Principal Component Analysis (PCA) in MATLAB - Mini Project: Build & Apply

Principal Component Analysis (PCA) in MATLAB

📖 Scenario: You have collected data from three different sensors measuring environmental conditions. You want to reduce the data dimensions to understand the main patterns without losing important information.

🎯 Goal: Build a MATLAB program that performs Principal Component Analysis (PCA) on a given dataset to find the main components and display the transformed data.

📋 What You'll Learn

Create a matrix called data with the exact values provided

Create a variable called numComponents to specify how many principal components to keep

Use MATLAB's pca function to compute principal components and scores

Display the transformed data matrix called transformedData

💡 Why This Matters

🌍 Real World

PCA helps reduce data size while keeping important patterns, useful in fields like image processing, finance, and biology.

💼 Career

Data scientists and engineers use PCA to simplify data, improve machine learning models, and visualize complex datasets.

1

DATA SETUP: Create the data matrix

Create a matrix called data with these exact values: [2.5 2.4 0.5; 0.5 0.7 1.2; 2.2 2.9 0.3; 1.9 2.2 0.4; 3.1 3.0 0.7]

MATLAB

% Your code here

Hint

Use square brackets and semicolons to create the matrix exactly as shown.

2

CONFIGURATION: Set the number of principal components

Create a variable called numComponents and set it to 2 to keep two principal components.

MATLAB

data = [2.5 2.4 0.5; 0.5 0.7 1.2; 2.2 2.9 0.3; 1.9 2.2 0.4; 3.1 3.0 0.7];
% Your code here

Hint

Just assign the number 2 to the variable numComponents.

3

CORE LOGIC: Perform PCA on the data

Use MATLAB's [coeff, score, latent] = pca(data) to compute principal components. Then create a variable called transformedData by selecting the first numComponents columns of score.

MATLAB

data = [2.5 2.4 0.5; 0.5 0.7 1.2; 2.2 2.9 0.3; 1.9 2.2 0.4; 3.1 3.0 0.7];
numComponents = 2;
% Your code here

Hint

Use the pca function and then select the first two columns of score.

4

OUTPUT: Display the transformed data

Write a line to display the variable transformedData using disp.

MATLAB

data = [2.5 2.4 0.5; 0.5 0.7 1.2; 2.2 2.9 0.3; 1.9 2.2 0.4; 3.1 3.0 0.7];
numComponents = 2;
[coeff, score, latent] = pca(data);
transformedData = score(:, 1:numComponents);
% Your code here

Hint

Use disp(transformedData) to show the result.

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