Abhimanyu Aryan **|** May 22, 2018 · 1 min read

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

y*i such that y*i = +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)