How can I improve low probabilities when using probabilistic neural networks?

I am using Probabilistic Neural Networks (NEWPNN) to classify samples into one of four possible classes. I notice that although the results are accurate, for some samples the probability is very low (rows 1 to 3 in the dataset below). Columns 1 to 4 are the probabilities of the sample belonging to each one of the four classes. Column 5 is the PNN final classification and column 6 the sample's original class.

 0.2500    0.2500    0.2500    0.2500    1.0000    1.0000  

0.2500    0.2500    0.2500    0.2500    1.0000    1.0000

0.2501    0.2500    0.2500    0.2500    1.0000    1.0000

0.8596    0.0468    0.0468    0.0468    1.0000    1.0000

0.9932    0.0023    0.0023    0.0023    1.0000    1.0000

0.8760    0.0413    0.0413    0.0413    1.0000    1.0000

Notice that the probabilities are all very close (~0.25) for the first few observations.

Answer 1

[MathWorks Support Team]

To improve the low probabilities when using the NEWPNN function, one variable you can adjust is the 'spread' of the radial basis functions. If the spread is too small, then vectors between prototypes that the network has learned can end up with low probabilities.

   net = newpnn(x,t,spread)

Since the best spread value varies with the problem, you can adjust it until the network does best at a test set of data (and reserve additional test data to validate the final result).

But simply normalizing the probabilities as with SOFTMAX (which is already being done in the function currently) is also a good solution.

You can also use SOFTMAX to normalize the output of a PATTERNNET network after it is trained.