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Hello and welcome back to the course
on Deep Learning.

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In the previous tutorial,
we found out what Convolutional

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Neural Networks are all about.

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And today
we're going to dive into step one.

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Can evolution.

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So this is the convolution function.

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I know we try to stay away from
mathematics and keep things intuitive,

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but I couldn't help but share this formula
for you because it is so simple.

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A convolution is basically a combined
integration of two functions.

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And it shows you
how one function modifies,

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the other, modifies
the shape of the other.

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And if you've done any signal processing
or electrical engineering

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or a profession
where signal processing is required,

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you would have inevitably
come across the convolution function.

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It is quite popular.

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Now once again, we're going to, keep the
mathematics lights or keep them separate.

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And if you'd like to get into the math
behind the convolutional neural networks,

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a great additional read is, Introduction
to Convolutional Neural Networks

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by Jensen Wu, who is a professor
at the Nanjing University in China.

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This paper was published
literally days ago, like 5 or 6 days ago.

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And it is oriented specifically at people
who are starting out,

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at beginners who are getting to know
convolutional neural networks.

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So, the mathematics
there should be accessible.

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I actually emailed,
a professor Shan seen Wu, and,

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yeah, he said his whole goal is to

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make, break, the complex things down

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so that people who are new to
this field can understand. And.

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also, he mentioned that he's got some
materials available on his homepage.

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So if you in the URL,

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if you just remove the last two parts
and you just go to, like

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to that part, that's his homepage
and you'll be able to find

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more additional tutorials and materials
which haven't been published as papers.

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But he uses them in his tutorials.

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So, you might find those useful.

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So browse around there
if you'd like to get an introduction

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into the mathematics behind
convolutional neural networks and kind of,

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build a solid. Base around that.

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Area, but we're going to move on and, 
we're going to talk about the convolution.

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So what is a convolution
in intuitive terms

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here on the left
we've got an input image as we discussed.

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that's how we're going to look at images.

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Just ones and zeros to simplify things.

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And you can see the smiley face there.

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There we've got a feature detector.

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So feature detectors a three by three
matrix doesn't have to be three by three.

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No it doesn't.

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AlexNet. I think it uses, seven.

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By seven.

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and then some other, one of those other.

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Famous ones
uses like five by five feature detectors.

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they can be different, but usually
you'll see that there are three by three.

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And, They are, you know, reasons
to make them three by three.

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So we're going to stick
to the conventional way.

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Having a three by three feature detector.

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also the feature detectors called

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these are important terms
because you might come across them.

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They're many different terms,
for the feature detector.

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But the most common ones
are feature detector.

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Or you might hear it being called kernel,
or you might hear it being called filter.

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So in this course we're going to be using
either filter or a feature detector

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interchangeably.

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But just bear in mind
that it has those names.

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And A convolution operation is signified
by an X

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in a circle,
just as you saw in the formulas before.

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And here what happens
is, on an intuitive level,

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or just to think of it in terms of what
is actually happening in the background

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rather than the mathematics, well,
you take this feature detector,

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or filter and you put it on your image
like you see on the left.

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So you cover the, for instance,
in this case

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the top left corner, 
nine pixels in the top left corner.

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And you basically multiply

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each value by each value,
so respective values.

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So, the top zero by the top left
go value by the top left value.

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Then basically it's position number.

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One, one by position number one.

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One position by a number or zero, one by
zero, one zero, two by zero two and so on.

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So just it's, element
wise multiplication of these matrices

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and then you add up the results.

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So in this case nothing matches up.

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So always always either
a zero by zero zero by one.

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So the result is zero.

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Here you can see that one.

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Of them matched up the one on the left.

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Matched up.
And therefore we got a one here.

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Nothing matched up. Nothing matched up,
nothing matched up.

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Then we move on to the next row.

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So, and the step at which we're moving

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this whole, filter is called the stride.

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So here we have a stride of one pixel.

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So here you can see again something
matched up the bottom right corner.

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Matched up.

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Against stride.

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But Bottom one in the middle matched up.

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here. Top right, one matched up.

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Then nothing. Mentioned.
The stride is one.

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you can change the stride.

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you can make it one, two.

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you can make it three. Whatever you like.

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the conventionally the one that works
well is usually a two.

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So that's what people stick to.

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And we'll we'll talk about what the stride
is, towards the end of this tutorial.

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So here we've got, we're matching up.

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So we just keep our eye here.

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You can see we've got a two
because two of them matched up.

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And so on and so on, so on.

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there we go. There's
another one that matched up.

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There we go.

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And there we're done.

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So what's what have we created?

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Right.

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a couple of important things here.

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the image on the right is called
a feature map.

