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Following table gives fat and protein content of items. Apply single linkage clustering and construct dendogram.

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Calculate the distance matrix using Euclidian distance formula:

√((x1-x2)2 + (y1-y2)2)

=√((1.1-8.2)2+ (60-20)2)

=√((-7.1) 2 + (40)2)

=√(50.41 + 1600)

=√1651.41

=40.62 enter image description here Similarly calculations are performed for the rest.

From the above table the minimum distance between any two points is 4.01and this distance is between C3 and C7. So these two points can be merged into a single cluster and is called C37 enter image description here Therefore dis(C37,4)=min(dis(3,4),dis(7,4))

=min(14.25,18.19)

=14.25

Similarly calculate other distances to get the distance matrix.

From the above table the minimum distance between any two points is 5.03 and this distance is between C2 and C5. So these two points can be merged into a single cluster and is called C25.

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From the above table the minimum distance between any two points is 5.08and this distance is between C1 and C6. So these two points can be merged into a single cluster and is called C16.

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From the above table the minimum distance between any two points is 6.77 and this distance is between C25 and C4. So these two points can be merged into a single cluster and is called C254.

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From the above table the minimum distance between any two points is 14.25 and this distance is between C254 and C37. So these two points can be merged into a single cluster and is called C25437.

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So finally combine the clusters C25437 and C16 . Dendogram is given below.

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