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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Given below are two statements:
If two variables $V_1$ and $V_2$ are used for clustering, then consider the following statements for $k$ means clustering with $k=3$.
Statement I: If $V_1$ and $V_2$ have correlation of $1$, the cluster centroid will be in straight line.
Statement II: If $V_1$ and $V_2$ 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:
If two variables $V_1$ and $V_2$ are used for clustering, then consider the following statements for $k$ means clustering with $k=3$.
Statement I: If $V_1$ and $V_2$ have correlation of $1$, the cluster centroid will be in straight line.
Statement II: If $V_1$ and $V_2$ 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:
Solution
Statement I is true.If $V_1$ and $V_2$ have correlation $1$, then they have perfect positive linear relationship.
So, all data points lie on a straight line.
In $k$ means clustering, centroids are calculated as the mean of points in each cluster.
Mean of points lying on a straight line also lies on the same straight line.
Therefore, the cluster centroids will be in a straight line.
Statement II is false.
If $V_1$ and $V_2$ have correlation $0$, then there is no linear relationship between them.
So, the data points are not necessarily on a straight line.
Therefore, the cluster centroids will not necessarily be in a straight line.
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