Question

In: Statistics and Probability

Consider the following eight examples: A1 = (4,20), A2 = (4,10), A3 = (16,8), A4 =...

Consider the following eight examples:
A1 = (4,20), A2 = (4,10), A3 = (16,8), A4 = (10,16), A5 = (14,10), A6 = (12,8), A7 = (2,4), A8 = (8,18)
The distance function is Euclidian distance.
Use single-link, complete-link agglomerative clustering, and centroid techniques to cluster these
examples. Show your calculations and draw the dendrograms for each technique.

Expert Solution

ANSWER:

Given that,

IN SINGLE LINK APPROACH

1. COMPUTE THE EUCLIDEAN DISTANCE BETWEEN ALL POINTS.

2. CHOOSE THE MINIMUM DISTANCE FROM TABLE AND CREATE SUBSET OF IT

in complete link method choose maximum distance the apply the same process .

	A1	A2	A3	A4	A5	A6	A7	A8
A1	0	17.088	17.88	17.088	16.49	16.49	16.12	18.86
A2	17.088	0	10	8.48	7.211	7.211	6.324	11.66
A3	17.88	10	0	10	8.944	8.944	8.246	12.806
A4	17.088	8.48	10	0	7.211	7.211	6.3246	11.661
A5	16.49	7.211	8.944	7.211	0	5.6569	4.4721	10.7703
A6	16.49	7.211	8.944	7.211	5.6569	0	4.4721	10.7703
A7	16.12	6.324	8.246	6.3246	4.4721	4.4721	0	10.198
A8	18.86	11.66	12.806	11.661	10.7703	10.7703	10.198	0

Minimum distance is 4.4721 between points( A5, A7 )

The minimum distance between (a1,a5) and(a1,a7) is considered as distance between (A5,A7) to A1

	A1	A2	A3	A4	A5,A7	A6	A8
A1	0	17.088	17.88	17.088	16.12	16.49	18.86
A2	17.088	0	10	8.48	6.324	7.211	11.66
A3	17.88	10	0	10	8.246	8.944	12.806
A4	17.088	8.48	10	0	6.3246	7.211	11.661
A5,A7	16.12	6.324	8.246	6.3246	0	4.4721	10.198
A6	16.49	7.211	8.944	7.211	4.4721	0	10.7703
A8	18.86	11.66	12.806	11.661	10.198	10.7703	0

The minimum distance between two points 4.4721

the clustered points are (A5,A7) and A6

	A1	A2	A3	A4	(A5,A7)A6	A8
A1	0	17.088	17.88	17.088	16.12	18.86
A2	17.088	0	10	8.48	6.324	11.66
A3	17.88	10	0	10	8.246	12.806
A4	17.088	8.48	10	0	6.3246	11.661
(A5,A7)A6	16.12	6.324	8.246	6.3246	0	10.198
A8	18.86	11.66	12.806	11.661	10.198	0

Now the min distance is between((A5,A7)A6),A2

	A1	A3	A4	((A5,A7)A6),A2	A8
A1	0	17.88	17.088	16.12	18.86
A3	17.88	0	10	8.246	12.806
A4	17.088	10	0	6.3246	11.661
((A5,A7)A6),A2	16.12	8.246	6.3246	0	10.198
A8	18.86	12.806	11.661	10.198	0

MIN DISTANCE IS (((A5,A7)A6),A2),A4

	A1	A3	((((A5,A7)A6),A2),A4)	A8
A1	0	17.88	16.12	18.86
A3	17.88	0	8.246	12.806
(((A5,A7)A6),A2),A4)	16.12	8.246	0	10.198
A8	18.86	12.806	10.198	0

the minimum distance between(( (A5,A7),A6)A2)A4) ,A3

	A1	((((A5,A7)A6),A2),A4),A3	A8
A1	0	16.12	18.86
(((A5,A7)A6),A2),A4),A3	16.12	0	10.198
A8	18.86	10.198	0

A8 IS MERGED WITH ((((A5,A7)A6),A2),A4),A3)

	A1	((((A5,A7)A6),A2),A4),A3),A8
A1	0	16.12
(((A5,A7)A6),A2),A4),A3),A8	16.12	0

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