Harper asked . 2021-04-07

nftool output transfer function

Hello,

I am using nftool to build a network that takes a vector of 8192 data points (in reality spread across a frequency dimension), which goes through a hidden layer with the standard tansig transfer function, then is reduced to 3 outputs that describe the intensity of certain features in the frequency domain data. The three outputs must sum to 1, and can have any value from 0 to 1 for each parameter. My training data samples this with increments of 0.01 for each of the three parameter values. I am currently using nftool with 30 nodes in the hidden layer and 3 outputs. I tried using two outputs since the third variable is not independent, but that seemed to make things worse.

Upon training my network converges rapidly, and the regression plot loks good. When I test the net with new simulation data, it is remarkably robust, extracting the correct values even when the noise makes the data "bad" to my eye. However, when I use my actual data, the network returns negative values for some of the variables, which should not be possible. The output layer has a linear transfer function. I am wondering if using a sigmoidal output function with values of 0 to 1 would solve this issue in a straightforward way? I am also exploring the posibility that my simulated noise (randn) does not recapitulate the noise in my system as well, but using a sigmoidal output layer might be the easiest way to take care of this. Once I generate my netwrok using nftool, can I change the output layer transfer function prior to training? If I can change that transfer function, could I complete the training inside nftool? I find it very easy to use and would like to stick to it for simplicity.

simulink , matlab , simulation deep learning

Expert Answer

Kshitij Singh answered . 2025-03-21 19:06:27

Your use of the Neural Network Fitting Tool (nftool) is well-suited for regression tasks, such as mapping a high-dimensional frequency domain vector to a low-dimensional output that describes specific features. Let’s address your situation and challenges, including the requirement for outputs to sum to 1 and potential adjustments to your network setup.

Key Considerations and Recommendations:

Enforcing the Constraint (Outputs Sum to 1):
- Neural networks do not inherently enforce constraints such as $output1+output2+output3=1\text{output}_1 + \text{output}_2 + \text{output}_3 = 1$ $output_{1} + output_{2} + output_{3} = 1$ . To achieve this:
  - Use a softmax activation function for the output layer. This ensures all outputs are between 0 and 1 and their sum equals 1.
  - To implement this in nftool, you may need to:
    - Train the network as usual with your target data scaled so the outputs naturally meet the constraint.
    - Post-process the raw outputs using a softmax function to enforce the sum-to-1 constraint explicitly.
Example of the softmax function:
$softmax(zi)=exp?(zi)∑j=13exp?(zj)\text{softmax}(z_i) = \frac{\exp(z_i)}{\sum_{j=1}^3 \exp(z_j)}$
Here, $z_i$ are the raw network outputs before applying softmax.

If using MATLAB's nftool, this might require writing custom code outside the GUI for post-processing.
Output Dimensionality:
- Using two outputs instead of three makes sense if the third output is linearly dependent ( $output3=1−output1−output2\text{output}_3 = 1 - \text{output}_1 - \text{output}_2$ ).
- However, reducing dimensionality may lead to worse performance, especially if the network struggles to model the interdependency correctly.
Recommendation: Stick with 3 outputs and enforce the sum-to-1 constraint explicitly.
Hidden Layer Configuration:
- Your choice of 30 nodes in the hidden layer is reasonable. However, you might experiment with different sizes (e.g., 20, 40) to find the optimal balance between underfitting and overfitting.
- Use cross-validation to ensure the network generalizes well to unseen data.
Training Data Granularity:
- Your training data increments of 0.01 provide a fine granularity, which is good for regression tasks.
- Ensure the data is evenly distributed across the entire input and output space to avoid bias during training.
Performance Evaluation:
- Use metrics such as Mean Squared Error (MSE) or Mean Absolute Error (MAE) to evaluate the network's performance.
- Check for overfitting by comparing training and validation errors.

Implementation in MATLAB (Example):

Here’s how you can set up a neural network programmatically in MATLAB, enforcing the sum-to-1 constraint via a softmax layer:

% Load your data
input_data = ...;   % (8192 x num_samples matrix)
target_data = ...;  % (3 x num_samples matrix)

% Create the network
hiddenLayerSize = 30;
net = feedforwardnet(hiddenLayerSize);

% Configure the network
net.layers{2}.transferFcn = 'softmax';  % Enforce sum-to-1 constraint on outputs

% Divide data for training, validation, and testing
net.divideParam.trainRatio = 0.7;
net.divideParam.valRatio = 0.15;
net.divideParam.testRatio = 0.15;

% Train the network
[net, tr] = train(net, input_data, target_data);

% Evaluate the performance
outputs = net(input_data);
performance = perform(net, target_data, outputs);

% Display performance
disp(['Performance (MSE): ', num2str(performance)]);

Why Using Softmax Helps:

The softmax activation ensures your outputs are valid probabilities, summing to 1. Without softmax, the network's output layer can produce unconstrained values, making it harder to meet your requirement.

Troubleshooting Tips:

If Overfitting Occurs:
- Reduce the number of hidden nodes.
- Increase the size of your training dataset.
- Apply regularization techniques (e.g., weight decay).
If Convergence is Slow:
- Normalize your input data to have zero mean and unit variance.
- Initialize weights properly.
If the Model Underperforms:
- Experiment with different training algorithms (trainlm, trainbr, etc.).
- Check the quality and distribution of your training data.

Let me know if you need further clarification or assistance in implementing these ideas!

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