In this video, we'll talk about
a spatial or geometric way

to understand how
supervised learning works.

Now, in the previous section,

I talked about a prototypical
machine learning problem,

which is taking an image
and outputting a label

such as "cat" or "dog."

Now, to understand how

a machine learning algorithm
might learn how to do this,

let's think about how images
are actually represented.

So, each image consists of pixels
and each pixel has three colors.

And so, each image is actually
a long list of numbers

specifying the colors of each pixel.

So, when we're provided with
our training data set,

which would be a list
of pictures and labels,

The pictures are long lists of numbers

which - in the literature -
are sometimes called "vectors."

Now, these vectors
can be thought of as points

in a very high-dimensional space.

For example,
if you have a thousand pixels

and each pixel has three colors,

that would be a point
in 3000-dimensional space.

Now, the machine learning algorithm,
in some sense,

actually thinks
in this high-dimensional space.

But, for us to simplify things
conceptually,

were going to be thinking about
these images

in a lower dimensional representation.

Specifically, you can see how
we can think of each of these images

as a point in some kind of abstract,
two-dimensional space,

just for visualization
and conceptualization purposes.

Now, in this example of the images,

you are provided with a training data set.

As I've mentioned,

all the images in a training data set
are just points in a space.

And here, I've also colored the points

according to their label -
"cat" or "dog."

So, the red points are the cat images
and the blue points are the dog images.

And, this is what the training data set
looks like geometrically.

Now, a supervised learning algorithm
does the following:

it essentially tries to find a surface
that separates points of one class -

so the dog points -
from points of the other class -

cat points.

And, it does this by adjusting knobs,
which are called "parameters,"

so as to best separate,
in this case,

the red points from the blue points...

okay?

And, once it's found this surface,
what it can do is

it can now take an image
it has never seen before,

which is going to be also
another point in this space,

and it can say:

"Does it lie on the dog side
of the surface

"or the cat side of the surface?"

Okay?

And, given which side it lies on,
it makes a prediction about

whether this image
it has never seen before

is a dog or a cat.

Now, that's basically the visual way,
or geometrical way,

to think about supervised learning.

And, in the next section,

we'll talk about ways to
quantify or think about

how good this separating surface is.

which is called - in the literature -
the "generalization."