Gaussian Affinity is a type of affinity or self-similarity function between two points $\mathbb{x\_{i}}$ and $\mathbb{x\_{j}}$ that uses a Gaussian function:

$f\left(\mathbb{x\_{i}}, \mathbb{x\_{j}}\right) = e^{\mathbb{x^{T}\_{i}}\mathbb{x\_{j}}}$

Here $\mathbb{x^{T}\_{i}}\mathbb{x\_{j}}$ is dot-product similarity.