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Okay, so welcome everybody to pattern recognition.

So it seems today I have to fill in again for Professor Hornegger.

And well, the good news is I have an iPad now, so my complaining actually worked.

And it seems maybe I will give more of these lectures in the future.

Okay, so actually you guys, it would be nice if you could fill me in a bit where you actually stopped.

So I heard that you were introducing support vector machines.

How much of this have you actually heard?

So you've seen this slide, yeah?

So you remember support vector machines and...

Okay, so let's start over with the whole topic, okay?

So that we all get on the same page.

And then I heard that you were discussing an example about castles

and how to select the size of the cannonball to fire through a tunnel.

Did you discuss that?

Yeah, it's a real life example.

So if you ever have to figure out the size of a cannonball

that you can actually shoot through a tunnel,

then this is a really important algorithm that you should remember.

No, actually support vector machines are being used heavily in research.

And there's a lot of things going on with the support vector machines.

And now today we will discuss a simple version,

which will be somewhat familiar to what you already know.

And the nice thing is that you can extend the support vector algorithm

and that you can get a very, very nice interpretation

and you can do very nice tricks with it.

So this is why we take some time to explain the support vector machines.

And you will also realize that this is somewhat similar to the Rosenblatt perceptron,

which I found exciting and you guys hopefully also find exciting.

So let's look at the motivation.

So let's assume you have two linearly separable classes.

So we know that from somewhere, right?

You remember the Rosenblatt perceptron?

We also assumed linearly separable classes.

There's one problem with linearly separable classes.

For example, you cannot solve the XO problem.

Have you looked at the XOR problem?

Yeah?

So I don't have to repeat that.

So it's basically if you, well, I can at least take my time now

to practice how to operate the iPad,

which I obviously didn't do before coming here.

Okay, now we want to save to this file.

So let's consider you have a set of classes and the one class is here and here and here and here.

This is like the XO problem.

So if I start separating this with a single line, we cannot do that.

So let's say I come up with the idea that I want to draw a line along here.

I'm not separating the classes.

If I try to draw a line here, I'm not separating the classes

because the actual thing that I need to do, who wants to pick a color?