,linear regression attracts particular attention.It attempts to model the relationship between one or more explanatory variables and a response variable by fitting a linear equation to the interval-valued observations.Despite of the well-known methods such as CM,CRM and CCRM proposed in the literature,further study is still needed to build a regression model that can capture the complete information in interval-valued observations.To this end,in this paper,we propose the novel Complete Information Method(CIM) for linear regression modeling.By dividing hypercubes into informative grid data,CIM defines the inner product of interval-valued variables,and transforms the regression modeling into the computation of some inner products.Experiments on both the synthetic and real-world data sets demonstrate the merits of CIM in modeling interval-valued data,and avoiding the mathematical incoherence introduced by CM and CRM.