Society of Actuaries (SOA) PA Practice Exam

When using PCA, what can be said about the number of principal components that are typically chosen?

1. All components must always be retained

2. Only a few components are used while capturing variance

3. All principal components have equal importance

4. Dimension choice is arbitrary with PCA

The correct answer is: Only a few components are used while capturing variance

When utilizing Principal Component Analysis (PCA), it is important to recognize the typical practice of retaining only a few principal components that effectively capture the majority of the variance within the data. This approach allows for a reduction in dimensionality while preserving as much information as possible. The reasoning behind choosing a limited number of components often stems from the observation of the explained variance ratio, which demonstrates how much of the total dataset's variance is captured by each principal component. Analysts commonly look for a point in the variance cumulative plot (scree plot) where the incremental gain in explained variance diminishes significantly, indicating that additional components contribute less meaningful information. Therefore, selecting only a few components facilitates a more manageable dataset for further analysis, modeling, or visualization while still retaining the essential features of the original data structure. This selection process is guided by the principle of balance between simplicity and information retention rather than arbitrary choice or equal weighting of all components, hence reinforcing the effectiveness and efficiency of PCA in data processing tasks.