K-Means Clustering Explainer
K-means is an unsupervised algorithm that divides examples into k clusters. It represents each cluster by a centroid, or mean location, and assigns each example to the nearest centroid under a chosen distance measure, usually squared Euclidean distance.
Training alternates between two steps: assign points to the nearest current centroid, then recompute each centroid from its assigned points. The process stops when assignments or centroid positions stabilize enough. Because the objective can have multiple local solutions, different initial centers may produce different results.
The number k must be chosen outside the basic algorithm. Feature scaling is important because a variable with a large numeric range can dominate distance. K-means also tends to favor compact, roughly spherical groups and can perform poorly with elongated shapes, unequal densities, outliers, or categorical data.
A cluster is a mathematical grouping, not automatically a meaningful real-world category. Analysts inspect examples, stability, domain usefulness, and alternatives before assigning labels or decisions to clusters. Apparent segments can reflect measurement choices and sampling bias as much as natural structure.
K-means clustering divides data into a chosen number of groups by repeatedly updating group centers and assignments.
Key terms include cluster, centroid, k, assignment step, update step, Euclidean distance, initialization, scaling and local optimum.
The assignment step groups each point with its nearest centroid; the update step moves each centroid to the mean of its current group.
Multiple restarts and careful initialization reduce the chance that one unlucky starting arrangement determines the reported clusters.
Irregular shapes, very different cluster sizes, outliers, or unsuitable distance measures can make the partition misleading.
Choosing k and interpreting the result require external evidence because the algorithm does not discover the one true segmentation of a population.
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