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What is a Confusion Matrix?

What is a Confusion Matrix

Machine learning and Artificial Intelligence are popular and relevant topics today, and everyone’s scrambling to wrap their mind around the concepts and what they mean for society today. But both concepts are highly complex and have many components to them.

This article focuses on a critical aspect of machine learning, notably the confusion matrix. We will find out what a confusion matrix is, why they’re necessary, the role of the confusion matrix in machine learning and AI, how to create and scale a confusion matrix, and how you can get experience creating them in an online AI and ML bootcamp.

So, buckle up; we’re about to get technical here. Let’s start this fascinating data science journey with a definition.

What Are Confusion Matrices?

Machine learning practitioners and data scientists realize that AI algorithms aren’t perfect and are prone to error. So, these professionals must fathom what errors the algorithm is committing. This process will enable them to improve the algorithm and build a model that increases the business’s value while reducing the chance of error.

This process, called “evaluation metrics,” includes many types, such as the area under the curve (also known as AUC), log loss, and mean squared error. Some organizations even design metrics that better align with their Key Performance Indicators (KPIs for short) or unique business problems. One such popular performance measurement for classification tasks is called the confusion matrix.

Confusion matrices are performance measurement tools typically used for Machine Learning classification tasks and are particularly useful when measuring accuracy, precision, recall, specificity, and the AUC of a classification model. Confusion matrices are employed when the model’s output could be two or more classes (i.e., multiclass classification and binary classification).

Or, a confusion matrix in machine learning is a matrix of numbers that shows the data scientist where their model gets confused. It’s a class-wise distribution of the classification model’s predictive performance, an organized method of mapping predictions to the original classes where the data belongs.

The matrix summarizes the number of correct and incorrect predictions with count values and breaks them down by each class. This way, the data scientist gains insight into the errors the classifier is making and, even more importantly, the kinds of errors it’s making.

Here is what the basic layout of a confusion matrix looks like:

basic layout of a confusion matrix

Why Do We Need Confusion Matrices?

Confusion matrices are essential because they give us a better understanding of how a model performs than classification accuracy can. You can better understand what the classification model is getting right because the matrix directly compares values such as True Positives, False Positives, True Negatives, and False Negatives.

Here’s a summary of why confusion matrices are important.

  • They detail the classifier’s errors as well as the kinds of errors that are happening
  • They show how predictions are being made by a classification model that needs to be clarified and more organized
  • They help overcome the drawbacks of depending solely on classification accuracy
  • They can be used in situations where one class dominates over the others, and the whole classification problem needs to be more balanced
  • They can effectively and successfully calculate accuracy, precision, recall, specificity, and the AUC-ROC curve

Bear in mind that classification accuracy by itself can be misleading if there is an unequal number of observations in each class or if your dataset has more than two classes. Confusion matrices address this issue and give you a clearer idea of what the model is doing right, where it falls short, and what kind of errors it’s making.

Also Read: What is Machine Learning? A Comprehensive Guide for Beginners

Commonly Used Confusion Matrix Terms

You should become familiar with the associated terminology if you intend to use confusion matrices in your ML algorithms. Incidentally, you practice creating them in an AI and ML program.

Here are the most common confusion matrix terms.

  • Accuracy. Accuracy shows how frequently the model predicts the correct outputs. The ratio of the number of correct predictions the classifier makes to the total number of predictions it makes is one of the most essential parameters in measuring the accuracy of the classification problems.
  • Area Under the Curve (AUC). The AUC measures the binary classification model’s unique potential. When the AUC is high, the actual positive value will be more likely to be specified with a higher probability than its actual negative value.
  • Cohen’s Kappa. Cohen’s Kappa shows how well the classifier performed compared to how well it would have done randomly. Put another way, a model has a high Kappa score if its null error rate and accuracy differ considerably.
  • F-Measure. If two models have low precision but high recall, or vice versa, it’s hard to compare them. To address this, data scientists used an F-score. Both precision and recall can be evaluated at the same time by calculating the F-score.
  • Misclassification rate. This term explains the error rate, defined as how often the model gives incorrect predictions. Data scientists can calculate the error rate by considering the ratio of the number of wrong predictions to the total number of predictions made.
  • Null error rate. The null error rate shows how frequently the model is incorrect in situations where it consistently predicted the majority class.
  • Precision. The precision determines whether or not the model is trustworthy. It measures the number of accurately predicted positive values. In other words, it shows the number of accurate outputs the model released, considering all the positive values it correctly predicted. It is especially handy when the chance of a false positive is higher than that of getting a false negative.
  • Recall. The recall is the number of actual positive values the model correctly predicted.
  • Receiver Operating Characteristic (ROC) Curve. This graph shows the classifier’s performance for all desirable thresholds. In addition, a ROC graph is drawn between true positive and false positive rates on the x-axis.

