Euclidean Distance - Practical Machine Learning Tutorial with Python p.15 Video Lecture | Machine Learning with Python - AI & ML

what is going on everybody and welcome
to part 15 of the machine learning with
Python tutorial series in this tutorial
we're going to be building on the last
couple which we're talking about K
nearest neighbors we talked about the
intuition it's basically how close is
this point to the K closest points and
whatever the majority classes of those K
closest points we say this new point is
that class and in the previous tutorial
exactly what we did was apply K nearest
neighbors to real-world data set we
found that it's actually fairly accurate
which was very cool so now we're going
to break down the K nearest neighbors
algorithm and rewrite it ourselves from
scratch in code but first we have to
cover what everything hinges on right it
hinges on this distance so what is that
distance it is Euclidean distance so
what is Euclidean distances of course
named after Euclid famous mathematician
popularly referred to as the father of
geometry definitely wrote the book on it
right Euclid's elements which is
arguably the Bible for mathematicians
and scientists also fun fact is you know
whenever someone would would create a
printing press the first thing you'd
start popping out was the Bible of
course and then the second thing was
most likely Euclid's elements so anyways
what is Euclidean distance first we have
is the sum to N and in this case n
represents the number of dimensions in
your data so just think of it as in this
case as dimensions but really this means
sum to n where I starts off at least as
being equal to 1 ok so it really just
means I starts as one goes up to n where
I actually is your dimensions so if you
just have one dimension it would just
you would just do this one time and it's
the sum of what and in let's do
parentheses here it is going to be Q I
minus P I
squared and then this entire calculation
we do the square root of it and this is
Euclidean distance so I is just the
dimensions cube is one point P is a
different point right so this would in
theory if you just if you got rid of N
and I you got rid of the whole sum and
you just left the parentheses part like
if you just left I hate to circle legs I
want to mess it up but if you just left
the whole parenthesis squared this would
be that would be the calculation for a
one-dimensional distance between two
points in Euclidean space anyways but
now let's actually break this down into
simple mathematics I always like to do
it by hand for some things we won't
always do by hand we won't actually do
the calculation but I'll show you how
you would plug it in at least so we'll
start off and say Q is equal to 1 comma
3 so these are the coordinates for our
data point and then P the coordinates
for p x and y so this is two dimensions
is two five those are the coordinates so
then how would we calculate the
Euclidean distance well it's going to be
the square root of basically a couple
things so we know we have two dimensions
so we know that basically what's going
to start off as will be something like
it'll be you know the square root
without that dot there square root and
we know we're going to have at least two
of these right because we've got two
dimensions here we recall it's the
summation of these so it'll be a plus
here and then this will be squared and
this will be squared and then we just
need to fill in the subtractions so
initially it'll be q1 minus p1 so it
would be 1 minus 2 right 1 and then over
here we'll just put a 3 and then it's
minus minus 2 and 5 and that would be
the Euclidean distance okay
so simple enough let's head over to
Python and actually create this so in
Python here let's just recreate exactly
what we just did by hand so I'm instead
of Q and P let's say plot 1
equals and we'll do one three and plot
two equals to five okay now we're going
to let's go up to the top and say from
math import sq RT which is just
importing the square root so coming back
down here converting this to Euclidean
distance or basically calculating the
Euclidean distance between these two
plots is the following so Euclidean
underscore distance equals s qrt so
remember it's the square root of the sum
of each of the dimensions - that same
dimension in each of the plots or two
plots really you're going to calculate
distance between two plots so in this
case it would be for example plot one
the zeroeth element so the X of plot one
minus the X of plot - right so - plot 2
and the X so the zeroeth okay so that's
1 and remember it was the sum of all of
these so it would be that plus and then
basically the exact same thing on the
instead of the 0 if it would be the one
all right so 0 1 1 so you can think of
these as your dimensions right so this
is dimension 0 and this is dimension 1
so this is two dimensions as indeed it
is so that would be the eye in that
equation just for the record
so anyways Euclidean distance boom done
let's go ahead and oh these also need to
be squared so that squared and this
squared right so that is squared
this is squared and then the entire
operation is we get to grab the square
root of that so now let's print the
Euclidean distance so we get two point
two three six zero and so on but
basically that is your Euclidean
distance so now that we know how to
calculate Euclidean distance we
basically the crux of everything we need
to do K nearest neighbors but we have
kind of like a lot of framework to
create regardless so that's what we read
in the next tutorial is creating the
framework that will take a data set and
use K nearest neighbors to classify
points so if you have any questions or
comments up to this point feel free to
leave them below otherwise as always
thanks for watching thanks for all the
support and subscriptions and until next
time