Centroidbased

Centroidbased refers to methods that use the centroid as a central representative point for a group of data points. In clustering, centroid-based approaches summarize each cluster by its centroid, typically the arithmetic mean of the cluster’s members. The standard example is k-means, where each iteration assigns points to the nearest centroid and then updates centroids to the mean of assigned points. Centroids provide simple, fast summaries and can scale to large datasets, but they assume roughly convex, evenly sized clusters and are sensitive to outliers and initialization.

In classification, centroid-based methods compute a centroid for each class from training examples and classify new instances by nearest centroid, using a distance metric such as Euclidean distance. The nearest centroid classifier is straightforward, computationally efficient, and effective for high-dimensional data with well-separated classes, such as text representations. Performance can suffer with imbalanced classes, overlapping classes, or non-spherical class distributions.

Variants and extensions include normalization or cosine similarity in high-dimensional spaces, robust centroids based on medians, and spherical k-means, which uses unit-length vectors and cosine distance. Other uses include vector quantization and image or signal processing, where centroids serve as prototype representations of regions or features.

Limitations: centroid-based methods rely on a single representative point per cluster or class, which may oversimplify structure, ignore covariance, and produce misleading results when clusters have complex shapes or varied densities. They are commonly complemented with other techniques or combined with feature scaling and dimensionality reduction.