On some significance tests in cluster analysis

DOI10.1007/BF01908065zbMath0587.62048OpenAlexW4249589601MaRDI QIDQ1072282

Hans-Hermann Bock

Publication date: 1985

Published in: Journal of Classification (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01908065

zbMATH Keywords

classificationasymptotic normalityclusteringhomogeneitysimilarityheterogeneitycluster analysismean distanceasymptotic powersignificance testsk-means algorithmgap testmaximum F statisticminimum within-cluster sum of squaresneighboring alternatives

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Parametric hypothesis testing (62F03) Asymptotic properties of parametric tests (62F05)

Related Items (19)

Probabilistic models in cluster analysis ⋮ On the number of clusters ⋮ A unified framework for detecting groups and application to shape recognition ⋮ Some peculiar boundary phenomena for extremes of r-th nearest neighbor links ⋮ An entropy criterion for assessing the number of clusters in a mixture model ⋮ Probabilistic clustering via Pareto solutions and significance tests ⋮ Algorithmic paradigms for stability-based cluster validity and model selection statistical methods, with applications to microarray data analysis ⋮ On the enumeration of rectangular (0, 1)-matrices ⋮ Asymptotics of a clustering criterion for smooth distributions ⋮ Trimming algorithms for clustering contaminated grouped data and their robustness ⋮ MCS: A method for finding the number of clusters ⋮ Large-sample results for optimization-based clustering methods ⋮ Comparison of three hypothesis testing approaches for the selection of the appropriate number of clusters of variables ⋮ Identifying genuine clusters in a classification ⋮ Using combinatorial optimization in model-based trimmed clustering with cardinality constraints ⋮ An asymptotic result on principal points for univariate distributions ⋮ Loevinger's measures of rule quality for assessing cluster stability ⋮ Resampling Method for Unsupervised Estimation of Cluster Validity ⋮ The next‐generation K‐means algorithm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Validity studies in clustering methodologies
• An infinite-dimensional approximation for nearest neighbor goodness of fit tests
• Goodness of fit testing in \(R^ m \)based on the weighted empirical distribution of certain nearest neighbor statistics
• On the asymptotic distribution of k-spacings with applications to goodness-of-fit tests
• Strong consistency of k-means clustering
• Sums of functions of nearest neighbor distances, moment bounds, limit theorems and a goodness of fit test
• A central limit theorem for k-means clustering
• On the unimodality of spherically symmetric stable distribution functions
• Asymptotic distributions for clustering criteria
• Statistische Modelle und Bayessche Verfahren zur Bestimmung einer unbekannten Klassifikation normalverteilter zufälliger Vektoren
• Probabilities for a \(k\)-th nearest neighbor problem on the line
• Note on Grouping
• A Test of Fit Based on the Largest Sample Spacing
• Uniqueness of locally optimal quantizer for log-concave density and convex error weighting function
• Multivariate Tests for Clusters
• Quantization and the method of<tex>k</tex>-means
• Multiple local optima in vector quantizers (Corresp.)
• Sufficient conditions for uniqueness of a locally optimal quantizer for a class of convex error weighting functions
• The limit distribution for maxima of ‘weighted' rth-nearest-neighbour distances
• Probabilities for the Size of Largest Clusters and Smallest Intervals
• Limit theorems for dissociated random variables
• Bayesian cluster analysis
• Asymptotic behaviour of classification maximum likelihood estimates
• Die asymptotische Verteilung von Koinzidenzen
• Ordered Families of Distributions

This page was built for publication: On some significance tests in cluster analysis