Struggling to Improve Neural Network Performance

I am working on creating a function fitting neural network with the neural network toolbox but I haven’t had much success getting it to work correctly. I have an input matrix with two features. I currently use fitnet (I’ve tried cascadeforwardnet/feedforwardnet without much difference) and have two hidden layers, each with 10 neurons. I’ve been using `trainbr` because it has given me better results than `trainlm`. I’m trying to normalize or standardize the data but haven’t had much success. I know that fitnet uses mapminmax by default and I’ve seen Greg Heath’s suggestion that I use zscore to standardize first. The problem is, every time I’ve used the zscore standardization I haven’t gotten very good neural network results. My output needs to be completely positive after de-standardization yet I still get negative values. Because of this, I have used log10 to normalize the data, therefore keeping all of the values positive.

In order to see prediction error, I have found the maximum percent error at any individual output point. I cannot get error lower than 40%, and there are multiple other points with decently high error.

Is there anything else that I can do, whether it be normalization/standardization or network reconfiguration to improve my network performance?

EDIT:

I’m not sure if this is of any help but the regression plot shows that the R = 0.99984 so it seems very accurate.

ANSWER

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>Why is it that MSE is the best measure of error and >the way I was calculating error is no good? Is it >because the toolbox focuses on minimizing that error >so me trying to minimize a different type of error >is of little help?

That’s part of it. The other part is does percent error really make sense in a regression problem?

>I made the changes you suggested and run 10 trials >where each trial has some multiple of 3 hidden neurons >where the multiple is between 3 and 30. Each of these >trials builds & simulates 10 ANNs, each with a random >split of training/testing/validation data. I made it >so that the training data must be between 60% and 93% >of the total input data. I calculate the r squared and >output it to the below 10x10 matrix. Now that I have >this, I see that many of the values in the matrices >are above 0.99. How am I supposed to differentiate >between these values?

Ideally, N is sufficiently large so that the tst results are accurate and UNBIASED while the val results are relatively accurate and only SLIGHTLY BIASED.

Typically, the training goal I use is to minimize H subject to the constraint Rtrnsq > 0.99. I first obtain four 10x10 Rsq matrices for trn, val, tst and all. Next, these are reduced to four 4x10 matrices containing the min, median, mean and maximum Rsq vs H. Finally, the four rows of the four matrices are plotted.

As far as choosing one design, I would favor a net with Rsq > 0.99 at the smallest value of H.

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