Fitted Parameters & Mathematical Equation for ANN and ANFIS

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Armin Niaki 2017-6-20

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/345568-fitted-parameters-mathematical-equation-for-ann-and-anfis

评论： Greg Heath 2017-6-25

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*)

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Answer 1

Greg Heath 2017-6-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/345568-fitted-parameters-mathematical-equation-for-ann-and-anfis#answer_271383

在 MATLAB Online 中打开

            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

Ntrneq >= Nw              (Don't overfit!)
Validation subset stopping (MATLAB default)
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

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Armin Niaki 2017-6-23

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.