Aspire Faculty ID #19258 · Topic: UGC NET Computer Science June 2019 (Paper II) · Just now
UGC NET Computer Science June 2019 (Paper II)

$K$-mean clustering algorithm has clustered the given $8$ observations into $3$ clusters after $1^{st}$ iteration as follows:

$C1:{(3,3),(5,5),(7,7)}$

$C2:{(0,6),(6,0),(3,0)}$

$C3:{(8,8),(4,4)}$

What will be the Manhattan distance for observation $(4,4)$ from cluster centroid $C1$ in second iteration?

Solution

Cluster $C1$ contains the points

$(3,3),(5,5),(7,7)$

Centroid of $C1$ is

$\left(\dfrac{3+5+7}{3},\dfrac{3+5+7}{3}\right)$

$=(5,5)$

Now, Manhattan distance between $(4,4)$ and $(5,5)$ is

$|4-5|+|4-5|$

$=1+1$

$=2$

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