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# Finding best neural network structure using optimization algorithms and cross-validation

Hi.

I’m using optimization algorithm to find best structure+inputs of a ‘patternnet’ neural network in MATLAB R2014a using 5-fold cross validation. Where should i initialize weights of my neural network?

*Position_1(for weight initialization)* for i=1:num_of_loops

*Position_2(for weight initialization)* - repeating cross validation

for i=1:num_of_kfolds

*Position_3(for weight initialization)*

- Cross validation loop end

end

I’m repeating 5-fold cross validation (because random selection of cross validation) to have more reliable outputs (average of neural network outputs). Which part is better for weight initialization (Position_1,Position_2 or Position_3) and why?

# ANSWER

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To help understanding, I will assume Nval = Ntst = 0. Search for the nonzero examples in the NEWSGROUP and ANSWERS.

To design a typical I-H-O net with Ntrn training examples, try to not let the number of unknown weights

`Nw = (I+1)*H+(H+1)*O`

exceed the number of training equations

`Ntrneq = Ntrn*O`

This will occur as long as H <= Hub where Hub is the upperbound

`Hub = -1+ceil( (Ntrneq-O) / (I+O+1) )`

Based on Ntrneq and Hub I decide on a set of numH candidate values for H

0 <= Hmin:dH:Hmax <= Hmax numH = numel(Hmin:dH:Hmax)

and the number of weight initializations for each value of H, e.g.,

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