A confusion matrix, also known as an error matrix, uses a special table to help visualize the performance of your classification model. That way, you can easily see how successful your model was when predicting the class.
What You'll Learn
- Overview of what a confusion matrix is, how to create your matrix, and why you should use it
- True positives and negatives, target classes, and predictive models
Welcome to this quick introduction to the confusion matrix. If you’ve ever looked at a confusion matrix for the first time, you’ve might have found it, well, confusing. But it doesn’t have to be.
A confusion matrix is a simple way to lay out how many predicted categories or classes were correctly predicted and how many were not. It is used to evaluate the results of a predictive model with a class outcome to see the number of classes that were correctly predicted as their true class. To understand what’s going inside this confusion matrix of correct classes versus incorrect classes, we first need to understand true positives, true negatives, false positives, and false negatives. Kind of confusing, right? Well, let’s relabel these terms to make it a bit clearer.
Essentially, the confusion matrix is just keeping track of Class A correctly predicted as Class A, Class B correctly predicted as Class B, Class A incorrectly predicted as Class B, and Class B incorrectly predicted as Class A. Where true and false comes into it, is we want to know if our target Class A was correctly predicted as A which is true, or incorrectly predicted as B when in fact was A, which is false. Our target Class A is our positive and the other Class B is our negative, so then a true positive and a true negative is a positive Class A correctly predicted as Class A, and negative Class B correctly predicted as B. We want to get as many predictions of A and B as possible, aiming for more trues rather than falses. So, then how do we organize this in a way to lay out the number of correct A’s and B’s versus incorrect A’s and B’s?
Well, we draw a grid. We place these into a matrix grid where the x-axis is the predictions made and the y-axis is the actual class label. So, let’s just say we have 200 subjects of which 100 are from Class A and 100 from class B. 60 of the actual A cases on the y-axis were correctly predicted as their true class, A on the x-axis. For class B, 30 actual B classes on the y-axis were truly predicted as Class B on the x-axis. If you look at the diagonal counts, that’s how many subjects were correctly predicted as their classes. So, these are all the trues for the positive and negative classes.
Now you have a way of identifying which class is predicted correctly most of the time compared to other classes. And evaluate whether your predictive model is, you know, guessing right most of the time, or is it guessing wrong on each of these classes. One last thing, how do we decide what is Class A and what is Class B? What should be a positive class, and what should be a negative class?
Well, most of the time it doesn’t matter which class you assign to positive or negative, as the confusion matrix would tell you how many subjects were correctly predicted from each class. But here are some examples of a target class you might want to differentiate from a non-target class. In standard binary classification you could be interested in returning customers as, you know, the positive target class versus new customers as the negative class. Or it could be one target class versus all other classes, such as aggressive cancer versus all other passive type cancers as the single negative class. Either way, you’re comparing how many were correctly or incorrectly classified from each class. The confusion matrix will tell you how many times actual class a was predicted as B and vice versa, or if they were correctly classed as their true labels. And that sums up the confusion matrix.
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Rebecca Merrett - Rebecca holds a bachelor’s degree of information and media from the University of Technology Sydney and a post graduate diploma in mathematics and statistics from the University of Southern Queensland. She has a background in technical writing for games dev and has written for tech publications.