Fitted Parameters & Mathematical Equation for ANN and ANFIS

I am trying to figure out how I can obtain the number of fitted parameters and the mathematical equation for both ANN and ANFIS models.

Neural Network Model:

• Feed-Forward Multi-layer Perceptron network with Back-Propagation
• Learning/Training Algorithm: Levenberg-Marquardt
• Transfer function(Hidden layer): Tan-Sig
• Transfer function(Output): Linear
• X's (inputs): 9 inputs
• Y (response): 1 response
• Number of nodes in the hidden layer: 15
• Best Validation performance obtained at epoch 7

Fuzzy Logic (2models):

• X's (inputs): 5 inputs
• Y (response): 1 response
• Subclustering: (Range of influence/radius=[0.5,0.6] - Squash factor [1000-2000] - Accept/Reject Ratios=1.25 - 6 rules*)
• Grid Partitioning: (Input membership function type='trapmf' - defuzzification method='wtaver' - 32 rules*)

Answer 1

[Greg Heath]

            MULTILAYER PERCEPTRON (MLP)
 [ I N ] = size(input)
 [ O N ] = size(target)
 [ O N ] = size(output)
 Ntrn    = N-2*round(0.15*N) % No. of training inputs
 Ntrneq  = Ntrn*O % No of training equations

H      = number of hidden nodes (single hidden layer)
I-H-O  = topology of a single hidden layer MLP  
Nw     = (I+1)*H + (H+1)*O % No. of unknown weights
Nw > Ntrneq ==> Overfitting ==> H > Hub
Hub    = (Ntrneq-O)/(I+O+1)  % ub => upper bound

 NOTE: Overfitting can lead to unstable iterative solutions. 
       In particular, overtraining an overfit net can lead to 
       poor generalization (i.e., poor performance on nontraining 
       data).

OVERFITTING MITIGATION

    1. Ntrneq >= Nw              (Don't overfit!)
    2. Validation subset stopping (MATLAB default)
    3. Bayesian Regularization    (via trainbr)

ANALYTIC SOLUTION

 output = B2 + LW*tanh(B1+IW*inputs)

Search both the NEWSGROUP and ANSWERS for details

                             SEARCH HITS
 SEARCHWORDS           NEWSGROUP       ANSWERS
 B1 B2 IW LW              73             208
 B1 B2 IW LW GREG         45             145

Hope this helps

Thank you for formally accepting my answer

Greg

[Armin Niaki]

Greg,

Thank you for your detailed and thorough response, I really appreciate it. Could you please explain a little bit more how I am supposed to implement this?

I am having trouble understanding your response to obtain the fitted parameters and mathematical equation of the neural network.

[Greg Heath]

Sorry, have no time for this now.

However, I have posted zillions of examples in both NEWSGROUP and ANSWERS.

Hope this helps.

Greg