Confusion Matrix

A confusion matrix is a way of measuring how well a machine learning model can classify different types of data. For example, suppose you have a model that can recognize images of cats and dogs. You want to know how accurate your model is, and also what kind of mistakes it makes.

To do this, you can use a confusion matrix. A confusion matrix is a table that shows the number of images that the model correctly or incorrectly classified as cats or dogs. Here is an example of a confusion matrix for this problem:

The rows of the table represent the actual labels of the images, and the columns represent the predicted labels by the model. The diagonal cells show the number of images that the model correctly classified as cats or dogs. These are called true positives (TP) and true negatives (TN). The off-diagonal cells show the number of images that the model incorrectly classified as cats or dogs. These are called false positives (FP) and false negatives (FN).

From the confusion matrix, we can calculate some metrics that tell us how good the model is. One of the most common metrics is accuracy, which is the percentage of images that the model classified correctly. To calculate accuracy, we use this formula:

This means that the model is 85% accurate in recognizing cats and dogs.

However, accuracy is not always enough to evaluate a model. Sometimes, we care more about how well the model can identify a specific class, such as cats. For this, we can use other metrics, such as precision and recall. Precision is the percentage of images that the model predicted as cats that are actually cats. Recall is the percentage of images that are actually cats that the model predicted as cats. To calculate precision and recall, we use these formulas:

In this example, the precision and recall for the cat class are:

This means that the model is 89% precise and 80% recall in recognizing cats.

A confusion matrix can also be used for more than two classes. For example, suppose you have a model that can recognize images of cats, dogs, and birds. You can use a confusion matrix to show the number of images that the model correctly or incorrectly classified as cats, dogs, or birds. Here is an example of a confusion matrix for this problem:

The diagonal cells show the true positives for each class, and the off-diagonal cells show the false positives and false negatives for each class. From this confusion matrix, we can calculate the accuracy, precision, and recall for each class, as well as the overall metrics for the model.

A confusion matrix is a useful tool for evaluating and improving a machine learning model. It helps us understand the strengths and weaknesses of the model, and also identify the sources of error and the areas of improvement. By using a confusion matrix, we can make our model more accurate and reliable.