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Also has several terms.

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It also can be called sometimes,
it convolved feature.

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So when you apply a convolution
operation operator to something,

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it doesn't become convoluted.

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It becomes convolved.

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And yeah, I use sometimes I like I.

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Think to myself in the.

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Wrong way,
but it's the correct term is convolved.

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it's a kind of old feature.

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Or it can also be called
the activation map,

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but we're going to be calling it
a feature map in this course.

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so it can be called it.

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Any one of those things.

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And what have we done here.

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Well, as you can see,
we've reduced the size of the image.

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That's number one.

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And that's the important thing
I wanted to mention about,

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your input image and the feature detect
and the stride.

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Right.

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If you have a stride of one,
you can see the image reduced a bit.

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But if you have a Strided two,
the image is going to reduce more.

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So the feature map
is going to be even smaller.

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And that's an, a very important, 
function of the feature

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detector of this whole convolution
step is to make the image smaller.

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because that will be
it'll be easier to process it.

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and. it'll be just faster.

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It will and,

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It'll be just faster
because imagine like here

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we've got a what, a seven by seven image.

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But imagine
if you have a proper photo, right.

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or you have a, like a 256 by 256
pixel image.

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That's it's a huge number of pixels
by 256, squared.

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or like let's say
you have a 300 by 300 pixels.

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So, so we don't get confused
with the RGB 256.

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Let's just say we have a 300 by 300, image
in terms of size in pixels.

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Then you have 300 squared
number of pixels.

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That's a huge number.

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and therefore feature detectors,
will reduce the size of the image.

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And therefore stride of two
is actually beneficial.

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But then the question is
do we lose information

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or are we losing information
when we're applying the feature detector.

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Well, some information we are losing

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of course, because we have less values
in our resulting matrix.

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But at the same time, the purpose of
the feature detector is to detect certain

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features, certain parts of the image
that are integral.

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And so, for instance,
if you think about it this way,

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like the feature
detector has a certain pattern on it,

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the highest number in your feature map
is when that pattern matches up.

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In fact,
the highest number you can get is in.

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Another simplified example is when,
the feature is that it matches exactly.

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And you can see with that number four
we have in our feature map.

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That's exactly.

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So if you look over here, that's exactly
where this feature detector,

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because there's only four ones in
it matched perfectly.

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So you can see this this part over here.

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So the feature was detected here.

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And as we discussed
at the very start of this section

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that features is

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how we see things,
is how we recognize things.

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We don't look at every single.

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Pixel, so to speak,

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in what we see on an image
or in real life.

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We don't look at every single pixel.

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We look at features, we look at the
the nose, the hat, the the feather.

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the, the, eyes under

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or the little black marks
under the cheetah's, eyes to distinguish

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it between a cheetah and a leopard
or the shape of the train.

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We don't, to distinguish between a bullet
train, a normal train, and so on.

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So we don't look at everything,

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we look at features,
and that's what we're preserving.

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And that's
what the feature map helps us preserve.

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Actually, that's what it
it's, allows us to bring forward

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and get rid of all of the unnecessary
things that even as humans,

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we don't processes so much information.

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going into your eyes at the, at any
given time, like gigabytes of information,

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if you look at every single, dot,
if not terabytes of information

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going into your eyes per second,
and still we're able

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to process that
because we get rid of what is unnecessary.

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We only focus on the important features
of features that are important to us.

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And, 
that is exactly what the feature map does.

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So now moving on.

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This is our input image.

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And you we create a feature map.

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So the front one let's say
the front one is the one we just created.

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But then how come there's many of them.

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But we create multiple feature maps.

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because we use different filters.

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Right.

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And that's another way.

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That we preserve lots of the information.

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So we don't just have one feature map,
we look for certain features

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and then, or basically
the network decides through its training.

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And this is something we'll discuss
towards the end of this section.

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Through its training,
it decides which, features

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are important for certain types
or certain categories, and.

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It looks for them, and therefore.

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We'll have different filters.
And we'll talk about filters just now.

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But basically it'll apply these filters.

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So to get this feature map
it applied a filter like the one we saw.

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But then to get this feature map
but apply a different filter

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to get this feature map
to apply a different filter and so on.

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and. So

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basically
it just creates these feature maps.

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And actually that's why personally
I think the term feature detector

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is better than filter.

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So remember over here

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we have this filter
which we also can call a feature detector.

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Well actually the word feature detector
I think is better suited.

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And the reason for that
is that's what the purpose is, right?

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We don't want to just we don't want to
just filter out our image.

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But even though that's the whole

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that's the same same
just a question of terminology.

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But basically we want to detect features.
All right.

