Given below are two statements: If two variables 𝑉1 and 𝑉2 are used for…
2020
Given below are two statements:
If two variables 𝑉1 and 𝑉2 are used for clustering, then consider the following statements for 𝑘 means clustering with 𝑘=3:
Statement I: If 𝑉1 and 𝑉2 have correlation of 1 the cluster centroid will be in straight line
Statement II: If 𝑉1 and 𝑉2 have correlation of 0 the cluster centroid will be in straight line
In the light of the above statements, choose the correct answer from the options given below
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
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Correct answer: C
Answer: Statement I is correct; Statement II is false.
Key idea: In k-means clustering each cluster centroid is the mean (average) of the points assigned to that cluster.
Why Statement I is correct: A correlation of 1 means one variable is an exact linear function of the other, so all data points lie on a single straight line. The mean of any subset of points on that line also lies on the same line, so all cluster centroids will be collinear.
Why Statement II is false: A correlation of 0 indicates no linear relationship on average but does not imply that points lie on a straight line. Points can be spread in two dimensions with zero linear correlation while cluster centroids can form non-collinear arrangements (for example, clusters located near the vertices of a triangle).
Therefore, the correct choice states that the perfect-correlation case produces collinear centroids, while the zero-correlation case does not guarantee collinear centroids.
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