Principal Component Analysis (PCA) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to load the data matrix X.

MATLAB

X = [1]('data.csv');

Drag options to blanks, or click blank then click option'

Areadtable

Bimportdata

Ccsvread

Dload

Attempts:

3 left

💡 Hint

Common Mistakes

Using load which expects .mat files.

Using readtable which returns a table, not a matrix.

The csvread function reads numeric data from a CSV file into a matrix.

2fill in blank

medium

Complete the code to center the data by subtracting the mean of each column.

MATLAB

X_centered = X - mean(X, [1]);

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A2

B1

C3

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using dimension 2 subtracts mean of columns, not rows.

Using 0 is invalid dimension.

Subtracting the mean along dimension 1 (rows) centers each feature (column).

3fill in blank

hard

Fix the error in the covariance matrix calculation.

MATLAB

cov_matrix = (X_centered' * X_centered) / [1];

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Asize(X_centered, 1)

Bsize(X_centered, 2)

Clength(X_centered)

Dnumel(X_centered)

Attempts:

3 left

💡 Hint

Common Mistakes

Dividing by number of columns instead of rows.

Using length which may be ambiguous.

The covariance matrix divides by the number of observations (rows), which is size(X_centered, 1).

4fill in blank

hard

Fill both blanks to compute eigenvectors and eigenvalues of the covariance matrix.

MATLAB

[V, D] = [1](cov_matrix); % V: eigenvectors, D: eigenvalues diagonal matrix
[eigenvalues, idx] = sort(diag(D), '[2]');

Drag options to blanks, or click blank then click option'

Aeig

Bsort

Cascend

Ddescend

Attempts:

3 left

💡 Hint

Common Mistakes

Using sort instead of eig to get eigenvectors.

Sorting eigenvalues in ascending order.

eig computes eigenvectors and eigenvalues. Sorting eigenvalues in descending order helps select principal components.

5fill in blank

hard

Fill all three blanks to project data onto the first k principal components.

MATLAB

k = 2;
V_sorted = V(:, idx);
projected_data = X_centered * V_sorted(:, [1]:[2]);
unexplained_variance = sum(eigenvalues([3]:end)) / sum(eigenvalues);

Drag options to blanks, or click blank then click option'

A1

Bk

Ck+1

Dend

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong column indices for projection.

Incorrect range for unexplained variance calculation.

Projecting onto the first k components uses columns 1 to k. The unexplained variance is from k+1 to end.

Practice

1.

What is the main purpose of Principal Component Analysis (PCA) in MATLAB?

easy

A. To reduce the number of variables by finding main directions of data

B. To sort data in ascending order

C. To calculate the sum of all data points

D. To generate random numbers for data simulation

Solution

1. Step 1: Understand PCA goal

   PCA finds new axes (principal components) that capture most data variation.

2. Step 2: Identify main purpose

   It reduces data dimensions by focusing on important directions, simplifying analysis.

3. Final Answer:

   To reduce the number of variables by finding main directions of data -> Option A

4. Quick Check:

   PCA = Dimensionality reduction [OK]

Hint: PCA simplifies data by finding main directions [OK]

Common Mistakes:

• Thinking PCA sorts data
• Confusing PCA with summing data
• Assuming PCA generates random data

2.

Which MATLAB command correctly performs PCA on a data matrix X?

easy

A. score = pca(X, 'score');

B. pca = X.coeff();

C. [coeff, score, latent] = pca(X);

D. coeff = pca(X, 'coeff');

Solution

1. Step 1: Recall MATLAB PCA syntax

   The function pca returns coefficients, scores, and variances as outputs.

2. Step 2: Match correct syntax

   Only [coeff, score, latent] = pca(X); correctly calls PCA and stores outputs.

3. Final Answer:

   [coeff, score, latent] = pca(X); -> Option C

4. Quick Check:

   Correct PCA syntax = [coeff, score, latent] = pca(X); [OK]

Hint: Use brackets to capture multiple PCA outputs [OK]

Common Mistakes:

• Using dot notation on matrix
• Passing output names as strings
• Assigning only one output without brackets

3.

Given the MATLAB code below, what is the size of score if X is a 100x5 matrix?

 [coeff, score, latent] = pca(X); 

medium

A. 5x5

B. 100x5

C. 100x100

D. 5x100

Solution

1. Step 1: Understand PCA output sizes

   score contains transformed data points in principal component space, same rows as X.

2. Step 2: Match dimensions

   Since X is 100x5, score is 100x5 (100 samples, 5 components).

3. Final Answer:

   100x5 -> Option B

4. Quick Check:

   score size = samples x components = 100x5 [OK]

Hint: Score matches rows of X and number of components [OK]

Common Mistakes:

• Confusing score size with coeff size
• Assuming score is square matrix
• Swapping rows and columns

4.

Identify the error in this MATLAB PCA code snippet:

 X = rand(50,3);
 [coeff, score, latent] = pca(X);
 disp(score(1,4)); 

medium

A. Indexing score at column 4 causes an error

B. Missing semicolon after rand function

C. Incorrect function name, should be pca_analysis

D. Matrix X size is invalid for PCA

Solution

1. Step 1: Check size of PCA outputs

   Input X has 3 columns, so score has 3 columns (components).

2. Step 2: Identify indexing error

   Accessing score(1,4) tries to get 4th column which does not exist, causing an error.

3. Final Answer:

   Indexing score at column 4 causes an error -> Option A

4. Quick Check:

   score columns = 3, index 4 invalid [OK]

Hint: Check matrix size before indexing columns [OK]

Common Mistakes:

• Assuming more components than input columns
• Ignoring MATLAB indexing errors
• Thinking semicolon omission causes error here

5.

You want to reduce a dataset X (200x10) to 2 principal components using MATLAB PCA. Which code correctly achieves this?

 % Options:
 A) [coeff, score] = pca(X, 'NumComponents', 2);
 B) [coeff, score] = pca(X, 'NumComponents', 2); score = score(:,3:4);
 C) [coeff, score] = pca(X); score = score(:,11:12);
 D) [coeff, score] = pca(X, 'Components', 2); 

hard

A. [coeff, score] = pca(X, 'Components', 2);

B. [coeff, score] = pca(X, 'NumComponents', 2); score = score(:,3:4);

C. [coeff, score] = pca(X); score = score(:,11:12);

D. [coeff, score] = pca(X, 'NumComponents', 2);

Solution

1. Step 1: Understand PCA dimension reduction parameter

   MATLAB's pca accepts 'NumComponents' to limit output components.

2. Step 2: Identify correct usage

   [coeff, score] = pca(X, 'NumComponents', 2); uses correct parameter 'NumComponents', 2 to get 2 components directly.

3. Step 3: Check other options

   B: [coeff, score] = pca(X, 'NumComponents', 2); score = score(:,3:4); tries to slice non-existent columns 3-4; C: [coeff, score] = pca(X); score = score(:,11:12); tries to slice non-existent columns 11-12; D: [coeff, score] = pca(X, 'Components', 2); uses invalid parameter.

4. Final Answer:

   [coeff, score] = pca(X, 'NumComponents', 2); -> Option D

5. Quick Check:

   Use 'NumComponents' to limit PCA output [OK]

Hint: Use 'NumComponents' to get desired PCA components [OK]

Common Mistakes:

• Using wrong parameter name 'Components'
• Using invalid slice indices on PCA score
• Assuming PCA auto-limits components without parameter