 $$\begin{aligned} {0}     \hat{k}(\overline{\mathbf{x}}_i,\overline{\mathbf{x}}_j) = k_i(\overline{\mathbf{x}}_i,\overline{\mathbf{x}}_j) &= \text{exp}\left( -\frac{0}{0}          (\overline{\mathbf{x}}_i-\overline{\mathbf{x}}_j)