AE 16: Principal component analysis

Suggested answers

In this application exercise, we will:

1. Learn about Principal Component Analysis.

2. Load the Penguins Dataset: Import and explore the dataset to understand its structure and the features available for analysis.

3. Preprocess the Data: Clean the data by handling missing values and standardize the numerical features for PCA.

4. Perform PCA: Apply Principal Component Analysis to reduce the dimensionality of the data and extract the principal components.

5. Visualize the PCA Result: Create a scatter plot of the principal components to visualize the clustering of different penguin species.

Learn about PCA

Exercise 1

Watch this video on Principal Component Analysis:

• What were three takeaways from this video? Include how you think linear algebra contributes to PCA:

Answer will vary.

PCA in Python

Packages

We will primarily use the seaborn and sklearn packages.

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

Exercise 2

Load the Penguins Dataset using seaborn

import seaborn as sns
import pandas as pd

penguins = sns.load_dataset('penguins')

print(penguins.head())

  species     island  bill_length_mm  bill_depth_mm  flipper_length_mm  \
0  Adelie  Torgersen            39.1           18.7              181.0   
1  Adelie  Torgersen            39.5           17.4              186.0   
2  Adelie  Torgersen            40.3           18.0              195.0   
3  Adelie  Torgersen             NaN            NaN                NaN   
4  Adelie  Torgersen            36.7           19.3              193.0   

   body_mass_g     sex  
0       3750.0    Male  
1       3800.0  Female  
2       3250.0  Female  
3          NaN     NaN  
4       3450.0  Female  

Exercise 3

Preprocess the data

We need to handle missing values and select the numerical features for PCA.

penguins.dropna(inplace=True)

features = ['bill_length_mm', 'bill_depth_mm', 'flipper_length_mm', 'body_mass_g']
X = penguins[features]

from sklearn.preprocessing import StandardScaler
scaler = StandardScaler()
X_scaled = scaler.fit_transform(X)

Exercise 4

Perform PCA

Use PCA from sklearn to reduce the dimensionality of the data. Hint: use two principal components

from sklearn.decomposition import PCA

pca = PCA(n_components=2)

principal_components = pca.fit_transform(X_scaled)

pca_df = pd.DataFrame(data=principal_components, columns=['PC1', 'PC2'])

pca_df['species'] = penguins['species']

Exercise 5

Visualize the PCA Result

Use seaborn to visualize the principal components.

plt.figure(figsize=(8, 6))
sns.scatterplot(data=pca_df, x='PC1', y='PC2', hue='species', palette='colorblind')
plt.title('PCA of Penguins Dataset')
plt.xlabel('Principal Component 1')
plt.ylabel('Principal Component 2')
plt.show()