(Solved): a) Using the k-means clustering algorithm, Cluster the following eight points (with (x,y) repre ...

a) Using the k-means clustering algorithm, Cluster the following eight points (with $$(x,y)$$ representing locations) into three clusters. Initial cluster means are $$\mathrm{A}1,\mathrm{A}4$$, and $$\mathrm{A}7$$. $$\text{ A1 }(2,10),A2(2,5),A3(8,4),A4(5,8),A5(7,5),A6(6,4),A7(1,2),A8(4,9)$$ b) Use the following data points to form the density-based clusters where eps=10 and MinPts=3. Clearly mention your steps and tell the noise points as well. $$\begin{array}{l}\text{ A1 }(0,10),\text{ A2 }\left(0^{?},20\right),\text{ A3 }(0,27),A4(10,15),A5(20,10),A6(25,20),\text{ A7 }(0,30),\\ \text{ A8 }(10,20),\text{ A9 }(60,70),A10^{?}(65,70),A11(67,71),A12(67,72),\text{ A13 }(5,40)\end{array}$$