Neural Network Output :Scaling the output range.

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Ashikur
Ashikur 2012-1-28
Hi,
The output layer of my neural network (3 layered) is using sigmoid as activation which outputs only in range [0-1]. However, if I want to train it for outputs that are beyond [0-1], say in thousands, what should I do?
For example if I want to train
input ----> output
0 0 ------> 0
0 1 ------> 1000
1000 1 ----> 1
1 1 -------> 0
My program works for AND, OR, XOR etc. As input output are all in binary.
There were some suggestion to use,
Activation:
-----------
y = lambda*(abs(x)*1/(1+exp(-1*(x))))
Derivative of activation:
-------------------------
lambda*(abs(y)*y*(1-y))
This did not converge for the mentioned training pattern. Are there any suggestion please?

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采纳的回答

Greg Heath
Greg Heath 2012-1-31
Hello Greg,
Thanks again for answering the question. For my case, no rigid bound,
1. INCORRECT. ALL 3 VARIABLES ARE BOUNDED:
0 <= X1, Y <= 1000
0<= X2 <= 1.
2. HOWEVER, SINCE THE INPUT SCALES ARE DIFFERENT BY A FACTOR OF THOUSAND, X1 AND Y SHOULD BE TRANSFORMED BY VIA LOGS AND/OR POWERS. E.G.,
X1n = LOG10( 1 + X1 ) / LOG10( 1001 ) ==> 0 <= X1n <= 1
SIMILARLY FOR Y
HOPE THIS HELPS.
GREG

更多回答（1 个）

Greg Heath
Greg Heath 2012-1-29
If the target has rigid bounds, scale the data to either [0,1] or [-1,1] and use either LOGSIG or TANSIG, respectively.
Otherwise, standardize to zero-mean/unit variance and use PURELIN.
To recover the original data scale, just use the reverse tranformations.
Hope this helps.
Greg
  1 个评论
Ashikur
Ashikur 2012-1-29
Hello Greg,
Thanks again for answering the question. For my case, no rigid bound, So I will use purelin or f(x) = x
1. Standardize what? the input? each input vector individually? or the whole training input matrix?
2. Do I need to do the same standardization for desired output too?
I used purlin (f(x)=x) in my output, but it seems not to converge for,
0 0 ------> 0
0 1 ------> 1000
1000 1 ----> 1
1 1 -------> 0
The codes are in below link,
https://docs.google.com/document/d/18kGXAgeVP1kOlJHZJ2KmV_mkxY61f255LQjPcr6uwnI/edit?pli=1
https://docs.google.com/document/d/13YVWHUXug6XrngQD3a52IgzPxMH2M9sgECkb7peRckA/edit?pli=1
Hope you will have some times to see the problem.

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