Lab 3 Case Study: Unsupervised Learning in Learning Analytics

Introduction

Learning analytics is the use of data to understand and improve learning. Unsupervised learning is a type of machine learning that can be used to identify patterns and relationships in data without the need for labeled data.

In this case study, you will use unsupervised learning to analyze learning data from a Simulated School course. You will use dimensionality reduction to reduce the number of features in the data, and then use clustering to identify groups of students with similar learning patterns.

Data

The data for this case study is generated with the simulated function below. The data contains the following features:

Student ID: A unique identifier for each student Feature 1: A measure of student engagement Feature 2: A measure of student performance

simulate_student_features <- function(n = 100) {
  # Set the random seed
  set.seed(260923)
  
  # Generate unique student IDs
  student_ids <- seq(1, n)

  # Simulate student engagement
  student_engagement <- rnorm(n, mean = 50, sd = 10)

  # Simulate student performance
  student_performance <- rnorm(n, mean = 60, sd = 15)

  # Combine the data into a data frame
  student_features <- data.frame(
    student_id = student_ids,
    student_engagement = student_engagement,
    student_performance = student_performance
  )

  # Return the data frame
  return(student_features)
}

This function takes the number of students to simulate as an input and returns a data frame with three columns: student_id, student_engagement, and student_performance. The student_engagement and student_performance features are simulated using normal distributions with mean values of 50 and 60, respectively, and standard deviations of 10 and 15, respectively.

To use the simulate_student_features() function, we can simply pass the desired number of students to simulate as the argument:

student_features <- simulate_student_features(n = 100)

# PCA for dimensionality reduction
pca <- prcomp(student_features[, -1], scale. = TRUE)

# Print summary of PCA
summary(pca)

## Importance of components:
##                           PC1    PC2
## Standard deviation     1.0104 0.9895
## Proportion of Variance 0.5104 0.4896
## Cumulative Proportion  0.5104 1.0000

#Clustering using KMeans
kmeans_clustering <- kmeans(pca$x[, 1:2], centers = 3)

# Print cluster centers
print(kmeans_clustering$centers)

##            PC1        PC2
## 1  1.044392617 -0.4654233
## 2 -0.900902816 -0.5128470
## 3 -0.002811599  1.0925446

# Plot clusters
plot(pca$x[, 1:2], col = kmeans_clustering$cluster)
points(kmeans_clustering$centers, col = 1:3, pch = 8, cex = 2)

We can then use this data frame to perform unsupervised learning to identify groups of students with similar learning patterns,

Tasks

• Simulate the data.
  
• Perform dimensionality reduction on the data using PCA.
  
• Cluster the data using KMeans and other clustering algorithms.
  
• Interpret the results of your analysis.

#Interpret the results - The PC1 and PC2 explain most of the variance in the data. Together these actually account for 100% of the variance in the data. It is almost a 50 50 split in proportion but PC1 has a slight edge of about 1%. - Since the clusters in the graph are very well seperated it means that the features we used for clustering are clear and informative. This means there is a clear difference between student, their performance, and how much they are engaged in the course.

Submission

Submit a report containing the following:

• A brief description of your approach to dimensionality reduction and clustering.
  
• The results of your analysis, including the number of clusters identified, the characteristics of each cluster, and any other insights you gained from the data.
  
• A discussion of the implications of your findings for learning analytics.
  
• Provide at least one scholarly reference.

REPORT

-I used a PCA to reduce the dimensionality of the dataset, and then I used kmeans to cluster and identify groups of students with similar learning patterns.

-KMeans identified 3 clusters, Cluster 1 indicates students who have a high engagement but a moderate to low performance in the course, Students in Cluster 2 have relatively high performance and a modest amount of engagement, while cluster 3 shows that students have low engagement and low performance. These results show us the different groups of students and that there may almost be a bell shaped curve in regards to how well a student performs given their engagement.

• Some implications from these resutls are that now a teacher or instructor can take action early and be able to make a difference for each group of student. Instead of teaching a certain way or structuring the class a certain way in order to accomidate for one specific group, they can tailor to each of the learning groups and try and make an impact earlier on for each student. “Early Student performance prediction can help universities to provide timely actions, like planning for appropriate training to improve students’ success rate.” (Eyman Alyahyan)

-Bharara, S., Sabitha, S., & Bansal, A. (2018). Application of learning analytics using clustering data Mining for Students’ disposition analysis. Education and Information Technologies, 23, 957-984.

Your report should include your code. Submit the published RPubs link to Blackboard.