Problem $5$: $(14$ points$)$ Clustering Algorithm Analysis

$1)(5$ Points$)$ Given a scenario, K$-$means cluster may NOT work very well $(2$ points$).$

Explain why $(3$ points$).$

$2)(5$ Points$)$ Given a scenario, DBSCAN algorithm could NOT work very well $(2$ points$).$

Explain why $(3$ points$).$

$3)(4$ Points$)$ How can we improve the random initialization of classic K$-$means$$algorithm$?$