Centroid
A centroid is a central point representing a geometric figure or set of points, commonly calculated as the coordinate-wise mean, with weights when applicable.
Advanced Algorithms and Data Structures
A center of mass is the point representing the coordinate-weighted average location of a body or collection of points.
- How it is used
- Locates spherical SS-tree envelopes and represents clusters for nearest-centroid assignment in k-means.
- How deep it goes
- Defines the center of mass and implements coordinate-wise means, node-envelope updates, and iterative recentering; defers smallest-enclosing-sphere approximation details.
- Examples
- Illustrates nearest-centroid insertion, a three-centroid k-means iteration, and contrasting centroid-centered and minimum covering spheres.
- What you can do after
- Build it from scratch to update SS-tree envelopes or recenter k-means clusters, while recognizing overlap and outlier trade-offs.
Read how Advanced Algorithms and Data Structures explains centroid →
D3.js in Action, Third Edition
A centroid is the geometric center of a shape or region.
- How it is used
- Positions labels at the visual center of arcs in pie and donut charts.
- How deep it goes
- Explains centroid calculation, returned coordinates, and SVG alignment, but defers general shape-centroid mathematics.
- Examples
- Demonstrates a 35% precipitation label and percentage labels placed on multiple donut-chart arcs.
- What you can do after
- Apply it via D3’s arc generator to calculate and align labels inside pie or donut-chart arcs.
Data Without Labels
A centroid is the arithmetic mean position of a set of points and represents a cluster in centroid-based clustering.
- How it is used
- Represents clusters so centroid-based clustering can compare points with groups by distance.
- How deep it goes
- Works through iterative assignment and mean-based center updates, then retrieves fitted centers; defers further centroid mathematics to an appendix.
- Examples
- Uses an illustrated three-center iteration and a standardized vehicle dataset clustered and profiled with Python.
- What you can do after
- Apply it via scikit-learn to retrieve cluster centers and use them to profile a fitted vehicle-clustering result.
Outlier Detection in Python
A cluster center is a representative location or point associated with a cluster and used to measure observations' proximity to that cluster.
- How it is used
- Uses cluster centers as reference locations for judging how unusual observations are within clustered data.
- How deep it goes
- Explains center-relative and cluster-relative distance scoring, including an optional size adjustment, without deriving how centers are estimated.
- Examples
- Illustrates scoring with single- and multiple-cluster results and contrasts it with DBSCAN flags for unassigned points.
- What you can do after
- Apply it via Gaussian mixture clustering and Mahalanobis distance to compare points with their own cluster’s typical distance.
Statistics Slam Dunk
A centroid is the central position of a set of points, commonly calculated as the coordinate-wise mean.
- How it is used
- Uses centroids to assign data points to nearby clusters and recalculate cluster centers during K-means.
- How deep it goes
- Explains centroids through iterative assignment, mean recalculation, convergence, and within-cluster variation.
- Examples
- Uses NBA team payrolls and regular-season wins to calculate four cluster centroids and assign every team.
- What you can do after
- Apply it via base R's kmeans() and interpret cluster means as centroids.
Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A centroid is a representative center of a cluster, typically computed as the mean position of its member points.
- How it is used
- Uses centroids to partition normalized data points into a user-selected number of clusters.
- How deep it goes
- Explains centroid assignment, coordinate-wise mean updates, convergence, initialization, and practical limitations.
- Examples
- Demonstrates centroids with Swift Point3D data and governor longitude-age clusters.
- What you can do after
- Build it from scratch with a Swift KMeans type that initializes, updates, and tests centroid convergence.
Cyber Threat Hunting
A centroid is the arithmetic mean of the data points assigned to a cluster and represents that cluster's center.
- How it is used
- Uses centroids to assign data points to clusters and identify potentially interesting smaller groups in traffic data.
- How deep it goes
- Explains centroid calculation, distance assignment, iteration, scaling, and outlier sensitivity without deriving the algorithm’s implementation.
- Examples
- Uses a 14-feature traffic table, four clusters, two-dimensional plots, histograms, and cluster-size counts.
- What you can do after
- Apply it via scikit-learn to fit k-means, label rows, visualize clusters, and compare cluster sizes.
Related concepts
- K-means clusteringused by · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
- meanuses · A mean is a measure of central tendency, calculated as the arithmetic average of values or, for a random variable, as the probability-weighted average of its possible values.
- k-means++ initializationused by · K-means++ initialization is a procedure that selects initial centroids using probability proportional to squared distance from previously selected centroids.
- getBoundingClientRectproduced by · getBoundingClientRect is a DOM method that returns an element's size and position relative to the viewport.
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