Data mining53

0. Given six points with the following attributes:
Point x coordinate y coordinate
p1 0.4005 0.5306
p2 0.2148 0.3854
p3 0.3457 0.3156
p4 0.2652 0.1875
p5 0.0789 0.4139
p6 0.4548 0.3022
Table: X-Y coordinates of six points.
p1 p2 p3 p4 p5 p6
p1 0.0000 0.2357 0.2218 0.3688 0.3421 0.2347
p2 0.2357 0.0000 0.1483 0.2042 0.1388 0.2540
p3 0.2218 0.1483 0.0000 0.1513 0.2843 0.1100
p4 0.3688 0.2042 0.1513 0.0000 0.2932 0.2216
p5 0.3421 0.1388 0.2843 0.2932 0.0000 0.3921
p6 0.2347 0.2540 0.1100 0.2216 0.3921 0.0000
Table: Distance Matrix for Six Points
Which of the following clustering representations and dendrogram depicts the use of MIN or Single link proximity fucntion in hierarchical clustering:

A
B
C
D

Answer
Comment
Array

Option : A
Explanation :
For the single link or MIN version of hierarchical clustering, the proximity of two clusters is defined to be the minimum of the distance between any two points in the different clusters. For instance, from the table, we see that the distance between points 3 and 6 is 0.11, and that is the height at which they are joined into one cluster in the dendrogram. As another example, the distance between clusters {3, 6} and {2, 5} is given by dist({3, 6}, {2, 5}) = min(dist(3, 2), dist(6, 2), dist(3, 5), dist(6, 5)) = min(0.1483, 0.2540, 0.2843, 0.3921) = 0.1483.

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