Calculating a Confusion Matrix

Here’s how to calculate a confusion matrix in just a few easy steps:

  • Acquire a validation data set or a test dataset with expected outcome values
  • Make predictions for each row in the test data set
  • From your expected outcomes and predictions, count the following:
    • Each class’s number of correct predictions
    • Each class’s number of incorrect predictions is arranged by the predicted class
  • Organize these numbers into a table or a matrix like this:
    • Each matrix row corresponds to a predicted class (expected down the side)
    • Each matrix column corresponds to an actual class (predicted across the top)
  • Fill the counts of correct and incorrect classification into the table
  • The total number of correct predictions for a class goes into the expected row for that class value, and the predicted column for that class value
  • The total number of incorrect predictions for a class goes into the expected row for that class value and the predicted column for that class value

Also Read: AI ML Engineer Salary – What You Can Expect

How to Create a 2×2 Confusion Matrix

With the confusion matrix explained, it’s now time to create one. But before creating our 2×2 confusion matrix, let’s define the classifier’s predicted and actual values.

  • True Positive. This value is the number of times the actual positive values equal the predicted positives. Thus, you predicted a positive value, and it’s correct.
  • False Positive. This value is the number of times the model wrongly predicts a negative value as a positive. So, you predicted a negative value, but it’s actually positive.
  • True Negative. This value is the number of times the actual negative values are equal to the predicted negative values. Hence, you predicted a negative value, but it is actually negative.
  • False Negative. Finally, this is the number of times the model wrongly predicts a negative value as a positive. So, you predicted a negative value, but it is actually positive.

And here is what a 2×2 confusion matrix looks like with all the above values in place:

2x2 confusion matrix

For instance, let’s create a 2×2 confusion matrix that classifies individuals on whether their primary language is English or Spanish. Here’s the matrix:

confusion matrix

Based on our template, we can see that:

  • True Positives (TP) equal 86
  • True Negatives (TN) equal 79
  • False Positives (FP) equal 12
  • False Negatives (FN) equal 10

But more is needed to determine the model’s performance. We need to apply the following classification measures.

  • Accuracy. Accuracy shows the amount of correctly classified values, telling us how often the classifier is right. We get this figure by taking the sum of all the true values and dividing it by the total values.

So, we use this: (86 +79) / (86 + 79 + 12 + 10) = 0.8823 = 88.23% accuracy.

  • Precision. Precision calculates the model’s ability to classify positive values correctly. In this case, we divide true positives by the total number of predicted positive values.

Thus: 86 / (86 + 12) = 0.8775 = 87.75% precision.

  • Recall. Recall calculates the model’s ability to predict positive values, showing us how often the model predicts the correct positive values. We arrive at this figure by dividing the true positives by the total number of actual positive values.

In our case: 86 / (86 + 10) = 0.8983 = 89.83% recall.

  • F1 Score. We use the F1 score when considering Precision and Recall, giving us a harmonic mean between the two metrics. It’s a number between 0 and 1 and is used to maintain a balance between the classifier’s precision and recall. The formula for calculating the F1 score is best shown as follows:

formula for calculating the F1 score

So, (2* 0.8775 * 0.8983) / (0.8775 + 0.8983) = 0.8877 = 88.77% F1 score.

Also Read: What are Today’s Top Ten AI Technologies?

When Should You Use Accuracy, Precision, Recall, or F1-Scores?

Each score serves a purpose, so you must decide which factors are the most important and choose accordingly. In this case:

  • Use Accuracy when the True Positives and True Negatives are most important since Accuracy is the metric best suited for Balanced Data
  • Use Precision whenever the False Positive is considerably more important
  • User Recall whenever the False Negative is most important
  • And use the F1 score when both the False Negatives and False Positives are most important since the F1 score is best suited for Imbalanced Data

Scaling a Confusion Matrix

Sometimes, you may need to expand your matrix and add more class values. Just increase the number of rows and columns as needed; all True Positives will be found along the diagonal, while all other values will be False Positives or False Negatives.

The confusion matrix is flexible enough to scale down, removing unnecessary entries along the horizontal and vertical planes.

Do You Want to Learn More About Artificial Intelligence and Machine Learning?

Confusion matrices are just a tiny piece of the vast, exciting worlds of Artificial Intelligence and Machine Learning. These technologies are the wave of the future, and as more organizations and businesses adopt AI, so will the demand for AI and ML professionals increase.

If you’re interested in becoming a part of this challenging new world, consider starting by taking this comprehensive AI course. This AI and ML bootcamp delivers a high-engagement learning experience that will enrich your skill set and keep you updated with the latest AI and ML innovations.

According to the job site, Machine Learning engineers working in the United States can earn an average annual salary of $133,359, topping $213K at the top end. So, if you’re ready for a career change or already working in the ML field but are seeking to upskill, sign up for this bootcamp and take your education to the next level.

Also Read: How Does AI Work? A Beginner’s Guide

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