Second-order optimization of variable projection SVM models and road abnormality detection

2026-10-07

AI Summary

This study addresses the low training efficiency of Variable Projection Support Vector Machines (VP-SVM) by proposing a second-order trust-region optimization framework tailored for variable projection functionals. This work represents the first introduction of second-order optimization into VP-SVM solving, significantly enhancing the training efficiency of kernel methods. Applied to road surface anomaly detection using one-dimensional signals from tire-mounted sensors, the proposed approach achieves both efficient and accurate identification. Ultimately, this research not only overcomes the longstanding optimization bottleneck of VP-SVM but also validates its practical utility in real-world scenarios.

Abstract

We introduce a novel second-order optimization framework for minimizing so-called variable projection functionals. We demonstrate that the proposed framework is especially usefulfor the training of variable projection based kernel methods. In particular, the problem of efficiently training variable projection support vector machines (VP-SVMs) is considered. We show the effectiveness of the proposed training methodology in a real-world application, namely we demonstrate how second-order trust region algorithms can be used to train VPSVM models to recognize road surface abnormalities based on 1D signals obtained from a tire sensor.

Problem

• variable projection
• support vector machines
• second-order optimization
• road abnormality detection
• kernel methods

Innovation

• Second-order optimization
• Variable projection
• Support vector machines
• Trust region algorithms
• Road abnormality detection