Mapping Nonlinear Functions By Using Artificial Neural Network

Question

I am dealing with an hard assignment which I could not move the pen. What is the way to solve the following problem? Any help would be appreciated.

f(x)=1/x and x is between 0.1 and 1

The problem is asking to traing the network by using back propagation algorithm with one hidden layer. Trainin set will have 200 input/output pattern, test set will have 100 and validation will have 50 patterns.

How can I solve this? Regards.

Answer 1

That sound much more complicated than it actually is. The network does not know anything about what you actually want to represent with the input and output pattern. So do not worry about that. All you need to do is setup such a network (I assume that you know how to do that - otherwise just check around there are couple of libs, but it is even possible in Excel to set it up quickly for testing purposes)

Then just run the test data against the network in a loop. Once the network is kind of stable store it and start testing.

I assume the representation of the patters has been defined already? It's one of the most important point that defines the quality. The closer the x/y pairs are semantically the closer the representation patterns have to be - meaning here the delta between x/y pairs. In particular for the small x value/large y pairs!

Otherwise the network will not "understand" that and you can teach forever - since there is no correct representation of the similarity - in this case the delta x and delta y

For example the value 7 in binary format is not close at all to the value 8. Meaning if the network did not "learn" that because it has never seen the 8 it will not work well.

So the closer the values the more similarities the representation of the values should be for the network! - That's the key.

Tweaking the parameters will then fine tune your model