Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion?

By Fionn Murtagh, Pierre Legendre. Journal of Classification, 2011

3,455 citations recorded by the source corpus.

The Ward error sum of squares hierarchical clustering method has been very widely used since its first description by Ward in a 1963 publication. It has also been generalized in various ways. Two algorithms are found in the literature and software, both announcing that they implement the Ward clustering method. When applied to the same distance matrix, they produce different results. One algorithm preserves Ward’s criterion, the other does not. Our survey work and case studies will be useful for all those involved in developing software for data analysis using Ward’s hierarchical clustering method.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/2f420d40bbef29f47005c1fc22c2aff98605f659

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Citations in the corpus

p-Adic mathematical physics: the first 30 years (2017, methodology): “For some other applications of p-adic, hierarchical and wavelet methods in data analysis and related fields see [245, 246, 45, 111, 244, 208, 209, 210, 211].”
Comprehensive survey on hierarchical clustering algorithms and the recent developments (2022, methodology): “Ward’s method (Murtagh and Legendre 2014) uses the smallest increase of the sum of square error when two clusters are merged.”
CIDR: Ultrafast and accurate clustering through imputation for single-cell RNA-seq data (2016, neutral): “D2 [26], and the number Fig.”
Algorithms for hierarchical clustering: an overview, II (2017, background): “In Murtagh and Legendre (2014), there is extensive comparative study of the Ward, or minimum variance, agglomerative hierarchical clustering algorithm.”
Pollution indices as useful tools for the comprehensive evaluation of the degree of soil contamination–A review (2018, methodology): “In this case, the estimation of differences between particular groups takes place (Murtagh and Legendre 2014).”
NbClust: An R Package for Determining the Relevant Number of Clusters in a Data Set (2014, positive): “D2" implements that criterion (Murtagh and Legendre 2014).”
Big data for cyber physical systems in industry 4.0: a survey (2019, methodology): “Typically, hierarchical methods iteratively group the previously generated clusters to form a hierarchical structure (Murtagh and Legendre 2014; Müllner 2013).”
An atlas of the protein-coding genes in the human, pig, and mouse brain (2020, methodology): “Dendrograms showing gene expression in heatmaps have been clustered using the Ward2 algorithm (58), an implementation of Ward’s minimum variance method (59) implemented as “Ward.”
Functional classifications and their application in phytoplankton ecology (2015, methodology): “Functional Groups were analysed by nonmetric multidimensional scaling (NMDS) and cluster analysis (Ward’s method), both applied to Euclidean distance matrices (Oksanen et al., 2013; Murtagh & Legendre, 2014).”