How do you set sigma for the Gaussian similarity kernel?

Question

Let's say we have $n$ two-dimensional vectors: $$\mathbf{x}_1,\dots,\mathbf{x}_i,\dots,\mathbf{x}_n=(x_{1_1},x_{1_2})^T,\dots,(x_{i_1},x_{i_2})^T,\dots,(x_{n_1},x_{n_2})^T$$ How do you set $\sigma$ for the Gaussian similarity kernel: $$s(\mathbf{x}_i,\mathbf{x}_j)=\exp\left(-\frac{||\mathbf{x}_i-\mathbf{x}_j||^2}{2\sigma^2}\right)$$