An adaptive residual subsampling algorithm designed for kernel based interpolation is presented. To determine optimally the kernel shape parameter, some cross validation (CV) criteria such as k-fold CV and leave-one-out CV (LOOCV) as a special case are analyzed. The implemented algorithm selects the shape parameter automatically and is applicable for any kind of kernel, guaranteeing existence and uniqueness of the kernel interpolant. Numerical results highlight accuracy and efficiency of the adaptive scheme in one and two dimensions. A comparative analysis with some existent methods supports this study.