Cluster Validation & Sampling

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Abstractions about k-means, medoids, determining cluster count, separation and agreement indices, cluster tendency, and multistage sampling.

8 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Davies–Bouldin index — An internal cluster-validity score averaging, over clusters, the worst ratio of combined within-cluster scatter to between-centroid separation, with lower values indicating better compactness-separation tradeoff.
• Determining the number of clusters in a data set — The model-selection problem of choosing a clustering resolution or number k that balances within-cluster fit, separation, stability, complexity, domain meaning, and intended use.
• Hopkins statistic — A nearest-neighbor statistic comparing observed data with uniform reference points to assess spatial cluster tendency.
• K-means clustering — An optimization method that partitions vectors into k groups by assigning each observation to its nearest centroid and minimizing total within-cluster squared Euclidean distance.
• Medoid — An observed member of a dataset or cluster minimizing total dissimilarity to the other members, used as a robust representative when an arithmetic centroid is unavailable or inappropriate.
• Multistage sampling — A probability-sampling design that selects successively nested units—such as regions, households and people—using explicit probabilities at each stage.
• Rand index — A pair-counting similarity measure for two partitions that counts element pairs on which both clusterings agree.
• Silhouette (clustering) — An internal cluster-validation score comparing each observation’s mean within-cluster dissimilarity with its smallest mean dissimilarity to another cluster.