Focal Loss

Focal Loss solves the imbalance of the Hard-Easy samples by generating the weight based on sample numbers. It derives from \(\alpha\)-balanced Cross Entropy loss. Then, adding a modulating factor \((1-p_{mci})^{\gamma}\) to the cross entropy loss, with tunable focusing parameter \(\gamma>0\), makes the final Focal Loss. The above can be summarized as the follow equation.

\[FL(p_{mci}) = -\alpha_{mci}(1-p_{mci})^{\gamma}log(p_{mci}) \label{eq:focaloss}\]

where \(\alpha\) is a weighting factor. \(\alpha\in[0,1]\) for class MCI and \(1-\alpha\) for class NC. \(p_{mci}\) represents the probability of the frame sequence attributing to MCI.

\[p_{mci} = \begin{cases} p & if\ y=MCI\\ 1-p & otherwise \end{cases}\]

where p is the model's predict score, y is the predicted label.