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There are many psychological applications that require collapsing the information in a two-mode (e.g., respondents-by-attributes) binary matrix into a one-mode (e.g., attributes-by-attributes) similarity matrix. This process requires the selection of a measure of similarity between binary attributes. A vast number of binary similarity coefficients have been proposed in fields such as biology, geology, and ecology. Although previous studies have reported cluster analyses of binary similarity coefficients, there has been little exploration of how cluster memberships are affected by the base rates (percentage of ones) for the binary attributes. We conducted a simulation experiment that compared two-cluster K-median partitions of 71 binary similarity coefficients based on their pairwise correlations obtained under 15 different base-rate configurations. The results reveal that some subsets of coefficients consistently group together regardless of the base rates. However, there are other subsets of coefficients that group together for some base rates, but not for others. [ABSTRACT FROM AUTHOR]

Affinity propagation is a message‐passing‐based clustering procedure that has received widespread attention in domains such as biological science, physics, and computer science. However, its implementation in psychology and related areas of social science is comparatively scant. In this paper, we describe the basic principles of affinity propagation, its relationship to other clustering problems, and the types of data for which it can be used for cluster analysis. More importantly, we identify the strengths and weaknesses of affinity propagation as a clustering tool in general and highlight potential opportunities for its use in psychological research. Numerical examples are provided to illustrate the method. [ABSTRACT FROM AUTHOR]

Cohen's κ, a similarity measure for categorical data, has since been applied to problems in the data mining field such as cluster analysis and network link prediction. In this paper, a new application is examined: community detection in networks. A new algorithm is proposed that uses Cohen's κ as a similarity measure for each pair of nodes; subsequently, the κ values are then clustered to detect the communities. This paper defines and tests this method on a variety of simulated and real networks. The results are compared with those from eight other community detection algorithms. Results show this new algorithm is consistently among the top performers in classifying data points both on simulated and real networks. Additionally, this is one of the broadest comparative simulations for comparing community detection algorithms to date. [ABSTRACT FROM PUBLISHER]

Purpose The purpose of this paper is twofold. First, the authors provide a survey of operations management (OM) research applications of traditional hierarchical and nonhierarchical clustering methods with respect to key decisions that are central to a valid analysis. Second, the authors offer recommendations for practice with respect to these decisions.Design/methodology/approach A coding study was conducted for 97 cluster analyses reported in six OM journals during the period spanning 1994-2015. Data were collected with respect to: variable selection, variable standardization, method, selection of the number of clusters, consistency/stability of the clustering solution, and profiling of the clusters based on exogenous variables. Recommended practices for validation of clustering solutions are provided within the context of this framework.Findings There is considerable variability across clustering applications with respect to the components of validation, as well as a mix of productive and undesirable practices. This justifies the importance of the authors’ provision of a schema for conducting a cluster analysis.Research limitations/implications Certain aspects of the coding study required some degree of subjectivity with respect to interpretation or classification. However, in light of the sheer magnitude of the coding study (97 articles), the authors are confident that an accurate picture of empirical OM clustering applications has been presented.Practical implications The paper provides a critique and synthesis of the practice of cluster analysis in OM research. The coding study provides a thorough foundation for how the key decisions of a cluster analysis have been previously handled in the literature. Both researchers and practitioners are provided with guidelines for performing a valid cluster analysis.Originality/value To the best of the authors’ knowledge, no study of this type has been reported in the OM literature. The authors’ recommendations for cluster validation draw from recent studies in other disciplines that are apt to be unfamiliar to many OM researchers. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue including the model-based clustering, the development of a regression mixture approach and the advancement of regression model-based clustering.

It is common knowledge that mixture models are prone to arrive at locally optimal solutions. Typically, researchers are directed to utilize several random initializations to ensure that the resulting solution is adequate. However, it is unknown what factors contribute to a large number of local optima and whether these coincide with the factors that reduce the accuracy of a mixture model. A real-data illustration and a series of simulations are presented that examine the effect of a variety of data structures on the propensity of local optima and the classification quality of the resulting solution. We show that there is a moderately strong relationship between a solution that has a high proportion of local optima and one that is poorly classified. [ABSTRACT FROM PUBLISHER]

An asymmetric one-mode data matrix has rows and columns that correspond to the same set of objects. However, the roles of the objects frequently differ for the rows and the columns. For example, in a visual alphabetic confusion matrix from an experimental psychology study, both the rows and columns pertain to letters of the alphabet. Yet the rows correspond to the presented stimulus letter, whereas the columns refer to the letter provided as the response. Other examples abound in psychology, including applications related to interpersonal interactions (friendship, trust, information sharing) in social and developmental psychology, brand switching in consumer psychology, journal citation analysis in any discipline (including quantitative psychology), and free association tasks in any subarea of psychology. When seeking to establish a partition of the objects in such applications, it is overly restrictive to require the partitions of the row and column objects to be identical, or even the numbers of clusters for the row and column objects to be the same. This suggests the need for a biclustering approach that simultaneously establishes separate partitions of the row and column objects. We present and compare several approaches for the biclustering of one-mode matrices using data sets from the empirical literature. A suite of MATLAB m-files for implementing the procedures is provided as a Web supplement with this article. [ABSTRACT FROM AUTHOR]

