Pairwise Loss

Definition

The pairwise loss compares pairs of items and determines their relative order. Instead of predicting absolute errors for individual items.

$L(W,Y,X_1,X_2)=\underset{\text{loss for similar pairs}}{\underbrace{(1-Y)L_S(D_W)}}+\underset{\text{loss for dissimilar pairs}}{\underbrace{Y{L}_D(D_W)}}$ where $Y$ is a binary label if a pair is similar then $0$, dissimilar then $1$, $D_W$ is a distance metric between the pair, parametrized by $W$.