I'm fitting an SVC model with linear kernel, after that i'm checking the dot product of the fitted weights by the input to understand the prediction better. From my understanding of the linear SVC model, $x_1$ will be assigned to the positive class if
$$ w \cdot x_1 + b > 1 $$
and the negative class if
$$ w \cdot x_1 + b < -1 $$
Is my understanding of how SVC generates the prediction after learning the weights of the features correct or am i missing something?
It's worth mentioning that the values in the histogram are identical to what i get from
decision_function(X) so to rephrase my question: how did the estimator in scikit-learn decide what values of the decision function are assigned to what class? Since as you can see from the histogram
decision_function > 0 are not assigned to the positive class and
decisioN_function < 0 are not assigned to the negative class.