Dimensionality Reduction in R

Dimensionality reduction is a technique used to reduce the number of input variables (features) in a dataset while keeping the most important information.

When datasets have too many columns, they become harder to analyze, visualize, and process efficiently.

Why Dimensionality Reduction Is Important

High-dimensional data often leads to problems such as slow computation and overfitting.

Reducing dimensions makes models faster, simpler, and easier to understand.

• Improves model performance
• Reduces noise in data
• Helps with data visualization
• Prevents overfitting

Common Dimensionality Reduction Techniques

R provides several methods for reducing dimensions.

• Principal Component Analysis (PCA)
• Singular Value Decomposition (SVD)

Principal Component Analysis (PCA)

PCA transforms original variables into new variables called principal components.

Each principal component captures maximum variance from the data.

Preparing Data for PCA

PCA works only with numeric data.

Data should be scaled so that each variable contributes equally.

data_scaled <- scale(data)

Applying PCA in R

The prcomp() function is commonly used to perform PCA.

Setting scale = TRUE ensures proper normalization.

pca_result <- prcomp(data, scale = TRUE)
summary(pca_result)

Understanding PCA Output

The summary shows how much variance each principal component explains.

Components with higher variance are more important.

Accessing Principal Components

You can extract transformed data using the PCA object.

pca_result$x

Visualizing PCA Results

Plots help understand how data points are distributed after reduction.

Scatter plots are commonly used for PCA visualization.

plot(pca_result$x[,1],
     pca_result$x[,2],
     xlab = "PC1",
     ylab = "PC2",
     main = "PCA Visualization")

How Many Components Should You Keep?

Usually, components that explain most of the variance are selected.

This balances information retention and simplicity.

Real-World Use Cases

• Reducing features before machine learning
• Visualizing high-dimensional datasets
• Noise reduction in analytics
• Improving model interpretability

📝 Practice Exercises

Exercise 1

Explain dimensionality reduction in simple terms.

Exercise 2

Scale a numeric dataset in R.

Exercise 3

Apply PCA to a dataset.

Exercise 4

Create a PCA scatter plot.

✅ Practice Answers

Answer 1

Dimensionality reduction reduces the number of features while keeping important information.

Answer 2

scaled_data <- scale(data)

Answer 3

prcomp(data, scale = TRUE)

Answer 4

plot(pca_result$x[,1], pca_result$x[,2])

What’s Next?

In the next lesson, you will learn about Spatial Analysis and how R handles location-based data.