Question $2$: Clustering $(2+2+2+2$ marks$)$

$($A$)$ Explain the term $$Conceptual clusters$$ with the help of an appropriate illustration.

$($B$)$ Describe the goal of Self$-$Organizing Map and explain what is meant by $$topology preserving

properties$$ of a self$-$organizing map.

$($C$)$ Describe the goal of K$-$means clustering and the connection between K$-$means clustering and

Self$-$Organizing Map

$($D$)$ Draw a $2-$dimensional dataset with two clusters that can be discovered with $100\%$ accuracy by

DBSCAN, but not by K$-$means when using K$=2.$ Explain your answer.