New approach to Support vector regression (SVR) with interval data

Abstract

This thesis develops several novel approaches to pursue the support vector regression (SVR) with interval data. Four approaches are proposed: (i) moment-based approach, (ii) equiprobability-based approach, (iii)boundary-point-based approach, and (iv) extended generalized-SVR. Applicability of each of the four proposed approaches varies depending upon the presence of the interval data in input and output observations. Interval data may be present only in input observations, or output observations, or in both. Thus, three cases may arise regarding the presence of interval data in input and output observations. All these three cases are considered in this thesis. The first two proposed approaches are applicable to all three cases. The boundary-point-based approach is applicable for the presence of interval data in output observations. The extended generalized-SVR approach is developed discerning the limitations of the existing generalized-SVR for the presence of interval data in both input and output observations. Therefore, extended generalized-SVR approach is applicable only when the interval data are present in both input and output observations. The separation strategy – where interval-valued inputs and outputs are dealt separately – is introduced to make the most time-consuming moment-based approach computationally tractable for the third case. This strategy is also utilized in proposing the extended generalized-SVR approach. The prediction accuracies and computational time of all the proposed approaches are compared within themselves as well as with the available existing method. Three real datasets and one synthetic dataset are used to experiment with the proposed approaches for their prediction accuracies and computational efficiency. Boundary-point-based approach and extended generalized-SVR approach are discerned as more efficient compared to the moment-based approach and equiprobability-based approach. It is shown that the moment-based approach always outperforms the equiprobability-based approach in terms of prediction accuracy for all three cases. However, prediction accuracy of the boundary-point based approach may be greater or less than that of the moment-based and equiprobability-based approach based on different cases. Prediction accuracies of existing generalized-SVR approach and extended generalized-SVR approach is always observed to be less than the other three approaches.