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K-means
Unsupervised learning algorithm that partitions a dataset into K clusters by minimizing the sum of intra-cluster distances, where each cluster is represented by its centroid.
Centroid
Geometric point representing the center of a cluster, calculated as the average of all data points belonging to that cluster and serving as a reference for assigning new observations.
Within-cluster inertia
Measure quantifying the dispersion of points within the same cluster, calculated as the sum of squared distances between each point and its respective centroid.
Elbow method
Heuristic technique to determine the optimal number of clusters K by plotting within-cluster inertia against K and identifying the point where the inertia reduction starts to decrease significantly.
K-means++
Initialization variant of K-means that intelligently selects initial centroids using a probability distribution based on distances, improving convergence and clustering quality.
Convergence
State reached when centroids no longer move significantly between successive iterations or when the assignment of points to clusters becomes stable, indicating that the algorithm has found a solution.
Silhouette score
Clustering evaluation metric measuring intra-cluster cohesion and inter-cluster separation, ranging from -1 (poor clustering) to +1 (optimal clustering).
Local optimum
Clustering solution where no improvement is possible through simple point reassignments, but which does not necessarily represent the best possible global configuration.
Mini-batch K-means
A variant of K-means that uses random subsets of data (mini-batch) to update centroids, offering faster convergence on large datasets.
Inter-cluster inertia
Measure of separation between clusters, calculated as the weighted sum of squared distances between different cluster centroids and the global centroid.
Vector quantization
Application of K-means clustering to compress vector data by representing groups of similar vectors by their common centroid, thus reducing information complexity.
K-means iteration
A complete cycle of the algorithm including the assignment phase of points to the nearest centroid and the update phase of centroids based on the average of assigned points.
Partitioning
Fundamental approach of K-means clustering aimed at creating a disjoint division of data where each observation belongs to exactly one cluster.
Clustering stability
Measure of the consistency of clustering results obtained by K-means across multiple runs with different initializations, evaluating the robustness of the found solution.