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The geometric center of a cluster, typically the mean of its points in feature space.
DESCRIPTION
In clustering, a centroid represents the average position of all points assigned to a cluster and serves as its prototype. Algorithms like k-means minimize distances of points to their centroids, iteratively updating assignments and centers. Centroids are sensitive to outliers and best suited to continuous, Euclidean feature spaces; medoids are robust alternatives when using arbitrary distance metrics. Centroid positions define decision boundaries and Voronoi partitions in k-means. They are also used in initializing clusters and explaining cluster characteristics.
ALTERNATIVE DEFINITIONS
Wolfram MathWorld
The centroid is the center of mass of a two-dimensional planar lamina or three-dimensional solid of uniform density.
Defines centroid in geometric and physical terms (center of mass).
scikit-learn
K-means clustering aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers).
Equates centroids with cluster means in k-means, linking definition to algorithm.
Encyclopaedia Britannica
Centroid, the centre of mass of a geometrical object of uniform density.
Concise geometric perspective highlighting mass center concept.
RELATED TERMS
K-Means Cluster Center Euclidean Distance Barycenter Voronoi Diagram Principal Component Analysis Silhouette Score Gaussian Mixture Mean Vector
COMPETING TERMS
Medoid
KNOWLEDGE AREAS
TARGET AUDIENCE
Data Scientist AI Engineer Data Analyst
EXTERNAL SOURCES
- Wikipedia - Centroid
- scikit-learn - Defines cluster centers in k-means
- Stanford CS229 - Unsupervised learning notes including k-means
- Wolfram MathWorld - Geometric definition of centroid
TOP QUESTIONS
What is a centroid in clustering?
A centroid is the mean vector of points assigned to a cluster. It represents the cluster’s center and is used to assign points by nearest distance.
Category: Overview
How is a centroid computed in k-means?
It’s the arithmetic mean of all points in a cluster. The algorithm alternates between assigning points to nearest centroids and recomputing centroids until convergence.
Category: Requirements
Why can centroids be sensitive to outliers?
Means shift toward extreme values, so a single outlier can significantly move the centroid. Robust methods like medoids reduce this effect.
Category: Risk
What is the difference between centroid and medoid?
A centroid is the mean point, while a medoid is an actual data point minimizing distance to all others. Medoids work with any distance metric.
Category: Misunderstanding
How does the centroid relate to decision boundaries?
In k-means, boundaries are Voronoi cells around centroids. Each point is assigned to the cluster with the nearest centroid.
Category: Example
What are common mistakes when using centroids?
Not standardizing features, using inappropriate distance metrics, and ignoring skewed or categorical data can produce misleading centroids.
Category: Mistakes
When should you prefer a medoid over a centroid?
Use medoids for non-Euclidean distances or when robustness to outliers is critical. They are ideal in k-medoids and PAM algorithms.
Category: Opinion
How do you interpret a centroid in high dimensions?
It summarizes average feature values for the cluster. Feature scaling and dimensionality reduction help make centroid interpretation meaningful.
Category: Requirements
What is a striking analogy for centroid?
Imagine a cloud of points as a weight distribution; the centroid is the balance point where the system would ‘hang’ evenly.
Category: Example