(Solved): In this question we explore clustering. The dataset that we will use in this ...

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In this question we explore clustering. The dataset that we will use in this question is shown in Figure 2. Figure 2 Let's start by considering the k-means algorithm, where \( k=4 \). Let's denote the four clusters by \( C_{1}, C_{2}, C_{3} \) and \( \mathrm{C}_{4} \). Consider a clustering arrangement where the initial prototype of cluster \( \mathrm{C}_{1} \) is in the location \( x_{A}=4 \) and \( x_{B}=0 \), the initial prototype of cluster \( \mathrm{C}_{2} \) is in the location \( x_{A}=4 \) and \( x_{B}=3 \), the initial prototype of cluster \( \mathrm{C}_{3} \) is in the location \( x_{A}=2 \) and \( x_{B}=5 \) and the initial prototype of cluster \( \mathrm{C}_{4} \) is in the location \( x_{A}=2 \) and \( x_{B}=6 \). The intra-cluster sample scatter for cluster \( \mathrm{C}_{1} \) is \( I\left(C_{1}\right)= \) and for cluster cluster \( \mathrm{C}_{4} \) is \( I\left(C_{4}\right)= \) Round the numerical values to 1 decimal place.