Problem $3($K$-$Means Clustering with MATLAB$)$: Implement and analyze the k$-$means

clustering algorithm to par$$on a given set of data points into three clusters.

Data Points

Cluster $1$: $(1,2),(2,1),(1,1)$

Cluster $2$: $(5,6),(6,5),(5,5),(6,6),(5,7)$

Cluster $3$: $(9,10),(10,9),(9,9),(10,10)$

Ini$$al Centers

Center $1$: $(1,2)$

Center $2$: $(5,6)$

Center $3$: $(9,10)$

Tasks

a$)$ Analy$$cal Calcula$$on:

$$ Apply k$-$means in batch mode to update centers un$$l convergence.

$$ Document the center updates at each itera$$on$.$

b$)$ MATLAB Coding:

$$ Code the k$-$means process star$$ng with the given points and centers.

$$ Iterate to update centers in batch mode un$$l convergence.

$$ Display centers at each itera$$on and plot final clusters.

Deliverables

$$ Analy$$cal calcula$$on of center updates.

$$ MATLAB code implemen$$ng k$-$means, with itera$$on displays and final plot.