What does P@1 mean in this scientific article?

Question

In this scientific article: Label Filters for Large Scale Multilabel Classification by Alexandru Niculescu-Mizil and Ehsan Abbasnejad, they use the notations P@1, P@5 and P@10 as the following table shows

I was thinking that they were $p$-values at the beginning, but it somehow doesn't make sense.

Could someone explain me what this notations mean?

Answer 1

The article you linked says:

Following previous work on large scale multilabel classification (Weston et al., 2013; Prabhu and Varma, 2014; Bhatia et al., 2015) we use precision at k (P@k) as the evaluation metric. Precision at k is defined as the fraction of true labels among the top k predictions made by the classifier.

Generally speaking, precision is a binary metric used to compare the results of the classifier under test with trusted external judgments. It is defined as a proportion of correctly labeled items in items predicted by the classifier, vaguely $$ \mathrm{precision}=\frac{|\{\text{correctly labeled items}\}\cap\{\text{predicted items}\}|}{|\{\text{predicted items}\}|}. $$ The @k part means that this metric is evaluated on top $k$ predictions retrieved by the classifier.

Answer 2

On the same page of the figure (Section 4) in the article, the notation is defined as follows:

"Following previous work on large scale multilabel classification (Weston et al., 2013; Prabhu and Varma, 2014; Bhatia et al., 2015) we use precision at k (P@k) as the evaluation metric. Precision at k is defined as the fraction of true labels among the top k predictions made by the classifier."