Let's work through the clustering of the provided data set using the k-means algorithm, with the initial centroids (seeds) being objects 2 and 5, with coordinate values (4,6) and (12,4).

Step 1: Convert the Data into Coordinates

We will use the given attributes to represent each object as a vector. For this case, let's consider each object as a vector based on CGPA and Assessment scores.

Given the dataLet's work through the clustering of the provided data set using the k-means algorithm, with the initial centroids (seeds) being objects 2 and 5, with coordinate values (4,6) and (12,4).

Step 1: Convert the Data into Coordinates

We will use the given attributes to represent each object as a vector. For this case, let's consider each object as a vector based on CGPA and Assessment scores.

Given the

Object	CGPA	Assessment
1	9.2	85
2	8	80
3	8.5	81
4	6	45
5	6.5	50
6	8.2	72
7	5.8	38
8	8.9	91

We will cluster based on these two variables: CGPA and Assessment.

The initial seeds are:

• Seed 1 (from Object 2): $(4,6)$
• Seed 2 (from Object 5): $(12,4)$

Step 2: Calculate Euclidean Distance

We compute the Euclidean distance between each point and the centroids.

The formula for Euclidean distance is: $d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

For each object and centroid, we calculate:

Distances to Centroid 1 (4,6):

$d_{i1} = \sqrt{(CGPA_i - 4)^2 + (Assessment_i - 6)^2}$

Distances to Centroid 2 (12,4):

$d_{i2} = \sqrt{(CGPA_i - 12)^2 + (Assessment_i - 4)^2}$

Now, we proceed to assign each object to the nearest centroid based on the distances. Let me calculate these distances and assign clusters for the first iteration.### First Iteration Results:

For each object, the distances to the two centroids are as follows:

Object	Distance to Centroid 1 (4,6)	Distance to Centroid 2 (12,4)	Cluster Assignment
1	79.17	81.05	1
2	74.11	76.11	1
3	75.13	77.08	1
4	39.05	41.44	1
5	44.07	46.33	1
6	66.13	68.11	1
7	32.05	34.56	1
8	85.14	87.06	1

Since all points were assigned to Cluster 1, this means no points are closer to the initial Centroid 2 (12,4). This requires recalculating the centroids and repeating the process. Would you like to proceed with recalculating centroids for further iterations?

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Questions for further exploration:

1. How do the centroids change after each iteration?
2. What if we use different initial seeds for k-means clustering?
3. How does the distance between points and centroids impact cluster assignment?
4. How many iterations does k-means typically take to converge?
5. Can you visualize the clustering results to better understand the data?

Tip: In k-means clustering, initial centroid selection can significantly affect the outcome, leading to different clusters depending on the starting points.