Optimal hidden nodes number

Hello everybody,

In order to determine optimal hidden neurons, Trial and error algorithm has been used (trial = 10, 10 < H < 100, dH = 100). I get the table on top but i can not determine the optimal hidden neurons. The table contains (Trials, Hidden neurons, test_mse, train_mse, val_mse, test_R, train_R, val_R)

Please i need your help. Thank you.

Answer 1

[Greg Heath]

I have posted hundreds of examples in both the NEWSGROUP (comp.soft-sys.matlab) and ANSWERS that determine the optimal number of hidden nodes defined by

 1. One Hidden Layer (ALWAYS SUFFICIENT!!!)
 2. Minimum Number of Hidden Nodes subject to my  
    practicality constraint

    TRAINING SUBSET RSQUARE >= 0.99 

    i.e.

    99% of the training subset target variance is
    successfully modeled by the net.

    Equivalently

    TRAINING SUBSET MSE <= 0.01*TRAINING SUBSET VARIANCE

 3. COMMENTS & CAVEATS

    a. The training subset must be a good representative of 
validation and test data

    b. A smaller number of hidden nodes can often be obtained 
by using multiple hidden layers

    c. The MSE minimization technique used for regression and 
curvefitting (e.g., via FITNET)is also successful for classification 
and pattern recognition (e.g., via PATTERNNET) where the 
minimization function is cross-entropy and the desired result is 
minimal error rate.

4. Suggested NEWSGROUP and ANSWERS search words for either FITNET or PATTERNNET

greg fitnet/patternnet msegoal nmse

5. The method is also used for timeseries

Hope this helps.

Thank you for formally accepting this answer

Greg

Answer 2

[Hamza Ali]

Hello, Thank you for your response. I compute R_square with following relationship :

R_square = 1 - (trainPerform / var(targets(trainInd));

Although i vary number of hidden neurons, the R_square doesn't considerably change. I read in Matlab documentation that the condition to validate network is on the one hand, the test error curve should have the same shape of validation error curve(which indicates the good division of dataset). And on second hand, you should have small test mse that is approximate to training mse in order to avoid overfitting.

My question is as follow :

1. How to validate model, with training data or with test data ? 
2. Is the R_square sufficient or we have to resort to other statistical indicators like (RMSE,MAE,MBE)? 
3. I would like to compute R_squared_ajusted, I can not determine n and p ?

Thank you a lot.

Answer 3

[Greg Heath]

             BASIC MATLAB NN DESIGN ASSUMPTIONS

The summary statistics of the Training, Validation and Test subsets are satisfactorially similar.

Training data is used to estimate net parameters

Validation data is used to verify ability to generalize (i.e., ability to obtain satisfactory performance on nontraining data)

Test data is used to obtain unbiased estimates of performance on non-design (including unseen) data

Overfitting occurs when the number of training parameters to be estimated exceeds the number of training equations

Overtraining occurs when the training exceeds the point at which the trend of the nontraining error is decreasing.

Normalized Mean Square error and Rsquare (Rsquare = 1-NMSE) tend to be sufficient for characterizing nonclassifier performance.

The normalization denominator for NMSE = MSE/MSEref is the minimum MSE for a constant output model. The minimizing constant output and corresponding MSEref are

    y      = mean(t,2)
    MSEref = mse(t-mean(t,2)) = mean(variance(t'),1)

Crossentropy is the default minimization quantity for MATLAB classifiers. However, the ultimate minimization goal is classification error rate.

Hope this helps.

Thank you for formally accepting my answer

Greg

[Hamza Ali]

Thank you so much.