How to choose "Nlocmin,Nlocmax" in non linear regression and curve fitting?

How can one choose "Nlocmin and Nlocmax" values for non linear regression using ANN feedforwardnet in the code mentioned by Greg sir??

Link to the thread

http://in.mathworks.com/matlabcentral/newsreader/view_thread/333427

2. Estimate, by trial and error, the minimum number of hidden nodes necessary for successfully approximating the underlying input-output transformation. For a smooth function with Nlocmin local minima and Nlocmax local maxima, a reasonable lower
bound is H >= 2*max(Nlocmin,Nlocmax). Sometimes it is prudent to count endpoint extrema as 1/2 a local extremum. The addition of real-world noise, interference and measurement error should not change that minimum number. However, the contamination may make it difficult to identify the significant error-free extrema.

Thanks

Kishore

Answer 1

[Greg Heath]

Plot the target and count the number of local extrema.

This will only work for relatively smooth functions.

Otherwise use the search over

 Hmin:dH:Hmax < Hub

with a preference for Hmax << Hub

For details, search NEWSGROUP and ANSWERS using

 greg Hub

Hope this helps

Thank you for formally accepting my answer

Greg

[Kishore]

1) What should be the criteria for selecting number of hidden neurons

   Hub ?? or Ndof ??

2) I put 2 for loops in my code one for varying number of neurons and one for Ntrails, i ran the code for until i get the Ndof as negative quantity..

i get this result

 R2 values for H = 0 to 3 and Ntrails = 1 to 10
0.753160684721697  0.815846821332570 0.935058715861745  0.954252137206118
0.753160684721697  0.815846821332570 0.935884289937718  0.980321755267376
0.753160684721697  0.815846821332570 0.917201138717953  0.997488719109723
0.753160684721697  0.815846821332570 0.930553054754834  0.960149651411815
0.753160684721697  0.762563239630275 0.951581078215140  0.993348125338601
0.753160684721697  0.815846821332570 0.900031911479721  0.979790825957402
0.753160684721697  0.815846821332570 0.885977723609531  0.998753726801378
0.753160684721697  0.815846821332570 0.895716885586277  0.999055291675377
0.753160684721697  0.815846821332570 0.931318496839154  0.960757183796528
0.753160684721697  0.779425009498547 0.918015150082236  0.947511177559573

my question is that how to choose particular number of hidden layers and Ntrails and how to reproduce the same R2??

suppose if i choose H=3 and Ntrails = 8 where i am getting R2 as 0.999

Thanks

Kishore

[Greg Heath]

1. Initialize the random number state before the loops and choose the 38th after that

2. Store the random number state before each design

3. Store the random number state and corresponding net if the new MSE is smaller than the previous minimum.