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We are tasked with clustering a dataset using the **k-means algorithm**, with specific initial cluster centroids. The data provided includes the attributes **CGPA, Assessment, Project Submitted**, and the initial cluster centers are:

1. **Cluster 1** initialized with coordinates (4,6).
2. **Cluster 2** initialized with coordinates (12,4).

The data points are based on the given table (ignoring the "Result" column as it's likely just an outcome of the clustering process).

### Table Details:

| S.No | CGPA | Assessment | Project Submitted |  
|------|------|------------|-------------------|  
| 1    | 9.2  | 85         | 8                 |  
| 2    | 8.2  | 80         | 7                 |  
| 3    | 8.5  | 81         | 8                 |  
| 4    | 6.0  | 45         | 5                 |  
| 5    | 6.5  | 50         | 4                 |  
| 6    | 8.2  | 72         | 7                 |  
| 7    | 5.8  | 38         | 5                 |  
| 8    | 8.9  | 91         | 9                 |  

### Steps in K-means clustering:
1. **Initialization**: Assign the two initial centroids as (4,6) and (12,4).
2. **Distance Calculation**: Calculate the Euclidean distance between each data point and the centroids. Based on the closest centroid, assign the data point to a cluster.
3. **Centroid Update**: Recompute the centroids by averaging the points assigned to each cluster.
4. **Repeat**: Repeat steps 2-3 until the centroids stabilize (no significant changes in clusters).

#### Let's first define the features to be used in this problem. We can use a 2D space where:
- **X-axis**: CGPA (this will be the first feature).
- **Y-axis**: Average of the other two parameters (Assessment and Project Submitted).

Let me calculate and perform the clustering steps. I'll start with the distance calculation.

It seems that during the centroid update, one of the clusters ended up with no points assigned to it, leading to an error when calculating the new centroids. This can happen when initial centroids are poorly chosen, causing some clusters to remain empty. To fix this, I will modify the algorithm to handle such cases by checking if a cluster has no points assigned before updating the centroids.

Let me adjust the code and rerun the clustering process.The k-means clustering process resulted in all data points being assigned to **Cluster 1**, leaving **Cluster 2** empty. This happened because the initial centroids were too far from the majority of the data points, making Cluster 2 less competitive.

Here are the results:

- **Cluster 1** centroid: (7.6625, 37.1875)  
- **Cluster 2** centroid: (12, 4)  
- All points are assigned to **Cluster 1**.

This outcome suggests that the initial seed for Cluster 2 may not be ideal for this dataset, causing it to remain unpopulated during the clustering process.

If you'd like to explore this further, I can attempt alternative centroid initializations or refine the current result. Do you want more details or have any questions?

### Related questions:
1. What are the consequences of choosing distant initial centroids in k-means?
2. How can we improve the initial centroid selection in k-means?
3. Why did all data points cluster around the first centroid?
4. Can k-means be used for non-spherical clusters?
5. How does k-means deal with empty clusters?

**Tip:** Try using the **k-means++** initialization to avoid poor initial centroid choices and improve clustering results.

Cluster the following set of data using the k-means algorithm with the initial value of objects 2 and 5 with the coordinate values (4,6) and (12,4) as initial seeds.

Cluster the given dataset using k-means with initial seeds (4,6) and (12,4) on CGPA, Assessment, and Project Submitted. The algorithm clusters the data based on Euclidean distance, updating centroids iteratively.

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