Question

consider a set of five 2-dimensional points p1=(0, 0), p2=(0, 1), p3=(5, 8), p4=(5, 7), and p5=(0, 0.5). euclidean distance is the distance function. single linkage clustering is used to cluster the p​

Answer 1

Answer:

{p1,p2,p5}  {p3,p4}

Explanation:

Answer 2

Answer:

Explanation:

Definition of Euclidean distance:

In mathematics, the length of a line segment connecting two points in Euclidean space is known as the Euclidean distance. It is sometimes referred to as the Pythagorean distance since it can be determined from the points' Cartesian coordinates using the Pythagorean theorem. Although Euclid did not describe distances as numbers and the Pythagorean theorem was not connected to distance calculation until the 18th century, these names derive from the ancient Greek mathematicians Pythagoras and Euclid.

The minimum distance between two pairs of points from the two items is typically used to determine the distance between two objects that are not points. There are formulas for calculating distances between many types of objects, such as the distance between two points.

Definition of single linkage clustering:

One of numerous hierarchical clustering techniques used in statistics is single-linkage clustering. It is based on bottom-up cluster grouping (agglomerative clustering), joining two clusters at each stage that contain the nearest pair of elements that do not yet belong to the same cluster. This approach has the disadvantage of producing long, thin clusters, where elements close to one another are separated by short distances, while members at opposite ends of a cluster may be separated by lengths that are much greater than those between two elements of other clusters. This could make it challenging to define classes that would effectively split the data.

Given:

set of five 2-dimensional points p1=(0, 0), p2=(0, 1), p3=(5, 8), p4=(5, 7),    and p5=(0, 0.5)

Answer:

{p1,p2,p5} {p3,p4}

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