Principal Component Analysis (PCA) in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

What does PCA primarily do to the data?

Imagine you have a dataset with many features. What is the main goal of applying Principal Component Analysis (PCA) to this data?

A It removes all noise from the data by deleting random samples.

B It increases the number of features by adding random values to the dataset.

C It finds new features that are combinations of the original ones, capturing the most variance.

D It sorts the data points based on their distance from the origin.

❓ Predict Output

intermediate

Output of PCA transformation on a simple dataset

What is the output of the following Python code using PCA?

ML Python

from sklearn.decomposition import PCA
import numpy as np

X = np.array([[2, 0], [0, 2], [3, 3]])
pca = PCA(n_components=1)
X_pca = pca.fit_transform(X)
print(X_pca.round(2))

A

[[-0.94]
 [-0.94]
 [ 1.89]]

B

[[2. 0.]
 [0. 2.]
 [3. 3.]]

C

[[ 2.83]
 [-1.41]
 [ 1.41]]

D

[[0. 0.]
 [0. 0.]
 [0. 0.]]

❓ Hyperparameter

advanced

Choosing the number of components in PCA

You want to reduce your dataset's dimensions using PCA but keep at least 90% of the variance. Which approach correctly helps you decide the number of components?

A Set n_components to the total number of original features always.

B Set n_components to a random number less than the number of features.

C Set n_components to 1 regardless of variance explained.

D Set n_components to 0.9 in PCA to keep 90% variance automatically.

❓ Metrics

advanced

Interpreting explained variance ratio from PCA

After fitting PCA on a dataset, you get explained variance ratios: [0.6, 0.3, 0.1]. What does this mean?

A Each component explains the same amount of variance.

B The first component explains 60% of variance, the second 30%, and the third 10%.

C The total variance explained is 30%.

D The components are sorted by increasing variance explained.

🔧 Debug

expert

Why does PCA output have unexpected shape?

You run this code but get an output shape of (5, 5) instead of (5, 2) as expected:

from sklearn.decomposition import PCA
import numpy as np

X = np.random.rand(5, 3)
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X)
print(X_pca.shape)

What is the most likely reason?

A You accidentally imported PCA from a different library that returns all components by default.

B The input data X has 5 features, so PCA returns 5 components ignoring n_components.

C You set n_components to 2 but the data has only 2 samples, so PCA returns 5 components.

D You did not fit PCA before transforming, so it returns the original shape.