Obtaining neural network formula

Hi, I'm trying to obtain the formula from neural network using a linear simple case:

F = [-9 1 2 3 4 5 6 7 8 9 10 30 60];%neural network input

T = F*3+1; %target

net = newff(F, T,[],{},'traingdx');

net1 = train(net,F,T,[],[]);

x = 5; %new input

y = sim(net1,x); %ann output ~= 16;

%now i'm trying to obtain the formula from NN:

IW = net1.IW{1};

 b = net1.b{1};

 y2 = b+IW*x;

%But y2 = 5 whereas y = 3*x+1 = 16!!!

I understand that mapminmax function is involved for normalization..

Do you know how to renormilize "y2" in order to obtain the "y" target ?

Any help will be really appriciated

Answer 1

[Greg Heath]

What are b, IW and LW?

Given those values and the fact that x and t are both scaled to [-1 1 ] before training and y is rescaled with the t inverse transformation after training , should lead you to the answer.

Thank you for formally accepting my answer

Greg

Answer 2

[Gino Massafra]

Dear Greg, I've found the answer to my question for this simple case:

F = [-9 1 2 3 4 5 6 7 8 9 10 30 60];%neural network input

T = F*3+1; %target

net = newff(F, T,[],{},'traingdx');

net.trainParam.epochs = 1000;

net.trainParam.goal = 2e-32;

net.trainParam.min_grad = 1e-16;

net.trainParam.max_fail = 15000;

net.performFcn='mae';

net.trainParam.showWindow=1;

net1 = train(net,F,T,[],[]);

x = 5; %new input

y = sim(net1,x); %ann output = 16; this is the goal I want to reach

%now i'm trying to obtain the formula from NN:

IW = net1.IW{1};

b = net1.b{1};

y2 = b+IW*x;

Tmin = cell2mat(net1.outputs.range(1));

Tmax = cell2mat(net1.outputs.range(2));

Fmin = cell2mat(net1.inputs.range(1));

Fmax = cell2mat(net1.inputs.range(2));

%y3 = (max(T)-min(T))*(y2-min(F))/(max(F)-min(F)) + min(T);

y3 = (Tmax-Tmin)*(y2-Fmin)/(Fmax-Fmin) + Tmin;

y3 is = 16 !!! That's it y = y3

Next step is how to find y3 if the input is not a single row vector:

F = [-9 1 2 3 4 5 6 7 8 9 10 30 60; 21 10 22 3 4 -10 7 8 9 33 22 0 -13];%neural network input

T = sum(F)*5+4; %target

net = newff(F, T,[],{},'traingdx');

net.trainParam.epochs = 1000;

net.trainParam.goal = 2e-32;

net.trainParam.min_grad = 1e-16;

net.trainParam.max_fail = 15000;

net.performFcn='mae';

net.trainParam.showWindow=1;

net1 = train(net,F,T,[],[]);

x = [5; 6]; %new input

y = sim(net1,x); % y = 59;

%now i'm trying to obtain the formula from NN:

IW = net1.IW{1};

b = net1.b{1};

y2 = b+IW*x;

Tmin = cell2mat(net1.outputs.range(1));

Tmax = cell2mat(net1.outputs.range(2));

Fmin = cell2mat(net1.inputs.range(1));

Fmax = cell2mat(net1.inputs.range(2));

y3 = (Tmax-Tmin)*(y2-Fmin)/(Fmax-Fmin) + Tmin;

But now y3 is different from y

This doesn't work because Fmin and Fmax are wrong:

A = net1.inputs.range;

 >> A{1,1}

ans =

    -9    60

   -13    33

Which is now Fmin and Fmax?

Please help me

[Steven Lord]

See this documentation page for information about pre- and post-processing functions.

[Gino Massafra]

I red it, but I can't find the solution in network inputs are not a simple row vector

[Gino Massafra]

Ok I SOLVED it: F = [-9 1 2 3 4 5 6 7 8 9 10 30 60; 21 10 22 3 4 -10 7 8 9 33 22 0 -13];%neural network input

T = sum(F)*5+4; %target

net = newff(F, T,[],{},'traingdx');

net.trainParam.epochs = 1000;

net.trainParam.goal = 2e-32;

net.trainParam.min_grad = 1e-16;

net.trainParam.max_fail = 15000;

net.performFcn='mae';

net.trainParam.showWindow=1;

net1 = train(net,F,T,[],[]);

x = [5; 6]; %new input

y = sim(net1,x); %ann output = 16;

%now i'm trying to obtain the formula from NN:

IW = net1.IW{1};

b = net1.b{1};

x2 = -1+2*(x-[min(F')]')./([max(F')]'-[min(F')]') %I normalize inputs in [-1 +1] range

y2 = b+IW*x2;

y3 = (y2+1)*(max(T)-min(T))/2+min(T);

Now y3 = y

Cheers