Which clustering approach partitions a dataset by locating observations based on centroids?

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Multiple Choice

Which clustering approach partitions a dataset by locating observations based on centroids?

Partitional clustering is the approach that splits data into a fixed number of non-overlapping groups by assigning each observation to the cluster with the nearest center, or centroid. In this setup, the centroid serves as the representative point for the cluster, and the algorithm iteratively updates centroids by averaging the points assigned to each cluster and reassigning observations to the closest centroid. This creates a clean partition of the dataset around these centroids, which is exactly what the question describes. For example, in the common K-means method, you initialize centroids, assign every data point to the nearest centroid, recompute each centroid as the mean of its assigned points, and repeat until assignments stop changing. This centroid-based partitioning is the hallmark of this clustering style. The other terms don’t fit as well. Data Clustering is a broad umbrella that can include many different approaches, not specifically centroid-based partitioning. PCA is a dimensionality-reduction technique, not a clustering method. Orthogonality is a linear-algebra concept about perpendicular vectors, not a clustering approach.

Partitional clustering is the approach that splits data into a fixed number of non-overlapping groups by assigning each observation to the cluster with the nearest center, or centroid. In this setup, the centroid serves as the representative point for the cluster, and the algorithm iteratively updates centroids by averaging the points assigned to each cluster and reassigning observations to the closest centroid. This creates a clean partition of the dataset around these centroids, which is exactly what the question describes.

For example, in the common K-means method, you initialize centroids, assign every data point to the nearest centroid, recompute each centroid as the mean of its assigned points, and repeat until assignments stop changing. This centroid-based partitioning is the hallmark of this clustering style.

The other terms don’t fit as well. Data Clustering is a broad umbrella that can include many different approaches, not specifically centroid-based partitioning. PCA is a dimensionality-reduction technique, not a clustering method. Orthogonality is a linear-algebra concept about perpendicular vectors, not a clustering approach.

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