Computational Statistics

Chapter 5 - Visualization of Multivariate Data

Dr. Mehdi Maadooliat

Marquette University
MATH 4750 - Spring 2025

Scatterplot Matrices

• Introduction to scatterplot matrices for multivariate data
• Example using the iris dataset

data(iris)

# Scatterplot matrix for virginica species
pairs(iris[101:150, 1:4], main="Scatterplot Matrix for Virginica", col="blue")

Customizing Scatterplot Matrices

• Customizing scatterplot matrices with density plots

# Adding density plots to scatterplot matrix
panel.d <- function(x, ...) {
    usr <- par("usr")
    on.exit(par(usr))
    par(usr = c(usr[1:2], 0, .5))
    lines(density(x), col="red")
}
pairs(iris[101:150, 1:4], panel = panel.d, main="Customized Scatterplot Matrix")

Correlation Plots

• Visualizing correlations between variables
• Example: Correlation plot with corrplot package

# Correlation plot for iris dataset
library(corrplot)
cor_iris <- cor(iris[, 1:4])
corrplot(cor_iris, method="circle", main="Correlation Plot for Iris Dataset")

3D Scatter Plots

• Visualizing 3D relationships between variables
• Example: 3D scatter plot using the scatterplot3d package

# 3D scatter plot for iris dataset
library(scatterplot3d)
scatterplot3d(iris$Sepal.Length, iris$Petal.Length, iris$Sepal.Width, color="darkgreen", pch=16, main="3D Scatter Plot of Iris Data")

Principal Component Analysis (PCA)

• Introduction to PCA for dimensionality reduction
• Example: PCA visualization using ggplot2

# PCA for iris dataset
library(ggplot2)
pca <- prcomp(iris[, 1:4], scale=TRUE)
pca_df <- data.frame(pca$x, Species=iris$Species)

# Visualizing PCA results
ggplot(pca_df, aes(PC1, PC2, color=Species)) +
  geom_point(size=2) +
  labs(title="PCA of Iris Dataset", x="Principal Component 1", y="Principal Component 2") +
  theme_minimal()

Conclusion

• Recap of visualization techniques for multivariate data
• Practice: Generate visualizations for other datasets and explore 3D plots