Introduction to Unsupervised Machine Learning - KMeans Clustering

 

Introduction to Unsupervised Machine Learning

What is Unsupervised Machine Learning?

Unsupervised machine learning involves algorithms that learn patterns from data without labeled outcomes. Unlike supervised learning, where the model is trained with input-output pairs, unsupervised learning finds hidden structures and relationships in the data. This type of learning is often used for clustering, association, and dimensionality reduction.

Key Concepts

No Labeled Data: The algorithm does not know the target output; it has to discover the structure from the input data.

Pattern Recognition: It identifies patterns, trends, or groupings within the data.

Clustering: A Core Technique

Clustering is one of the most popular unsupervised learning techniques. It involves grouping data points such that points in the same group (or cluster) are more similar to each other than to those in other groups.

Problem Statement: Clustering Universities Based on Academic and Financial Metrics

K-Means is a popular clustering algorithm used to partition a dataset into distinct groups (clusters) based on feature similarities. 

Here’s a step-by-step explanation of the logic behind K-Means:

1. Initialization

• Number of Clusters: Decide on the number of clusters $k$ to form. This is often done using methods like the Elbow Method.
• Initial Centroids: Randomly initialize $k$ cluster centroids. These centroids represent the center of each cluster.

K-Means is a popular unsupervised machine learning algorithm used for clustering data into a specified number of clusters, $k$. Here's how K-Means works:

Step-by-Step Explanation:

1. Initialization:

   • Choose the number of clusters, $k$: You decide how many clusters you want to group the data into.
   • Select initial centroids: The algorithm randomly selects $k$ points from the data as the initial "centroids" or "cluster centers."

2. Assignment Step:

   • Assign each data point to the nearest centroid: Each data point in the dataset is assigned to the nearest centroid, forming $k$ clusters. The "nearness" is usually measured using Euclidean distance.

3. Update Step:

   • Recalculate the centroids: After all data points are assigned to clusters, the centroids are recalculated as the mean (average) of all the data points in each cluster.
   • Repeat: Steps 2 and 3 are repeated until the centroids no longer change significantly or until a predefined number of iterations is reached.

4. Convergence:

   • The algorithm converges when the centroids stabilize (i.e., no longer change) or when the maximum number of iterations is reached. At this point, the algorithm has found the optimal clusters.

5. Result:

   • The final output consists of the cluster centroids and the assignment of each data point to a cluster.

Objective:

The goal is to group universities into clusters based on their academic performance and financial metrics. By applying K-Means clustering, we aim to identify distinct categories of universities that share similar characteristics. This can help in understanding the diversity among universities and aid in making informed decisions regarding applications, funding, and resource allocation.

 Dataset Overview:

 Univ: Name of the University.

SAT: Average SAT score of admitted students.

Top10: Percentage of students from the top 10% of their high school class.

Accept: Acceptance rate (%) of the university.

SFRatio: Student-to-faculty ratio.

Expenses: Annual educational expenses per student (in USD).

GradRate: Graduation rate (%).

Clustering Objective:

 Cluster 1: Identify universities with high academic performance and high graduation rates.

Cluster 2: Identify universities that are more accessible (higher acceptance rates) but may have lower graduation rates.

Cluster 3: Identify universities with unique financial or student-faculty characteristics.

Key Questions:

 Academic Performance: How do universities with high SAT scores and high percentages of top 10% students cluster together?

Accessibility vs. Quality: Are universities with higher acceptance rates grouped separately from those with lower acceptance rates but higher expenses?

Resource Allocation: How does the student-to-faculty ratio influence the clustering, and what does it reveal about university resources?

Approach:

 Data Preprocessing: Normalize the data to ensure all features contribute equally to the clustering process.

Applying K-Means: Run the K-Means algorithm to cluster the universities into a suitable number of clusters (e.g., 2-3 clusters).

Analysis of Clusters: Analyze the characteristics of each cluster to understand the commonalities and differences among universities in each group.

Visualization: Visualize the clusters to interpret the distribution and relationships among universities.

Expected Outcome:

By the end of this analysis, we expect to have a clear understanding of how universities are grouped based on their academic and financial metrics, which can be further used for strategic decisions in higher education management.

Data Normalization:

def norm_func(i):

    x = (i-i.min()) / (i.max() - i.min())

    return (x)

The norm_func function provided is an example of normalization, not standardization. Here’s why:

Normalization

• Purpose: It transforms the data so that the minimum value becomes 0 and the maximum value becomes 1, making all features comparable on a uniform scale.

 

 Download Dataset from here