Q&A 27 How do you uncover structure in high-dimensional data using a PCA plot?

27.1 Explanation

Principal Component Analysis (PCA) reduces high-dimensional data into 2 or 3 principal axes (components) that preserve the most variance. It helps:

• Reveal clusters or overlaps in feature space
  
• Understand group separation
  
• Prepare for clustering or modeling

It’s most useful for numeric data and can be colored by group (e.g., cut).

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27.2 Python Code

import pandas as pd
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
import seaborn as sns
import matplotlib.pyplot as plt

# Load and prepare data
diamonds = pd.read_csv("data/diamonds_sample.csv")
subset = diamonds[["carat", "depth", "table", "price", "x", "y", "z", "cut"]].sample(500, random_state=1)

# Standardize features
X = StandardScaler().fit_transform(subset.drop("cut", axis=1))

# PCA transformation
pca = PCA(n_components=2)
pca_result = pca.fit_transform(X)

# Combine with labels
pca_df = pd.DataFrame(pca_result, columns=["PC1", "PC2"])
pca_df["cut"] = subset["cut"].values

# Plot
plt.figure(figsize=(8, 6))
sns.scatterplot(data=pca_df, x="PC1", y="PC2", hue="cut", palette="Set2", alpha=0.7)
plt.title("PCA Plot: Diamond Features Colored by Cut")
plt.tight_layout()
plt.show()

27.3 R Code

library(readr)
library(ggplot2)
library(dplyr)

# Load and sample
diamonds <- read_csv("data/diamonds_sample.csv")
subset <- diamonds %>% select(carat, depth, table, price, x, y, z, cut) %>% sample_n(500)

# PCA
features <- subset %>% select(-cut)
features_scaled <- scale(features)
pca_result <- prcomp(features_scaled)

# Combine for plotting
pca_df <- data.frame(pca_result$x[,1:2], cut = subset$cut)

# Plot
ggplot(pca_df, aes(x = PC1, y = PC2, color = cut)) +
  geom_point(alpha = 0.7) +
  scale_color_brewer(palette = "Set2") +
  theme_minimal() +
  labs(title = "PCA Plot: Diamond Features by Cut")

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✅ PCA—Principal Component Analysis reduces complexity while preserving patterns. When plotted in 2D, it can reveal clustering, separation, or overlap between groups.