audio_classification

Apply Naive Bayes classifiers to solve basic binary classification problems in the area of audio signal processing.
In this problem, the feature we used to classify spectrograms are 250 binary variables W(1,1), ... , W(25, 10),
and W(i, j) = 1, if the ij-th block of the spectrogram has high energy and and 0 otherwise. Each binary variable
is conditionally independent of the others given audio class. According to the model description provided by the
problem, we estimate the likelihoods P(W(i, j) = 1 | class) as the proportion of the training data from that class
that has high energy at the corresponding block. And it is the same when we estimate the likelihoods P(W(i, j) = 0 | class). Besides we use the laplace smoothing to avoid calculation problems when low or high energy
appears zero time. We also compute the log-likelihood to avoid underflow. In training procedure, we first read binary text images from yes_train.txt and no_train.txt and store them into arrays.
Then, we compute the P(W(i, j) = 1 | class) through dividing the number of high energy in position ij of the binary
image plus the smoothing_factor by the total number of images plus the smoothing_factor * 2. Here, the smoothing_factor
is the Laplace smoothing constant. After several experiments, we set the smoothing_factor to be 0.1. After the training
procedure, we get all the model parameters stored in four two-dimensional arrays: likelyhood_yes_low, likelyhood_yes_high,
likelyhood_no_low, likelyhood_no_high.
In test procedure, we first read all the test data from yes_train.txt and no_test.txt. Then we use MAP classification,
that’s to say, we assign the images to the class with the highest posterior.
The formula we used here is: