Understanding the Confusion Matrix and How to Implement it in Python | by Terence Shin | Towards Data Science

IntroductionWhat is a Confusion Matrix?Confusion Matrix MetricsExample of a 2x2 MatrixPython Code
Introduction
What is a Confusion Matrix?
Confusion Matrix Metrics
Example of a 2x2 Matrix
Python Code
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Anyone can build a machine learning (ML) model with a few lines of code, but building a good machine learning model is a whole other story.
What do I mean by a GOOD machine learning model?
It depends, but generally, you’ll evaluate your machine learning model based on some predetermined metrics that you decide to use. When it comes to building classification models, you’ll most likely use a confusion matrix and related metrics to evaluate your model. Confusion matrices are not just useful in model evaluation but also model monitoring and model management!
Don’t worry, we’re not talking about linear algebra matrices here!
In this article, we’ll cover what a confusion matrix is, some key terms and metrics, an example of a 2x2 matrix, and all of the related python code!
With that said, let’s dive into it!
A confusion matrix, also known as an error matrix, is a summarized table used to assess the performance of a classification model. The number of correct and incorrect predictions are summarized with count values and broken down by each class.
Below is an image of the structure of a 2x2 confusion matrix. To give an example, let’s say that there were ten instances where a classification model predicted ‘Yes’ in which the actual value was ‘Yes’. Then the number ten would go in the top left corner in the True Positive quadrant. This leads us to some key terms:
Positive (P): Observation is positive (eg. is a dog).
Negative (N): Observation is not positive (eg. is not a dog).
True Positive (TP): Outcome where the model correctly predicts the positive class.
True Negative (TN): Outcome where the model correctly predicts the negative class.
False Positive (FP): Also called a type 1 error, an outcome where the model incorrectly predicts the positive class when it is actually negative.
False Negative (FN): Also called a type 2 error, an outcome where the model incorrectly predicts the negative class when it is actually positive.
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Now that you understand the general structure of a confusion matrix as well as the associated key terms, we can dive into some of the main metrics that you can calculate from a confusion matrix.
Note: this list is not exhaustive — if you want to see all of the metrics that you can calculate, check out Wikipedia’s page here.
This is simply equal to the proportion of predictions that the model classified correctly.
Precision is also known as positive predictive value and is the proportion of relevant instances among the retrieved instances. In other words, it answers the question “What proportion of positive identifications was actually correct?”
Recall, also known as the sensitivity, hit rate, or the true positive rate (TPR), is the proportion of the total amount of relevant instances that were actually retrieved. It answers the question “What proportion of actual positives was identified correctly?”
To really hit it home, the diagram below is a great way to remember the difference between precision and recall (it certainly helped me)!
Specificity, also known as the true negative rate (TNR), measures the proportion of actual negatives that are correctly identified as such. It is the opposite of recall.
The F1 score is a measure of a test’s accuracy — it is the harmonic mean of precision and recall. It can have a maximum score of 1 (perfect precision and recall) and a minimum of 0. Overall, it is a measure of the preciseness and robustness of your model.
If this still isn’t making sense to you, it will after we take a look at the example below.
Imagine that we created a machine learning model that predicts whether a patient has cancer or not. The table on the left shows twelve predictions that the model made as well as the actual result of each patient. With our paired-data, you can then fill out the confusion matrix using the structure that I showed above.
Once this is filled in, we can learn a number of things about our model:
Our model predicted that 4/12 (red + yellow) patients had cancer when there were actually 3/12 (red + blue) patients with cancer
Our model has an accuracy of 9/12 or 75% ((red + green)/(total))
The recall of our model is equal to 2/(2+1) = 66%
In reality, you would want the recall of a cancer detection model to be as close to 100% as possible. It’s far worse if a patient with cancer is diagnosed as cancer-free, as opposed to a cancer-free patient being diagnosed with cancer only to realize later with more testing that he/she doesn't have it.
Below is a summary of code that you need to calculate the metrics above:
# Confusion Matrixfrom sklearn.metrics import confusion_matrixconfusion_matrix(y_true, y_pred)# Accuracyfrom sklearn.metrics import accuracy_scoreaccuracy_score(y_true, y_pred)# Recallfrom sklearn.metrics import recall_scorerecall_score(y_true, y_pred, average=None)# Precisionfrom sklearn.metrics import precision_scoreprecision_score(y_true, y_pred, average=None)
There are three ways you can calculate the F1 score in Python:
# Method 1: sklearnfrom sklearn.metrics import f1_scoref1_score(y_true, y_pred, average=None)# Method 2: Manual CalculationF1 = 2 * (precision * recall) / (precision + recall)# Method 3: Classification report [BONUS]from sklearn.metrics import classification_reportprint(classification_report(y_true, y_pred, target_names=target_names))
Now that you know what a confusion matrix is as well as its associated metrics, you can effectively evaluate your classification ML models. This is also essential to understand even after you finish developing your ML model, as you’ll be leveraging these metrics in the model monitoring and model management stages of the machine learning life cycle.
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The BEST way to support me is by following me on Medium here.
Be one of the FIRST to follow me on Twitter here. I’ll be posting lots of updates and interesting stuff here!
Also, be one of the FIRST to subscribe to my new YouTube channel here!
Follow me on LinkedIn here.
Sign up on my email list here.
Check out my website, terenceshin.com.