Confusion Matrix Calculator

With this confusion matrix calculator, we aim to help you to calculate various metrics that can be used to assess your machine learning model's performance. The confusion matrix is the most prevalent way of analyzing the results of a classification machine learning model. It is thus a critical topic to understand in this field.

We have prepared this article to help you understand what a confusion matrix is and how to calculate a confusion matrix. We will also explain how to interpret the confusion matrix examples to make sure you understand the concept thoroughly.

You can see a confusion matrix as way of measuring the performance of a classification machine learning model. It summarizes the results of a classification problem using four metrics: true positive, false negative, false positive, and true negative.

However, the use of a confusion matrix goes way beyond just these four metrics. Using these four metrics, the confusion matrix allows us to assess the performance of the classification machine learning model using more versatile metrics, such as accuracy, precision, recall, and more.

We will talk about the definitions of these metrics in detail in the next section. You will be able, for example, to calculate accuracy from the confusion matrix all by yourself!

After understanding the definition of a confusion matrix in machine learning, it's time to talk about how to read a confusion matrix.

A confusion matrix has four components:

• True positive (TP) - These are the correct predictions made that are labeled as positive. You can input this and the below values in the confusion matrix calculator's first section.
• False negative (FN) - These are the wrong predictions made that are labeled as negative.
• False positive (FP) - These are the wrong predictions made that are labeled as positive.
• True negative (TN) - These are the correct predictions made that are labeled as negative.

Using these four components, we can calculate various metrics to help us in analyzing the performance of the machine learning model:

• accuracy - Accuracy is the proportion of the correct predictions in the confusion matrix out of all predictions made. You can calculate accuracy from confusion matrix, as well as other metrics, using our tool.
• precision - Precision is the proportion of the correct predictions in the confusion matrix out of all positive predictions.
• recall - Recall is the proportion of correct predictions in the confusion matrix out of all positive classes.
• F1 score - F1 score allows you to compare low-precision models to high-recall models, or vice versa, by using the harmonic mean of precision and recall to punish extreme values.
• TPR - True positive rate is the probability that a positive prediction will be true.
• FNR - False negative rate is the probability of getting a type II error, which is wrongly labeling a negative class as positive.
• FPR - False positive rate is the probability of getting a type I error, which is wrongly labeling a positive class as negative.
• TNR - True negative rate is the probability that a negative prediction will be true.
• FDR - False discovery rate is the ratio of the number of false positive to the total number of positive predictions.
• MCC - Matthews correlation coefficient, also known as the phi coefficient, is a metric that measures the association between two binary variables.

Next, let's look at the calculations of these metrics using the confusion matrix example.

Finally, it is time to talk about the calculations. We will use the confusion matrix example below to demonstrate our calculation. Let's take the classification results below as an example:

• TP: 80;
• FN: 70;
• FP: 20; and
• TN: 30.

The calculation of the metrics are shown below:

1. Accuracy

   To calculate accuracy from confusion matrix, use the formula below:

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

   The accuracy for this example is (80 + 70) / (80 + 70 + 20 + 30) = 0.55.

   You can also calculate the percentage versions of these metrics.

2. Precision

   The precision can be calculated using the formula below:

   precision = TP / (TP + FP)

   The precision for this example is 80 / (80 + 20) = 0.8.

3. Recall

   Find the recall using the formula below:

   recall = TP / (TP + FN)

   The recall for this example is 80 / (80 + 70) = 0.53.

4. F1 score

   To estimate F1 score, use the following formula:

   F1 score = (2 * precision * recall) / (precision + recall)

   The F1 score for this example is (2 * 0.8 * 0.53) / (0.8 + 0.53) = 0.64.

5. True positive rate

   The true positive rate TPR (also called sensitivity) can be calculated using the formula below:

   TPR = TP / (TP + FN)

   The TPR for this example is 80 / (80 + 70) = 0.53.

6. False negative rate

   We express the false negative rate FNR in a similar way:

   FNR = FN / (TP + FN)

   The FNR for this example is 70 / (80 + 70) = 0.47.

7. False positive rate

   The false positive rate FPR is as follows:

   FPR = FP / (FP + TN)

   The FPR for this example is 20 / (20 + 30) = 0.4.

8. True negative rate

   The true negative rate TNR (also called specificity) is:

   TNR = TN / (TN + FP)

   The TNR for this example is 30 / (30 + 20) = 0.6.

9. False discovery rate

   We can calculate the false discovery rate as follows:

   FDR = FP / (TP + FP)

   The FDR for our example is 20 / (80 = 20) = 0.2.

10. Matthews correlation coefficient

    Finally, we can calculate the Matthews correlation coefficient using the formula below:

    MCC = (TP * TN - FP * FN) / √((TP + FP) * (TN + FN) * (FP + TN) * (TP + FN))

    Hence, the MCC is (80 * 30 - 20 * 70) / √((80 + 20) * (30 + 70) * (20 + 30) * (80 + 70)) = 0.11547.

If all of these confusion matrix calculations look complicated, just use the confusion matrix calculator we have built for you!