How distance is equal to putting point in the equation of line?

#1

here at 1 : 10 sec , it is mentioned that if we want to calculate the distance between the point & plane we just put the point in the equation & we will get the distance of it . but this is absolutely wrong . by putting the point on the we can only get to know on which side of the line point lies. Assuming W vector is in the direction of the positive point so any point which is in the same direction of W will evaluate to some + ve value not to distance of the point from that plane.

and if it is like this that we are getting the distance then i think our objective must be equal maximizing the distance so that distance between +ve & -Ve point can be maximized…

but in reality i think logistic egression algo is just trying to classify maximum number of points correctly by which i mean to say that … if W(WX + b =0) is pointing towards +ve points then y[i](W*X[i] + b) > 0 where y[i] can take either value as +1(for positive point) and -1(for -ve points)

hope my understanding is correct ?

#2

correct time stamp is 2:10

#3

Q2 : is it necessary to set threshold as 0.5 ? can’t be be more strict with the confidence like 0.8 or 0.9 ? Because suppose if we are dealing with cancer data set then we have to very sure that if the probability that person is not having cancerous cells must me greater than 99% as we can’t afford false negative .

#4

Qeus 1. If i wanted to calculate distance of point from the plane or line than it would be (WX + b)/||w|| where ||w|| is L2 norm of all weights. For eg equation of line is ax + by + c = 0 than distance of any point will be (ax1 + by1+c)/sqrt(a^2 + b^2).

Now consider this, when we want to put all distance greater than zero which means (y[i](WX[i] + b)) / ||w|| > 0
but ||w|| can be taken to multiplication on other side and result becomes y[i](WX[i] + b) > 0. And hence this comes as the result. So ultimately we are trying to maximize the distance only for -ve and +ve class.

Ques 2. yes for different problems we need to change the threshold, like as in your example.

Hope this cleared your doubt. :blush:

#5

http://www.nabla.hr/CG-LinesPlanesIn3DA3.htm

#6

Referring to your link only, it same same as i told in my previous reply

Capture
Capture791×227 22.6 KB

The denominator is same as mentioned by me ||w||.

Happy learning :blush: