[Chapter 5 - SVM] - Bias Term and calculating the Support Vectors

Hi,

I have 2 queries on the code for Chapter 5: SVMs:

1. Why is the bias term in the code for the SVM equal to the decision function with (mean/scale) as the input?

In the code, b is written as:

b = svm_clf2.decision_function([-scaler.mean_ / scaler.scale_]) which is: b = array([-9.76416467])

Where if you disregard the scale var for now, effectively is the decision function on the mean of both the 2 features X1 and X2. ~ decision_function([mean of feature X1, mean of feature X2

**Does this mean that the bias term is always value / output the model generates for the mean values of the features?

2. when generating the support vectors in the code, the support vector indexes are given by the following:

support_vectors_idx = (t * (X.dot(w) + b) < 1).ravel()

However I thought that the support vectors were all those instances on the edge which I thought would satisfy this condition:

(t * (X.dot(w) + b) > -1) & (t * (X.dot(w) + b) < 1)

as this would be all of the instances who fall inside the decision boundaries at -1 and 1.

OR is it that the equation / conditions satisfying hard margins is that (t * (X.dot(w) + b) >= 1) and so all Support Vectors are the opposite of that condition and so:

Support vectors have the constraint: (t * (X.dot(w) + b) < 1)

Any help would be greatly appreciated.

cheers,
Dan