MRFT

# Application Example

## Detecting normal EKG pulses.

I will not enter into too much detail in this text in an attempt to _trick_ the

reader (you) into doing some research. But the basic idea is to train an MLP and

then use the results to try and deduce if a Pulse is normal or not (the same

approach can be used to detect specific pathologies).

This is **not** the usual approach which usually includes extracting features

like the a<sub>k</sub>s of the Fourier Transform, eigenvalues, and such. The

approach that will be described in this example is much simpler (albeit it has

a less accurate result... _or does it?_)

## About the EKG

EKGs or ECGs (whichever you like) is basically a set of five (three, five or

six) different signals or _derivations_. Most of the bibliographic

information and cardiological knowledge is in the time domain, and

unfortunately most of the features usually extracted for NN training are

frequency based, which brings us to a little problem, no cardiologist wants to

apply something that he/she can't understand.

We can of course analyze an ECG in the time domain, and with a little tinkering

the results are actually quite encouraging.

## Preprocessing

As you might know before throwing a signal at a NN and expecting great results

is usually coherent to to some filtering and transforming I'll keep the

filtering to a minimum, and mostly done in order to have nice function plots.

Let's start by getting a copy of [`mrft`]

and some EKG Data (for convenience there are some samples included in `mrft`),

in case you don't like them, you are free to search some, manufacture one, or

even use a synthesizer like [`Java ECG Generator`](http://www.mit.edu/~gari/CODE/ECGSYN/JAVA/APPLET2/ecgsyn/ecg-java/source.html).

## Training

Open `mrft` select the menu `Examples`->`EKG (Synth)` this will populate the

tables the following way: 

[[https://raw.githubusercontent.com/wiki/dktcoding/mrft/imgs/ekg/data.png|alt=Data]]

Go ahead and press `F5` (a training session should start and with some luck

converge to an _"acceptable"_ fit).

[[https://raw.githubusercontent.com/wiki/dktcoding/mrft/imgs/ekg/firstplot.png|alt=FirstPlot]]

There's something odd with the way this MLP is trained... do you see it? No?

(_Tip:_ in the lower plot both the training and validation errors stay very

close together! they should be diverging, or at the very least separate, remember over-fitting?)

This usually happens with synthetic data, since adjustment is **too perfect**

the training and validation datasets are basically one in the same.

## Adding some noise

Noise is a bad thing that should be removed, why do we want to add it? well

the fact is that NN tend to work better with noisy data (not so noisy mind

you).

There are several ways to add noise, but for this we'll use a transformation,

so go to `Dataset -> Transform... -> Custom Function (All)`, something like

 this should appear:

[[https://raw.githubusercontent.com/wiki/dktcoding/mrft/imgs/ekg/custransf.png|alt=FirstPlot]]

We'll leave the `x` value as it is, but in the `fx` text field write:

`gaussian2(fx, 0.1)` then click on apply, your data now must look

something like this:

[[https://raw.githubusercontent.com/wiki/dktcoding/mrft/imgs/ekg/secondplot.png|alt=SecondPlot]]

Try pressing `F5` now so it re trains...

Yes, I lied (not entirely) gaussian noise didn't change the validation error,

but I'll let you figure out why on your own (one clue: `Box–Muller`, the

rest is _simple_ math). For a bit more information about this see

`Adding noise` in [[Data manipulation]]

## Selecting the right weights

As the NN trains itself the synaptic weights of the training epochs are saved

(not all of them), so now we must decide which of all the weights to use,

click on the error table (`Error Plots` panel), and when you start selecting

rows, you should see two things, one is that the red plot of the function plot

changes, and the second one is that a line (or guide) appears in the error

plot this indicates in the graph the moment of that particular weight.

[[https://raw.githubusercontent.com/wiki/dktcoding/mrft/imgs/ekg/guide.png|alt=Guide]]

Once you are satisfied with the results (i.e. choose the "best" weights

<sup id="a1">[1](#f1)</sup>)

## Now what?

I don't actually have time to finish it today, but the gist is: we will use

that synaptic weight to predict values of an unknown EKG, and estimate how

similar is it with the training value (mse), with that, we'll choose the one

with the lowest mse (mean square error) is the one that we'll accept as

correct.

@TODO complete example

<b id="f1"><sup>1</sup></b> There are several criteria for choosing the "best"

as a rule of thumb pick the closest to the left with the lowest error, or the

point where the validation an training errors intersect. [↩](#a1)