# SVMs are useless?  ### What are SVMs? 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``

where,

``````w(vec) = parpendicular
u(vec) = random point and vector from median``````

If we take,

``w(vec) . x(some positive sample) + b >= 1``

likewise

``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) Written by

Abhimanyu Aryan

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