Possibilites about obtaining mathematical equation from neural network toolbox after training?

Hi, I was searching for a mathematical equation just like in the regression analysis where coefficient are formed for each independent valuable. Is it possible to find out an equation after performing the training parameter in neural network. As training is done by levenberg marquardt algorithum. As it is shown in the architecture of the neural network manual.

Answer 1

[Greg Heath]

Standard Equations for a single hidden layer feedforward multilayer perceptron:

 h  = tansig( IW*x + b1 ); % -1 < h <1

Regression:

 y1 = b2 + LW*h;           % Equivalent to using PURELIN
 y2 = tansig( y1 );        % -1 < y2 < 1

Classification:

 y3 = logsig( y1 );        % 0 < y3 < 1
 y4 = softmax( y1 );       % 0 < y4 < 1 , sum(y4) = ones(1,c), c classes

Answer 2

[Shashank Prasanna]

Neural Networks are non parametric methods, which means there are no parametrized equations. The model is expressed it as a weighted sum of several sigmoids or other transfer function depending on how many layers or nodes you have.

In short there is not small equation like in parametric regression analysis.

Wolfram has a nice explanation:

http://mathworld.wolfram.com/NonparametricEstimation.html