When we are dealing with Hyperplanes in Support Vector Machines,what is the effect of b, the bias.
wTx+b=0
Lets say I have a 1D Hyperplane on a 2D plane of (X,Y) that runs through y=5. So a straight line orthogonal to the X. what is the effect of b. If I go b=b+1 does it move vertically to y=6 or does it rotate around? I'm trying to understand visually what its doing to the line.
Changing bias will result in parallel shift of your hyperplane. Namely the hyperplanes $w^Tx+b_1 = 0$ and $w^Tx+b_2 = 0$ are parallel. To exploit some visual intuition, one can consider $2d$-plane. See the picture, where shaded lines are created by changing bias of the solid line.