Welcome back to pattern recognition. So you've seen that we discussed the linear

discriminant analysis and also associated classification and today we want to look

into a couple of applications of this technique and we want to show you that

this is not just something that you find in textbooks but this is actually being

used in several different variants.

So here you see The adidas_1 and this was a digital revolution in sports. So

this is actually work that has been done by a colleague of mine, Björn Eskofier,

and they significantly contributed to the development of this intelligent shoe.

So this was for the first time ever a shoe that actually had embedded sensing

and the sole of the shoe was constructed in a way that it had a sensing and a

motor element so the shoe could adjust the stiffness of the sole. So this is

very interesting because if you are running cross country then sometimes

you're on hard soil and in these cases you want your shoe sole to be very soft

but on other cases you're running on very soft soil and in these cases a hard

shoe sole can actually prevent injury. So an intelligent shoe that would then

adjust to the floor, to the soil, to the terrain that you're running on is a very

good idea in order to prevent any kinds of injury during sports. So this shoe

was actually made into a product by adidas and you could actually buy it in

the stores and the sensing and recognition system has been developed at

our lab. So what is the overview? Well you had this cushioning element that is

indicated by 0 1 here which has a magnetic system for compression

measurement, then you had a microcontroller and a user interface that

are essentially buttons on the shoe and this had a clock frequency of 24 megahertz

and you only had 8 kilobytes of program memory and then there was a motor for

adapting the cushion using a cable system. So you see the challenge here is

that you can compute only very little in a shoe. So this embedded system really

needs fast processing and simple methods in order to perform the classification

and this is exactly where our ideas with feature transforms now come in. So you

can only do a couple of very simple features on this shoe and they have to be

calculated in real time, then the classification itself also has to be

very efficient because you have these strong memory and compute limitations

and therefore the LDA classifier can really help us here and the nice thing

with the LDA classifier is that it essentially maps this two class problem

into a linear decision boundary and therefore we can approximate this two

class problem now with a polynomial of order one and we simply have to

introduce weights alpha i and features x i in order to compute that. So the

actual decision then is performed as the sign of the projection onto this class

boundary with the respective bias and then you decide whether you're on the

one side of the plane or the other side of this high dimensional hyperplane.

With respect to features there are 19 features that have been computed in this

shoe for the classification and then in the end only three features have been

selected for implementation and the idea of these feature computations are

essentially an analysis of the step signal and the change of the cushioning

material so you need to essentially detect when a step is performed and you

can then derive from the amount of the change of the cushioning element how

hard the actual impact on the surface is and you can also see on the steepness

how the material that you're running on or the entire system is reacting and

from this you can then control the stiffness of your shoe. So we can also

visualize this in a three-dimensional space because we have three features

and here you can see the hard and the soft surface classes and you see that