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.