Sample Questions
Question 1
Easy
In PCA, eigenvalues of the covariance matrix represent:
Solution
D is correct.
Each eigenvalue of the covariance (or correlation) matrix equals the variance of the data when projected onto the corresponding principal component. Larger eigenvalues indicate directions that capture more variation in the data.
Each eigenvalue of the covariance (or correlation) matrix equals the variance of the data when projected onto the corresponding principal component. Larger eigenvalues indicate directions that capture more variation in the data.
Question 2
Medium
In PCA, eigenvectors of the covariance matrix are also called:
Solution
E is correct.
The eigenvectors of the covariance (or correlation) matrix define the directions of the principal components. They are commonly referred to as loading vectors because they specify the weight (loading) each original variable receives in the linear combination.
The eigenvectors of the covariance (or correlation) matrix define the directions of the principal components. They are commonly referred to as loading vectors because they specify the weight (loading) each original variable receives in the linear combination.
Question 3
Hard
K-means is applied to 6 one-dimensional observations with . After convergence, cluster 1 contains and cluster 2 contains . What is the total within-cluster sum of squares (WCSS)?
Solution
A is correct.
Cluster 1: , centroid
Cluster 1 WCSS:
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- Sum =
Cluster 2: , centroid
Cluster 2 WCSS:
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- Sum =
Total WCSS .
Cluster 1: , centroid
Cluster 1 WCSS:
-
-
-
- Sum =
Cluster 2: , centroid
Cluster 2 WCSS:
-
-
-
- Sum =
Total WCSS .
