Ward's method

About: Ward's method is a research topic. Over the lifetime, 98 publications have been published within this topic receiving 29445 citations.

Hierarchical Grouping to Optimize an Objective Function

Abstract: A procedure for forming hierarchical groups of mutually exclusive subsets, each of which has members that are maximally similar with respect to specified characteristics, is suggested for use in large-scale (n > 100) studies when a precise optimal solution for a specified number of groups is not practical. Given n sets, this procedure permits their reduction to n − 1 mutually exclusive sets by considering the union of all possible n(n − 1)/2 pairs and selecting a union having a maximal value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. By repeating this process until only one group remains, the complete hierarchical structure and a quantitative estimate of the loss associated with each stage in the grouping can be obtained. A general flowchart helpful in computer programming and a numerical example are included.

Cluster Analysis

Abstract: Cluster analysis comprises a range of methods for classifying multivariate data into subgroups. By organising multivariate data into such subgroups, clustering can help reveal the characteristics of any structure or patterns present. These techniques are applicable in a wide range of areas such as medicine, psychology and market research. This fourth edition of the highly successful Cluster Analysis represents a thorough revision of the third edition and covers new and developing areas such as classification likelihood and neural networks for clustering. Real life examples are used throughout to demonstrate the application of the theory, and figures are used extensively to illustrate graphical techniques. The book is comprehensive yet relatively non-mathematical, focusing on the practical aspects of cluster analysis.

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

Abstract: 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.

Hierarchical Clustering via Joint Between-Within Distances: extending Ward's Minimum Variance Method

Abstract: We propose a hierarchical clustering method that minimizes a joint between-within measure of distance between clusters. This method extends Ward's minimum variance method, by defining a cluster distance and objective function in terms of Euclidean distance, or any power of Euclidean distance in the interval (0,2]. Ward's method is obtained as the special case when the power is 2. The ability of the proposed extension to identify clusters with nearly equal centers is an important advantage over geometric or cluster center methods. The between-within distance statistic determines a clustering method that is ultrametric and space-dilating; and for powers strictly less than 2, determines a consistent test of homogeneity and a consistent clustering procedure. The clustering procedure is applied to three problems: classification of tumors by microarray gene expression data, classification of dermatology diseases by clinical and histopathological attributes, and classification of simulated multivariate normal data.

Algorithms for Model-Based Gaussian Hierarchical Clustering

Abstract: Agglomerative hierarchical clustering methods based on Gaussian probability models have recently shown promise in a variety of applications. In this approach, a maximum-likelihood pair of clusters is chosen for merging at each stage. Unlike classical methods, model-based methods reduce to a recurrence relation only in the simplest case, which corresponds to the classical sum of squares method. We show how the structure of the Gaussian model can be exploited to yield efficient algorithms for agglomerative hierarchical clustering.