The cost function

We need our classifier to predict the probability of seizure, which is class 1. This means that our output will be constrained to [0,1] as it would be in a traditional logistic regression model. Our cost function, in this case, will binary cross-entropy, which is also known as log loss. If you've worked with classifiers before, this math is likely familiar to you; however, as a refresher, I'll include it here.

The complete formula for log loss looks like this:

This can probably be seen more simply as a set of two functions, one for case  and :

     

When  and

When

The log function is used here to result in a monotonic function (one that is always increasing or decreasing) that we can easily differentiate. As with all cost functions, we will adjust our network parameters to minimize the cost of the network.