Problem $2($Clustering with Hamming Distance$)$: The K$-$clustering algorithm is used to separate inputs into distinct groups based on its attributes. Let's classify three objects in binary space based on three attributes:

Object $A=$ is round, is orange, is large,

Object $B=$ is round, is orange, not large

Object $C=$ not round, not orange, is large

Let's also set two centers at

$c_1=$ is round, not orange, not large

$c_2=$ not round, not orange, large

What is the Hamming distance between these Objects and these centers? After recentering $c_1$ which cluster would Object A fall into?

Hint: To update cluster centers in binary space, calculate the mode $($most common value$)$ for each attribute among the assigned objects and set these as the new attributes of the center.