How do we separate negatives examples from positive examples? Widest Street Approach to separate between negatives and positives
How do you make decision rule to make a decision boundary?
Let’s make a vector parpendicular to the median & say we have another unknown
If the projection of that random vector is too big and if it’s too big than it must be in positive side
w(vec) . u(vec) + b >= 0 then it's a positive sample --> Decision Rule
w(vec) = parpendicular u(vec) = random point and vector from median
If we take,
w(vec) . x(some positive sample) + b >= 1
w(vec) . x(some negative sample) + b <= -1
so, lets introduce a variable y
yi such that yi = +1 for + samples -1 for - samples
y_i (x_i . w + b) >= 1 y_i (x_i . w + b) >= 1 (why is it positive?) y_i (x_i . w + b) -1 >= 0
For x_i in gutter(it’s the middle road. Any sample lying in road should be zero)
y_i (x_i . w + b) -1 = 0
so what’s the width of street?
WIDTH = (x+ - x-) . w(vec)/ w(magnitude)