GBSVR: Granular Ball Support Vector Regression

TL;DR

The paper addresses the scalability and robustness limitations of SVR in large and noisy datasets by introducing Granular Ball Support Vector Regression (GBSVR). It replaces dense data points with a compact set of Granular Regression Balls (GRBs) generated via a discretization-based quality metric and integrates these GRBs into a soft-margin SVR framework through a dual optimization that leverages ball centers $c_i$ and radii $r_i$. Key contributions include the GRB generation procedure with a purity threshold, the novel soft-margin GBSVR formulation with a dual expressed in terms $A$ and $B$, and extensive experiments across synthetic, UCI benchmark, stock, and wind datasets showing improved accuracy and substantially reduced training time. The results demonstrate that GBSVR achieves higher $R^2$ and lower MSE/MAE/RMSE while being more robust to outliers and noise, signaling significant practical impact for scalable regression in real-world, large-scale settings.

Abstract

Support Vector Regression (SVR) and its variants are widely used to handle regression tasks, however, since their solution involves solving an expensive quadratic programming problem, it limits its application, especially when dealing with large datasets. Additionally, SVR uses an epsilon-insensitive loss function which is sensitive to outliers and therefore can adversely affect its performance. We propose Granular Ball Support Vector Regression (GBSVR) to tackle problem of regression by using granular ball concept. These balls are useful in simplifying complex data spaces for machine learning tasks, however, to the best of our knowledge, they have not been sufficiently explored for regression problems. Granular balls group the data points into balls based on their proximity and reduce the computational cost in SVR by replacing the large number of data points with far fewer granular balls. This work also suggests a discretization method for continuous-valued attributes to facilitate the construction of granular balls. The effectiveness of the proposed approach is evaluated on several benchmark datasets and it outperforms existing state-of-the-art approaches

Figures (9)

• Figure 1: Granular Regression Ball Generation Process for sinc dataset
• Figure 2: Process of Granular Regression Ball Generation
• Figure 3: Schematic diagram of the GBSVR
• Figure 4: Stock Price Forecasting (APPLE and GOOGLE)
• Figure 5: Wind Speed Prediction