How does Keras compute validation accuracy and training accuracy for multi-class classification problems?

Question

I would like to know how Keras computes the validation and training accuracies for multi-class classification problems (ie, the function used). I set my model compile as follows:

model.compile(optimizer=Adam(lr=0.001), loss='categorical_crossentropy', metrics=['accuracy'])

But I am trying to understand how is the validation accuracy and training accuracy is computed (ie, explicit formulae).

I know the validation and training loss are determined by the categorical_crossentropy , but I am not sure about the accuracies.

Note: this is NOT a duplicate of this post . My question is looking for an explanation of the Python function used by Keras to compute accuracy, not the theoretical details given in the mentioned post.

Answer 1

You can find the metrics file and their implementation in the Keras github repo. In this case following metric applies:

def categorical_accuracy(y_true, y_pred):
    return K.cast(K.equal(K.argmax(y_true, axis=-1),
                          K.argmax(y_pred, axis=-1)),
                          K.floatx()) 

This calculates the accuracy of a single (y_true, y_pred) pair by checking if the predicted class is the same as the true class. It does this so comparing the index of the highest scoring class in y_pred vector and the index of the actual class in the y_true vector. It returns 0 or 1.

It uses this function to calculate the overall accuracy of the data set, by using the conventional accuracy formula, which is defined as

(amount of correct guesses)/(total amount of guesses)