Indefinite kernel ridge regression and its application on QSAR modelling

Recently, the use of indefinite kernels in machine learning has attracted numerous attentions. However most works are focused on the classification techniques and less are devoted to regression models. In this paper to adapt indefinite kernels to ridge regression model, an indefinite kernel ridge regression model is proposed. Instead of performing spectral transformation on the kernel matrix, a less restrictive semi-definite proxy kernel can be constructed to approximate the kernel which normally is positive semi-definite. The sensitivity of the distance between this indefinite kernel and the proxy kernel is controlled by a parameter ρ.This approach allows one to construct regression models of response values based on the similarities of corresponding objects, where the requirement on similarity measures to satisfy Mercers condition can be relaxed. To illustrate the use of this algorithm, it was applied to the quantitative structure-activity relationship (QSAR) modelling over 16 drug targets.