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In this in this layer
we're going to our in this.

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Feature map we've detected
where certain features are in the image.

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In this feature map
we've detected where certain

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other features are where
a certain specific feature is located.

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And this feature map we've detected where

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a certain other feature
is located on the image.

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So that's, that's what we were doing.

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And let's have a look
at a couple of examples.

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So, here, we're using
and this is, from GitHub, dawg.

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They're documentation.

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It's a free, 
like a kind of tool, like paint.

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And you can.

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Use it to adjust your images or work
with your images, but basically they have

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some valuable examples
in their documentation.

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And here
they have a picture of the Taj Mahal.

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And you can choose
which filter you want to apply.

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So if you download this program
and you upload a photo into it,

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and then you can actually, 
start a convolution matrix

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and apply filters,
and you will see that, these things,

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these convolution matrices are actually
applied in image processing and.

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Design and so on.

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So let's have a look at what we get,
what we get.

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So so if we apply this filter five in the.

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Middle of minus
one minus one minus one minus.

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One, you can see that it's sharpens
the image.

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And yeah.

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So this is, it's quite intuitive
if you think of it.

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So five is the pixel
the main pixel like in the middle of the,

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of the filter or the feature detector.

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And then minus one, minus one and minus.

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One just to kind of like reduces the 
pixels around the inner in an intuitive.

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sense.

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then blur.

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So basically it takes, c equal significant

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gives equal significance to all of the,
pixels around the one in the center.

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And therefore it combines them together
and you get a blur edge enhance.

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So here you can see that.

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minus one and one and then.

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You get zeros. Right.

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So you did delete remove the pixels
around, the main one in the middle.

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And you only keep this. One
at a minus one.

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And it gives you an edge.

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And this was a bit harder to. Understand.

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How it works.

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Like probably 100,
just to think of it intuitively.

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edge detect. Right.

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So this one probably makes more sense.
Right?

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You, take the middle one,
you reduce the middle one.

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The probably like the strength
of the middle pixel.

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And then you look
for the ones you look for.

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these ones you,

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increase the strength.

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Of the ones around them.

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So you have. The ones. There.

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yeah. So that's that.

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Gives you, like, an edge detection,
and you can see what you get there and.

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Boss, another one. So.

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the, the key here
is that it's asymmetrical.

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And you can see the image becomes
asymmetrical as well.

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So you.

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Got like that
kind of, feeling that it's standing out.

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Towards you.

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And that's what you get
when you have like minuses here.

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And pluses here.

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Again, this is very
this is getting a bit technical now.

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But at least we can get some kind of
intuitive understanding.

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Let's just go quickly through them again.

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So there's sharpen. There's blur.

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There's edge enhance. There's edge detect.

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There's emboss.

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And so as you can see these are great
examples of the same image.

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But we're getting feature maps.

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So we use different

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feature detectors to get different feature
maps of the same image.

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And therefore now we have lots of the lots
of this versions of this image.

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where
in each one we've tried to detect certain

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things, these terms,
they're not applicable to us.

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They're we can say like emboss is probably
not applicable to us

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in terms of convolutional neural networks,
but edge detect, that's important.

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We want to detect the edges.

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Edge enhance probably not blur sharpen.

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So certain things like edge detectors
probably the most important one

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for our type of, work.

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And in terms of understanding
like computers,

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they will decide for themselves.

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The neural network will decide for itself
what's important, what's not.

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And it probably won't be even,
recognizable to the human eye.

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You won't be able to understand
what those features

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mean, but the computer will decide.

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And that's the beauty
that, of neural networks,

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that they can process so many different.

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Things and understand without.

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Even having that intuition,
without having that,

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explanation why they will understand
which features are.

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Important to them,
whether we have a name for them or not.

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That's a whole that's an irrelevant
question for the artificial neural

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network.

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And my favorite one,
here's a image of Geoffrey Hinton.

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photo of Geoffrey Hinton.

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passed through, the,
one of these filters.

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All right, so that brings us
to the end of today's tutorial.

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I hope you enjoyed learning
about convolution.

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The key takeaway is that, convolution,
the the primary purpose of a convolution

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is to find features in your image
using the feature detector,

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put them into a feature map,
and by having them in a feature map,

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it still preserves
the spatial relationships,

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between pixels, which is very important
for us to, you know,

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because if they're completely jumbled up,
then we've, we've lost the pattern.

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And at the same time, it's important
to understand that most of the time,

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the features a neural network will detect
and use to recognize certain images

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and classes will mean nothing to humans,
but nevertheless, they work.

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And that's what convolution is.

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And I look forward
to seeing you on next tutorial.

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Until then, enjoy deep learning.