The Loss Function for a multiclass SVM loss for example $i$ is defined as (it’s a Loss Function for a multiclass SVM loss for example $i$ is defined as (it’s a Hinge Loss):
$L_{i}=∑_{j=y_{i}}max(0,s_{j}−s_{y_{i}}+Δ)$
where

$s_{j}=f(x_{i},W)_{j}$ is the score for the $j$-th class

$Δ$ can be interpreted as the minimum margin (use $Δ=1$), i.e. the correct class should be a minimum of $Δ$ away to make sure we incur 0 loss.

We omit $y_{i}$ as part of the calculation for loss because if not, the loss would be $Δ$, instead of 0, even though we have perfect predictions.

The loss over the full dataset is
$L=N1 i∑ L_{i}+λR(W)$

The first part is the Data Loss

The second part of the equation ($λR(W)$) is the Regularization loss, given by
$R(W)=k∑ l∑ W_{k,l}$ (this is L2 Regularization)