You are given a data set with $100$ records and are asked to cluster the data. You use K$-$means to cluster the data, but for all values of $K,1K100,$ the $K-$means algorithm returns only one non$-$empty cluster. You then apply an incremental version of K$-$means, but obtain exactly the same result. How is this posible? How would single link or DBSCAN handle such data: $*$

Consider the following four faces shown in Figure $7\mathrm{.}39.$ Again, darkness or number of dots represents density. Lines are used only to distinguish regions and do not represent points

A$.$ For each figure, could you use single link to find the patterns represented by the nose, eyes, and mouth? Explain.

B$.$ For each figure, could you use K$-$means to find the patterns represented by the nose, eyes, and mouth? Explain.

C$.$ What limitation does clustering have in detecting all the patterns formed by the points