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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

  1. Both Statement I and Statement II are true
  2. Both Statement I and Statement II are false
  3. Statement I is correct but Statement II is false
  4. Statement I is incorrect but Statement II is true
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C. Statement I is correct but Statement II is false …

 

Both data points would be in a straight line if the correlation between the variables V1 and V2 is 1. As a result, all three cluster centroids will form a straight line....

Hence the Statement I is correct but Statement II is false....

K-Means Clustering is an unsupervised learning algorithm used in machine learning and data science to tackle clustering problems...

Unsupervised Learning algorithm K-Means Clustering divides the unlabeled dataset into separate clusters....

K specifies the number of pre-defined clusters that must be generated during the process; for example, if K=2, two clusters will be created, and if K=3, three clusters will be created.…

 

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The answer is Statement I is correct but Statement II is false.

Statement I is true because:

  • When two variables have a correlation of 1, they have a perfect linear relationship. This means that the points in the scatter plot will fall exactly on a straight line.
  • In k-means clustering, centroids are positioned to minimize the sum of squared distances between data points and their assigned centroids.
  • If the data points form a straight line, the optimal position for the three centroids will also be along that line, as any deviation from the line would increase the overall distance.

Statement II is false because:

  • When two variables have a correlation of 0, they have no linear relationship. This means that the points in the scatter plot will be scattered randomly, not forming any clear pattern.
  • In this case, the optimal centroid positions will depend on the overall distribution of the points in the two-dimensional space, and they are unlikely to fall on a straight line. They will be positioned to capture the varying densities and clusters within the data, rather than aligning along a single axis.
Answer:

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