Categorical Cross Entropy is a loss function commonly used in machine learning, particularly in classification tasks where the goal is to predict one class out of multiple possible classes. It quantifies the difference between the predicted probability distribution produced by a model and the actual distribution of the classes observed in the data.
In mathematical terms, Categorical Cross Entropy is defined as:
Loss = -Σ (yi * log(pi))
where:
yiis the true distribution (one-hot encoded vector) of classes,piis the predicted probability of each class.
The function computes the negative log likelihood of the true classes given the predicted probabilities. A lower value of categorical cross entropy indicates better performance of the model, as it means the predicted probabilities are closer to the actual labels.
This loss function is particularly useful in scenarios with multiple classes, such as image classification, where each sample belongs to one and only one class. Categorical Cross Entropy is often used in conjunction with softmax activation in neural networks, as it effectively handles the probabilities that sum to one across all classes.