Hierarchical Approach for Multiscale Support Vector Regression

Support vector regression (SVR) is based on a linear combination of displaced replicas of the same function, called a kernel. When the function to be approximated is nonstationary, the single kernel approach may be ineffective, as it is not able to follow the variations in the frequency content in the different regions of the input space. The hierarchical support vector regression (HSVR) model presented here aims to provide a good solution also in these cases. HSVR consists of a set of hierarchical layers, each containing a standard SVR with Gaussian kernel at a given scale. Decreasing the scale layer by layer, details are incorporated inside the regression function. HSVR has been widely applied to noisy synthetic and real datasets and it has shown the ability in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by standard SVR. Results also compare favorably with multikernel approaches. Furthermore, tuning the SVR configuration parameters is strongly simplified in the HSVR model.