Free SOA Exam SRM (Statistics for Risk Modeling) Unsupervised Learning Techniques Practice Questions
Unsupervised learning on SOA Exam SRM covers principal component analysis (PCA), k-means and hierarchical clustering, and dimensionality reduction techniques for exploratory data analysis.
Sample Questions
Question 1
Easy
Which of the following statements about PCA is FALSE?
Solution
C is correct.
PCA is an unsupervised technique and does not require or use a response variable. It seeks directions of maximum variance in the feature space without regard to any outcome.
PCA is an unsupervised technique and does not require or use a response variable. It seeks directions of maximum variance in the feature space without regard to any outcome.
Question 2
Medium
When performing PCA, why is it important that the loading vectors (eigenvectors) have unit length?
Solution
D is correct.
Without the unit-length constraint, the optimization problem of maximizing variance would have no solution — the loadings could be scaled arbitrarily large to achieve infinite projected variance. The unit-length constraint makes the optimization well-defined and ensures a unique solution (the eigenvector).
Without the unit-length constraint, the optimization problem of maximizing variance would have no solution — the loadings could be scaled arbitrarily large to achieve infinite projected variance. The unit-length constraint makes the optimization well-defined and ensures a unique solution (the eigenvector).
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 .