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.

💡 Hint

Think about how PCA helps simplify data while keeping important information.

PCA transforms the original features into new features called principal components. These components are combinations of the original features and are ordered to capture the most variance in the data.

❓ 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.]]

💡 Hint

Remember PCA projects data onto the direction of maximum variance.

The PCA reduces the 2D data to 1D by projecting onto the principal component. The output shows the transformed values rounded to two decimals.

❓ 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.

💡 Hint

Check how sklearn PCA handles variance thresholds.

Setting n_components to a float between 0 and 1 tells PCA to select the minimum number of components that explain at least that fraction of variance.

❓ 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.

💡 Hint

Look at how variance ratios sum up and their order.

The explained variance ratio shows how much variance each principal component captures. They sum to 1 and are sorted from highest to lowest.

🔧 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.

💡 Hint

Check the PCA import source and its default behavior.

If PCA is imported from a library other than sklearn.decomposition, it might ignore n_components and return all components, causing unexpected output shape.

Practice

1. What is the main purpose of Principal Component Analysis (PCA) in machine learning?

easy

A. To reduce the number of features while keeping important information

B. To increase the number of features for better accuracy

C. To split data into training and testing sets

D. To normalize data by scaling features between 0 and 1

Solution

1. Step 1: Understand PCA's goal

   PCA aims to reduce many features into fewer main features without losing important information.

2. Step 2: Compare options with PCA's goal

   To reduce the number of features while keeping important information correctly states PCA reduces features while keeping key info. Other options describe different tasks.

3. Final Answer:

   To reduce the number of features while keeping important information -> Option A

4. Quick Check:

   PCA purpose = reduce features + keep info [OK]

Hint: PCA simplifies data by reducing features, not increasing them [OK]

Common Mistakes:

• Thinking PCA increases features
• Confusing PCA with data splitting
• Mixing PCA with data normalization

2. Which of the following is the correct way to import PCA from scikit-learn in Python?

easy

A. import PCA from sklearn.decomposition

B. import decomposition.PCA from sklearn

C. from sklearn import PCA

D. from sklearn.decomposition import PCA

Solution

1. Step 1: Recall correct import syntax for PCA

   In scikit-learn, PCA is in the decomposition module, imported as: from sklearn.decomposition import PCA.

2. Step 2: Check each option's syntax

   from sklearn.decomposition import PCA matches the correct Python import syntax. Others are invalid or incorrect.

3. Final Answer:

   from sklearn.decomposition import PCA -> Option D

4. Quick Check:

   Correct import = from sklearn.decomposition import PCA [OK]

Hint: Remember: PCA is in sklearn.decomposition module [OK]

Common Mistakes:

• Using wrong import order
• Trying to import PCA directly from sklearn
• Incorrect Python import syntax

3. Given the following Python code using PCA, what will be the shape of X_pca?

from sklearn.decomposition import PCA
import numpy as np
X = np.random.rand(100, 5)
pca = PCA(n_components=2)
X_pca = pca.fit_transform(X)

medium

A. (100, 5)

B. (2, 100)

C. (100, 2)

D. (5, 2)

Solution

1. Step 1: Understand input and PCA parameters

   Input X has shape (100 samples, 5 features). PCA is set to reduce to 2 components.

2. Step 2: Determine output shape after PCA transform

   fit_transform returns transformed data with shape (samples, n_components), so (100, 2).

3. Final Answer:

   (100, 2) -> Option C

4. Quick Check:

   Output shape = (samples, components) = (100, 2) [OK]

Hint: Output shape = (samples, n_components) after PCA transform [OK]

Common Mistakes:

• Confusing samples and features in output shape
• Mixing up n_components with original features
• Thinking PCA changes sample count

4. Identify the error in this PCA code snippet:

from sklearn.decomposition import PCA
import numpy as np
X = np.random.rand(50, 4)
pca = PCA(n_components=5)
X_pca = pca.fit_transform(X)

medium

A. n_components cannot be greater than number of features

B. Random data cannot be used with PCA

C. fit_transform should be called before PCA initialization

D. Import statement for PCA is incorrect

Solution

1. Step 1: Check PCA parameter n_components vs data features

   Data has 4 features, but n_components is set to 5, which is invalid.

2. Step 2: Validate other code parts

   Random data is fine, fit_transform is correctly called, and import is correct.

3. Final Answer:

   n_components cannot be greater than number of features -> Option A

4. Quick Check:

   n_components ≤ features = True [OK]

Hint: n_components must be ≤ number of original features [OK]

Common Mistakes:

• Setting n_components larger than features
• Misunderstanding fit_transform order
• Thinking random data is invalid

5. You have a dataset with 10 features and want to keep 95% of the variance using PCA. Which approach is best to choose the number of components?

hard

A. Set n_components=5 because it's half of 10 features

B. Set n_components=0.95 to keep 95% variance automatically

C. Set n_components=10 to keep all variance

D. Set n_components=1 to simplify data as much as possible

Solution

1. Step 1: Understand PCA's explained variance ratio parameter

   Setting n_components as a float between 0 and 1 tells PCA to select components to keep that fraction of variance.

2. Step 2: Evaluate options for keeping 95% variance

   Set n_components=0.95 to keep 95% variance automatically uses n_components=0.95, which automatically selects the right number of components. Others do not guarantee 95% variance.

3. Final Answer:

   Set n_components=0.95 to keep 95% variance automatically -> Option B

4. Quick Check:

   n_components=0.95 keeps 95% variance [OK]

Hint: Use n_components as float for variance ratio in PCA [OK]

Common Mistakes:

• Choosing fixed number without variance check
• Setting n_components too low or too high blindly
• Confusing number of features with variance percentage