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How to plot the decision boundary for a Gaussian Naive Bayes classifier in R?

Last Updated : 12 Jul, 2024
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Gaussian Naive Bayes (GNB) is a simple yet powerful algorithm often used for classification problems. One of the key ways to understand and interpret the behavior of this classifier is by visualizing the decision boundary. This article provides a step-by-step guide on how to plot the decision boundary for a Gaussian Naive Bayes classifier in R.

Introduction to Gaussian Naive Bayes

Gaussian Naive Bayes is a variant of the Naive Bayes classifier that assumes the features follow a Gaussian (normal) distribution. It is called "naive" because it assumes that the features are independent given the class label, which is often not the case in real-world data but works surprisingly well in practice.

What are decision boundaries?

A decision boundary is a surface that separates different classes in the feature space. For a classifier, it is the region in the feature space where the decision changes from one class to another. In simpler terms, it is the line (or hyperplane, in higher dimensions) that the classifier uses to distinguish between different classes based on the input features.

Now we will discuss step by step to plot the decision boundary for a Gaussian Naive Bayes classifier in R Programming Language.

Step 1: Install Required Packages

Before starting, ensure you have the necessary packages installed. For this task, we'll use e1071 for building the Gaussian Naive Bayes model and ggplot2 for plotting.

R
install.packages("e1071")
install.packages("ggplot2")

library(e1071)
library(ggplot2)

Step 2: Generate or Load a Dataset

For demonstration purposes, we will generate a synthetic dataset using the MASS package. Alternatively, you can load your own dataset.

R
set.seed(123)
n <- 200
x1 <- rnorm(n)
x2 <- rnorm(n)
y <- ifelse(x1 + x2 + rnorm(n) > 0, 1, 0)
data <- data.frame(x1, x2, y = as.factor(y))

Step 3: Train the Gaussian Naive Bayes Model

Next, we train the Gaussian Naive Bayes classifier using the naiveBayes function from the e1071 package.

R
model <- naiveBayes(y ~ ., data = data)

Step 4: Define a Grid for Plotting

We create a grid of values that cover the range of our features. This grid will be used to visualize the decision boundary.

R
x1_range <- seq(min(data$x1) - 1, max(data$x1) + 1, length.out = 100)
x2_range <- seq(min(data$x2) - 1, max(data$x2) + 1, length.out = 100)
grid <- expand.grid(x1 = x1_range, x2 = x2_range)

Step 5: Predict Class Probabilities for the Grid

Using the trained model, we predict the class probabilities for each point in the grid.

R
grid$y <- predict(model, grid, type = "raw")[,2]

Step 6: Plot the Decision Boundary

Finally, we use ggplot2 to plot the decision boundary. The decision boundary is where the predicted probabilities are equal (0.5).

R
ggplot(data, aes(x = x1, y = x2)) +
  geom_point(aes(color = y), size = 2) +
  stat_contour(data = grid, aes(x = x1, y = x2, z = y), breaks = 0.5, color = "red") +
  labs(title = "Decision Boundary for Gaussian Naive Bayes",
       x = "Feature 1", y = "Feature 2") +
  theme_minimal()

Output:

gh
plot the decision boundary for a Gaussian Naive Bayes classifier

This visualization helps in understanding how the Gaussian Naive Bayes classifier makes decisions based on the distribution of features in the dataset. It shows the regions of feature space where the classifier predicts different classes, thereby demarcating the decision boundary.

Conclusion

Plotting the decision boundary for a Gaussian Naive Bayes classifier in R allows us to visually inspect how the model separates different classes based on the feature distributions. By following the steps outlined above, you can effectively visualize and interpret the classification boundaries in your own datasets using R's powerful visualization tools.


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