Robust interval support vector interval regression networks for interval-valued data with outliers

Recently, the interval-valued data analysis is popular research topic in symbolic data analysis (SDA). For some of applications, it is natural to use interval-valued data because of uncertainty existing in the measurements, variability for defining a term (the minimum and the maximum temperature during a day), extremely behavior description (maximum wind speed in a given country), etc. However, the obtained data are always subject to outliers in some of applications. Moreover, the outliers may occur due to various reasons, such as erroneous measurements or noisy data from the tail of noise distribution functions. In order to handle the interval-valued data with outliers, a novel approach, called the robust interval support vector interval regression networks (RISVIRNs), is proposed. The RISVIRNs is extended from our previous work (e.g. the support vector interval regression networks; SVIRNs). It is easy to find that SVIRNs can have interval-valued data for outputs, but only can deal with the crisp input. Moreover, the outlier's effects are not discussed in SVIRNs. Hence, the support vector regression with interval-valued for input data (SVRI2) approach is proposed to determine the initial structure of RISVIRNs and to remove outliers form the interval-valued data set. Due to such approach can provide a better initial structure of RISVIRNs, the proposed approach can have fast convergent speed and robust against outliers. The experimental results with real data sets show the validity of the proposed RISVIRNs.