Neural Networks

The procedure for training the Neural Network for chord recognition was as follows:

Desing and training
We designed the network with only one hidden layer. Both the hidden layer and the output layer where desinged with sigmoidal functions returning values between -1 and 1.The output layer was composed of 24 output units. The labels (numbers betwee 1 and 24) where formated so that each number was represented by the 24 outputs of the neural network in the following way:

1 = [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
2 = [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
3 = [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
4 = [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]

... etc.

1. We trained one layer NN with 2 to 40 nodes in the hidden layer for all four data sets.
2. Tested recongnition accuracy on validation set.
The feature set that performed better overall was set number 2 (see left figure bellow). Then we tested performance of NN on set number 2 extended with the 12 permutations of each sample in the set.

Testing on the validation data we obtained better results on the training set without the added permutation samples that with them.

Classification performance of NN on all four training data sets for different number of hidden units.	Classification performance of NN on the data set #2 with all the 12 shifts of each chord added to the training set.

From the graphs we observe that numbers of hidden units between 15 and 20 should work fine for training and testing NN with the testing data.

We trained on set 2 (without its transpositions) with 17 nodes in the hidden layer and tested the network on both the original training data set and the set with shifted samples. We obtained the following accurate classifcation results for each data set.

Classification Results