Kernel methods have attracted considerable attention in machine learning area, such as pattern recognition Smola and Schlkopf (1998); Sun et al. (2012), regression estimation Wang (2003); Gautam et al. (2019); Tehrani (2021), function approximation Pillonetto et al. (2014), owing to their capability of working not only with linear inference models, but also to identify nonlinear relationships among input patterns Scholkopf et al. (1998); Cristianini and Shawe-Taylor (2007); Tang et al. (2019). The modelling of nonlinear relationships between input patterns has always been a critical task in machine learning, where kernel methods not only provide the possibility in a natural way, but also are largely founded on solid mathematics. In particular, the kernel methods Zhang and Cao (2011) embed data into an Euclidean space of higher or infinite dimensions, and provide the flexibility of modelling the complex relationship among data samples without explicitly computing a huge number of and potentially infinite dimensional feature vector.