Departure question
Read signals from chancePort 10 of 11Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
This voyage is an editorial path for understanding, not a claim of direct historical influence or sole invention.
The simplest way to group similar data into clusters. Place k centers at random → assign each point to its nearest center → recompute centers → repeat. The first tool for customer segmentation, image-color compression, gene-expression classification, and recommender systems.
Iteration | Step | Result |
|---|---|---|
Initialization | Choose k centers at random | Example: μ₁=(2,3), μ₂=(8,7) |
1 | Assign each point to its nearest center | Point (3,3) → cluster 1 |
1 | Recompute centers (cluster means) | New μ₁, μ₂ |
2 | Reassign → recompute | Some points switch clusters |
… | Repeat until nothing changes | Convergence (local minimum) |
Converged | Final cluster partition | Applications: customer segments, image color compression, gene clustering |
K-means can become trapped in a local minimum, so it is usually run several times with different initializations and the best result is selected.
The simplest grouping algorithm — from 1957 Bell Labs to every data scientist's first tool.
Ports in time
Follow the scenes to see problems, notation, standards of proof, and applications changing across different times and places.
Stuart Lloyd developed the algorithm for pulse-code modulation quantization, but the work remained unpublished in archival form for decades.
The recorded place matches a canonical map anchor
Continue this scene on the mapJames MacQueen presented and generalized the iterative clustering method under the name k-means.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearDavid Arthur and Sergei Vassilvitskii proposed a principled way to choose initial centers, improving both theoretical guarantees and practical reliability.
No reliable place is given, so time continues without an invented pin
Continue through the world of this yearCustomer segmentation, image compression, genomic analysis, recommendation systems, anomaly detection, and preparation of AI training data.
Curated sources and problems. Bring one discovery back from OEIS, Project Euler, MathOverflow, or arXiv.
No concept belongs to one person
These are not inventor credits. They are different ports: opening a problem, sharpening a language, or carrying it into another world.
Number lenses
These numbers are editorial lenses for the voyage, not required prerequisites.
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Travel from dice and insurance to data, noise, and learning algorithms—measuring uncertainty and turning it into decisions.
Open the number voyage
Concept genealogy
Concepts arriving from before
Current port
K-Means Clustering
Concepts opened from here
No direct successor port is curated yet.
Only direct editorial links are shown; this is not a complete learning order or historical influence line.
