I was just going through Neural-Network tutorials and I have some question regarding Bias neuron :-
1.] Is the act of introducing bias neuron same as introducing the X(index 0)=1 in the logistic regression i.e. [1, X1, X2]
2.] Is bias neuron an additional degree of freedom ?
3.] Can bias neuron be analogous to the constant term in the linear equation :-
because without C i can only rotate the line x around the origin, but if I take into consideration C also then I can translate this line up or down also.
For example consider the figure below :-
Then the blue line (hypothesis) is simply
Y=m*X (blue line passes through origin), so even if you keep fiddling with the m paramater but you wont be able to seperate the green and blue dots ever with just this hypothesis. So with just m to fiddle with, my hypothesis will always have to pass through the origin, i.e. I can choose from the infinite numbers of lines through the origin by tweaking the parameter 'm'.
Whereas if I include C/constant term (which Im calling the bias) in my hypothesis then my equation becomes
Y=m*X+C then a line like Y=.4*X+3
(magenta line ) easily classifies the data. So now that I have an additional parameter "C" , I can translate(shift up/shift down) apart from the rotation.
Is my understanding correct ?