# Precision and Recall Confusion matrix

I was wondering, is it a proper method to convey information via separate Recall and Precision Confusion matrix? I recently came across a paper which reported the following scores. I am puzzled and unable to interpret them. Is this a usual standard in the academics?

Edit 1: The paper is related to activity recognition. • You can compute precision and recall per label; in each case the other labels are all 'negative'. I suppose you could also find precision/recall for each label with just one other label considered 'negative', ignoring the others. But I'm not sure what the diagonal in this chart would mean then. – Sean Owen Mar 11 '20 at 14:01
• @Born2Code do you have a reference to the paper? – Bruno Lubascher Mar 11 '20 at 19:13

## 3 Answers

No. A confusion matrix is by definition a tabulation of real classes and predicted classes per subject. I've seen relative counts but they are not standard.

According to Wikipedia:

Each row of the matrix represents the instances in a predicted class while each column represents the instances in an actual class (or vice versa).

The matrices listed above don't do that, so they are not confusion matrices. I'm not familiar with this format, and I don't think it is an academic standard. I'm not really sure how to interpet them, in that sense they are confusing matrices.

PS: You can obtain precision and recall from a confusion matrix.

This is very unusual according to my experience, and I agree that it's difficult to interpret.

There is a single value for either precision or recall for a particular label, but since these tables are presented as confusion matrices the values cannot be precision/recall.

I notice that the matrices show percentages which sum to 100 across each row for the "recall" one and sum to 100 across each column for the "precision" one. Based on this observation my guess is that the values show:

• in the "recall" table, the percentage of instances predicted with class X (column) among true instances of class Y (row). Example: 12.23% of of instances where the true label is "carry" are labelled as "walk".
• in the "precision" table, the percentage of instances which are truly class X (row) among instances predicted as class Y (column). Example: 6.87% of the instances predicted as "walk" actually belong to class "carry".

In my opinion this kind of non-standard representation should be avoided unless there's a really good reason. In this case a regular confusion matrix would have been clearer.

I was wondering, is it a proper method to convey information via separate Recall and Precision Confusion matrix?

Usual or not this could be very important. They convey different things. So in medical purposes, or generally in different context, certain recall values for certain classes could be very interesting and important because we dont wont to commit this kind of mistake. Hence author maybe wanted to point to this.