Society of Actuaries (SOA) PA Practice Exam

What is a potential disadvantage of K-Means clustering?

1. It can only handle categorical data

2. It may converge to a local minimum

3. It requires a distance matrix for calculations

4. It can identify hierarchical structures

The correct answer is: It may converge to a local minimum

The potential disadvantage of K-Means clustering that stands out is that it may converge to a local minimum. This characteristic arises from the algorithm's design, which involves initializing cluster centroids and iteratively assigning data points to the nearest centroid and updating the centroid based on these assignments. If the initial placement of centroids is not optimal, the algorithm can settle into a local minimum rather than finding the global minimum, meaning that it may produce suboptimal clustering results. This aspect is particularly significant in scenarios where the dataset has complicated structures or varying distributions, as K-Means might not adequately capture the complexities of the data. As a result, practitioners need to be cautious about the initial centroid selection and often run the algorithm multiple times with different initializations to achieve better clustering outcomes. In contrast to this aspect, K-Means is not limited to categorical data; it efficiently operates on numerical datasets where a concept of distance can be applied. It does not require a distance matrix per se, as it computes distances on the fly during the clustering process. Additionally, K-Means clustering is not designed to identify hierarchical structures; it operates on a flat clustering model, considering each data point independently for its closest centroid without depicting relationships between the clusters.