Guide: How to Use and Features (ver.1.03)

4. Analyse the ANN TOC

• General statistical numbers
• Regression
• Sensitivity

From now on the ANN can be retrieved, at any time, by going to the ANN List link after you log on.

By clicking on the ANN ID, you will move to the ANN Analysis page, where you can have a glance at the quality of the trained ANN:

On the left upper field of the "ANN Analysis/Trained ANN Statistics" page you find statistical key values for the ANN presented as text, as shown in the figure on the left.
A more complete report is available by clicking on the links "text format report".

Now, if you have more than one output, like in this example, all the information shown referes to the selected output (the first one is selected by default).
The "Predicted vs. Observed Regression Graph" has the name of the selected output in the title.

So here you got:

r2=0.99959, which means that the ANN predicts quite well, as for the data submitted. 4 inputs with 5 optimal hidden nodes, which means that the complexity is not very high.

In order to get a new analysis, select the output for which you want the analysis for and then press "New Output Analysis".
 
Elements of the "Predicted vs. Observed Regression Graph".

open circles: values used for training the selected ANN, the one that you are going to use. It is the ANN which is the least biased, as determined by the cross validation procedure. In other words, the ANN which is best suited. crosses: values used for testing the selected ANN (these values were not used in the training of the elected/best ANN!) dashed line: represents the optimal/ideal case, where the predicted values are equal the observed values. solid line: linear regression of the testing values (the closer this line is to the dashed (ideal) line, the better)

This graph point to a good quality ANN.

1. No visible difference between ideal and observed regression line.
2. Aparently good distribution of the vaules over the range of interest.
3. Small number of values far away from the ideal regression.

In this example, the inputs "1" and "2" have high influence on the output (here for the sum: "a+b") but inputs "3" and "4" have not.

That is exactly what one would expect, since inputs "3" and "4" don't contribute at all to the sum.

There is another thing one can read from this figure:
Both bars, the red and the blue are of identical height.
This means, the respective input influences the output as much as the average.
That also is expected, since the inputs for the sum are the same as for the difference, and the weigths are equal for both.

In the real world, where you might not know the modell behind the data, the sensitivity analysis would have give you the hint that inputs "3" and "4" don't contribute at all to the output.

What else should be noted???

A separate ANN is developed for each output, using all inputs at a time. Therefore, there is no need to separate different sets of dependent variables according to their interdependencies, which can be recovered by cluster or factor analysis of their sensitivities.