カテゴリカルクロス エントロピー is a 損失関数 commonly 機械学習で使用される, 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.
数学的には、カテゴリカルクロスエントロピーは次のように定義されます：
Loss = -Σ (yi * log(pi))
ただし：
yiis the true distribution (one-hot encoded vector) of classes,piis the predicted probability of each class.
この関数は次を計算します 負の対数尤度 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 画像分類, 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.