A kernel path algorithm for general parametric quadratic programming problem

• Published in: Pattern recognition Vol. 116; p. 107941
• Main Authors: Gu, Bin, Xiong, Ziran, Yu, Shuyang, Zheng, Guansheng
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2021
• Subjects: Cross validation; Kernel path; Parametric quadratic programming; QR decomposition; Cross validation; Kernel path; QR decomposition; Parametric quadratic programming
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2021.107941

•We study a general PQP problem that can be instantiated into many learning problems.•Based on the general PQP problem, we provide a unified and robust kernel path implementation (i.e. GKP) for an extensive number of PQP problems, many of which still do not have kernel path algorithms.•We analyze the iterative complexity and computational complexity of GKP.•We conduct experiments on various datasets, these results not only confirm the identity between GKP and several exiting specific kernel path algorithms (SKP), but also show that our GKP is superior to SKP in terms of generality and robustness. It is well known that the performance of a kernel method highly depends on the choice of kernel parameter. A kernel path provides a compact representation of all optimal solutions, which can be used to choose the optimal value of kernel parameter along with cross validation (CV) method. However, none of these existing kernel path algorithms provides a unified implementation to various learning problems. To fill this gap, in this paper, we first study a general parametric quadratic programming (PQP) problem that can be instantiated to an extensive number of learning problems. Then we provide a generalized kernel path (GKP) for the general PQP problem. Furthermore, we analyze the iteration complexity and computational complexity of GKP. Extensive experimental results on various benchmark datasets not only confirm the identity of GKP with several existing kernel path algorithms, but also show that our GKP is superior to the existing kernel path algorithms in terms of generalization and robustness.