Let's look at the equation for the separating hyperplane:
w_1 * x_1 + w_2 * x_2 + w_3 * x_3 + ... + w_bias * x_bias = 0
Where x are the feature values and w are the trained "weights". The additional feature x_bias is a constant, whose value is equal to the bias. If bias = 0
, you will get a separating hyperplane going through the origin (0,0,0,...). You can imagine many cases, where such a hyperplane is not the optimal separator.
The value of the bias affects the margin through scaling of w_bias. Therefore the bias is a tuning parameter, which is usually determined through cross-validation similar to other parameters.