You are a data analyst in a retail company and have been tasked with segmenting customers

based on their shopping behaviors. You decide to use k$-$means clustering for this task. The

dataset you have contains information about the annual income and spending score of $200$

customers. The spending score is a metric based on customer behavior and spending data.

For simplicity, let's consider a small subset of this data:

Table $3$: Data Samples

Question: Implementing k$-$means Clustering

Explain the k$-$means clustering algorithm. How does it work?

Given the subset of the customer data above, perform k$-$means clustering with $k=2$

$($i$.$e$.,$ two clusters$).$ You can use the first two data points as the initial centroids for

simplicity.

For each iteration, update the centroids of the clusters until convergence. What are

the final centroids of the two clusters?

Assign each customer to the nearest cluster and provide the final clustering.

Discuss how the results of this clustering might be useful for the company's marketing

strategy.

What are some limitations of k$-$means clustering, and how might they affect the inter$-$

pretation of your results in this scenario?

Instructions: Use the Euclidean distance to measure the distance between points and cen$-$

troids. Update the centroids by calculating the mean of the points assigned to each cluster.

Stop the iterations when the centroids do not change significantly $($convergence$).$ Show all

calculations and steps for full credit.