Concatenation Affinity

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

$f\left(\mathbb{x\_{i}}, \mathbb{x\_{j}}\right) = \text{ReLU}\left(\mathbb{w}^{T}\_{f}\left[\theta\left(\mathbb{x}\_{i}\right), \phi\left(\mathbb{x}\_{j}\right)\right]\right)$

Here $\left[·, ·\right]$ denotes concatenation and $\mathbb{w}\_{f}$ is a weight vector that projects the concatenated vector to a scalar.