Principal Component Analysis (PCA) in ML Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Principal Component Analysis (PCA)?

PCA is a method to reduce the number of features in data by finding new features called principal components. These components keep most of the important information while making the data simpler.

beginner

Why do we use PCA in machine learning?

We use PCA to make data easier to work with by reducing its size. This helps models run faster and can improve their accuracy by removing noise and less important details.

intermediate

What are principal components in PCA?

Principal components are new features created by PCA. Each one is a combination of original features and shows a direction where the data varies the most.

intermediate

How does PCA find principal components?

PCA finds principal components by calculating directions (called eigenvectors) where data changes the most. It orders these directions by how much data varies along them (eigenvalues).

beginner

What is the role of variance in PCA?

Variance shows how spread out data is. PCA picks directions with the highest variance because they hold the most important information about the data.

What does PCA mainly help with in data?

A Changing data labels

B Increasing the number of features

C Adding noise to data

D Reducing the number of features

PCA reduces the number of features by creating new combined features that keep most information.

Which of these is a principal component?

A A new feature made from original features

B A label in the dataset

C A missing value

D A type of model

Principal components are new features created by combining original features.

What does PCA use to find directions of maximum variance?

A Eigenvectors

B Random guesses

C Labels

D Loss functions

PCA calculates eigenvectors to find directions where data varies the most.

Why is variance important in PCA?

A It changes data labels

B It removes all data points

C It shows where data has the most information

D It adds noise

Variance tells us how spread out data is, so PCA picks directions with high variance to keep important info.

What is a common use of PCA in machine learning?

A To label data automatically

B To simplify data before training models

C To increase data size

D To create new models

PCA simplifies data by reducing features, making it easier and faster for models to learn.

Explain in your own words what Principal Component Analysis (PCA) does and why it is useful.

Think about how PCA changes many features into fewer new features that still describe the data well.

Describe how PCA finds the directions (principal components) that capture the most variance in data.

Focus on the math steps PCA uses to find new features that show the biggest changes in data.

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