Society of Actuaries (SOA) PA Practice Exam

How does K-Means clustering determine the cluster assignment for a data point?

1. By assigning it to the nearest median

2. By assigning it to the nearest cluster centroid

3. Based on predefined categories in the dataset

4. Using random assignments at each iteration

The correct answer is: By assigning it to the nearest cluster centroid

K-Means clustering determines the cluster assignment for a data point by assigning it to the nearest cluster centroid. In this algorithm, each cluster is represented by a centroid, which is the mean of all data points assigned to that cluster. The process begins by initializing a set of centroids, typically by randomly selecting points from the dataset. As the algorithm iterates, it calculates the distance from each data point to the centroids. The assignment of each point is done based on the proximity to the centroids; specifically, each data point is assigned to the cluster whose centroid is the closest. This proximity is usually measured using Euclidean distance, though other distance metrics can be employed depending on the specific application. This approach ensures that data points within a cluster are more similar to each other than to those in other clusters, which is a fundamental aspect of K-Means clustering. The process of assigning points to the nearest centroid continues until the centroids stabilize and there are no further changes in cluster assignments. This method effectively summarizes the distribution of the data into distinct groups, making it a powerful technique in exploratory data analysis.