# What is the difference between Top-1 Accuracy and Recall?

I'm doing research on image classification, and I don't understand the difference between Top-1 Accuracy and Recall. Are they the same?

I found a link here What is the definition of Top-n accuracy? that explains what top-n accuracy is, which is the total number of correct guesses divided by the total number of images.

But isn't that recall? Recall is defined as the number of correct guesses divided by the total number of images

Given these laymen's terms definitions:

TP = Making a correct guess
TN = Not making a wrong guess
FP = Guessing the wrong class
FN = Missing the correct class
FP + TP = total number of guesses
FN + TP = total number of images


Accuracy is defined as

(TN + TP) / (TN + TP + FN + FP)

Recall is defined as

TP / (FN + TP)

But Top-1 Accuracy is defined as

TP / (FN + TP) where we only look at the 1st guess, ignoring others

Similarly Top-N Accuracy is defined as

TP / (FN + TP) where we only look at the top N guesses, ignoring others

Have I misunderstood what Top-1 Accuracy is? Shouldn't Top-1 Accuracy be Accuracy as it's defined (TN + TP) / (TN + TP + FN + FP)? Otherwise it should be called Top-1 Recall

Is Recall equal to Top-1 Accuracy and Recall is just a subset of Top-N Accuracy where N equals 1?

• Similarly could we measure Top-N Precision, (TP / total number of guesses)? Commented Jul 15, 2020 at 15:49

Accuracy is the fraction of images in which the classifier has guessed the true class (whichever it is) correctly. For a binary classifier it is computed as $$\frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}}$$. The top-$$n$$ accuracy is for a multiclass classifier, and this formula is not applicable anymore. But the textual definition still holds. Recall for a binary classifier is $$\frac{\text{TP}}{\text{TP} + \text{FN}}$$. It shows in what fraction, out of all images with cats, cats have been detected. I'm not sure I've ever seen the recall used with multiclass classification, but if one were to generalize it, it would make sense to compute it for a single class: Among images containing cats, in what fraction the ‘cat’ class is found among the top $$n$$ classes reported by the detector? You can see that this is different from the accuracy.