One of the most important distinctions that must be made in clustering research is the difference between models (or problems) and the methods for solving those problems. Nowhere is this more evident than with the evaluation of the popular affinity propagation algorithm (apcluster.m), which is a MATLAB implementation of a neural clustering method that has received significant attention in the biological sciences and other disciplines. Several authors have undertaken comparisons of apcluster.m with methods designed for models that fall within the class of uncapacitated facility location problems (UFLPs). These comparative models include the p-center (or K-center) model and, more importantly, the p-median (or K-median) model. The results across studies are conflicting and clouded by the fact that, although similar, the optimization model underlying apcluster.m is slightly different from the p-median model and appreciably different from the pcenter model. In this paper, we clarify that apcluster.m is actually a heuristic for a 'maximization version' of another model in the class of UFLPs, which is known as the simple plant location problem (SPLP). An exact method for the SPLP is described, and the apcluster.m program is compared to a fast heuristic procedure (sasplp.m) in both a simulation experiment and across numerous datasets from the literature. Although the exact method is the preferred approach when computationally feasible, both apcluster.m and sasplp.m are efficient and effective heuristic approaches, with the latter slightly outperforming the former in most instances. [ABSTRACT FROM AUTHOR]

Because of its deterministic nature, K-means does not yield confidence information about centroids and estimated cluster memberships, although this could be useful for inferential purposes. In this paper we propose to arrive at such information by means of a non-parametric bootstrap procedure, the performance of which is tested in an extensive simulation study. Results show that the coverage of hyper-ellipsoid bootstrap confidence regions for the centroids is in general close to the nominal coverage probability. For the cluster memberships, we found that probabilistic membership information derived from the bootstrap analysis can be used to improve the cluster assignment of individual objects, albeit only in the case of a very large number of clusters. However, in the case of smaller numbers of clusters, the probabilistic membership information still appeared to be useful as it indicates for which objects the cluster assignment resulting from the analysis of the original data is likely to be correct; hence, this information can be used to construct a partial clustering in which the latter objects only are assigned to clusters. [ABSTRACT FROM AUTHOR]

The minimum-diameter partitioning problem ( MDPP) seeks to produce compact clusters, as measured by an overall goodness-of-fit measure known as the partition diameter, which represents the maximum dissimilarity between any two objects placed in the same cluster. Complete-linkage hierarchical clustering is perhaps the best-known heuristic method for the MDPP and has an extensive history of applications in psychological research. Unfortunately, this method has several inherent shortcomings that impede the model selection process, such as: (1) sensitivity to the input order of the objects, (2) failure to obtain a globally optimal minimum-diameter partition when cutting the tree at K clusters, and (3) the propensity for a large number of alternative minimum-diameter partitions for a given K. We propose that each of these problems can be addressed by applying an algorithm that finds all of the minimum-diameter partitions for different values of K. Model selection is then facilitated by considering, for each value of K, the reduction in the partition diameter, the number of alternative optima, and the partition agreement among the alternative optima. Using five examples from the empirical literature, we show the practical value of the proposed process for facilitating model selection for the MDPP. [ABSTRACT FROM AUTHOR]

Aims This study used a person-centered approach to test whether drinking motive typologies could be identified. Design Longitudinal study of college students within the Intensive Multivariate Prospective Alcohol College- Transitions ( IMPACTS) data set. Setting University campus in the United States. Participants University students (baseline n reporting alcohol motives = 2158; baseline age = 18.60 years old). Measurements The Drinking Motives Questionnaire- Revised ( DMQ-R). Findings Using Steinley & Brusco's cluster analysis approach [based on the theoretical ratio expected between the within sum of squares and the total sum of squares when the data are divided into two clusters when no cluster structure is present; the cut-off for the ratio is 0.25 for uniform (multivariate uniform) distributions and 0.36 for normal (multivariate normal) distributions], we examined whether there was evidence for distinct clusters of individuals that differed on their overall level of motives to drink. We tested the fit of a one-group (cluster) solution compared to multi-cluster solutions. Both cross-sectionally and prospectively, the data could not be partitioned into two or more clusters [regardless of whether the cut-off assuming a multivariate uniform distribution (i.e. 0.25) or the more liberal multivariate normal distribution (i.e. 0.36) was used]. These findings showed that enhancement and coping drinkers do not form two distinct groups but, rather, these motives exist on a continuum such that individuals who are high in one internal motive tend to be high in the other motive. Conclusions Coping and enhancement drinkers do not form two distinct groups. Variable-centered approaches to drinking motives may be a better alternative to classifying all drinkers as either enhancement or coping drinkers for both clinical and research endeavors. [ABSTRACT FROM AUTHOR]

Abstract: To date, the vast majority of cluster analysis applications in OM research have relied on traditional hierarchical (e.g., Ward''s algorithm) and nonhierarchical (e.g., K-means algorithms) methods. Although these venerable methods should continue to be employed effectively in the OM literature, we also believe there is a significant opportunity to expand the scope of clustering methods to emergent techniques. We provide an overview of some alternative clustering procedures (including advantages and disadvantages), identify software programs for implementing them, and discuss the circumstances where they might be employed gainfully in OM research. The implementation of emergent clustering methods in the OM literature should enable researchers to offer implications for practice that might not have been uncovered with traditional methods. [Copyright &y& Elsevier]

A measure of “clusterability” serves as the basis of a new methodology designed to preserve cluster structure in a reduced dimensional space. Similar to principal component analysis, which finds the direction of maximal variance in multivariate space, principal cluster axes find the direction of maximum clusterability in multivariate space. Furthermore, the principal clustering approach falls into the class of projection pursuit techniques. Comparisons are made with existing methodologies both in a simulation study and analysis of real-world data sets. Furthermore, a demonstration of how to interpret the results of the principal cluster axes is provided on the analysis of Supreme Court voting data and similarities between the interpretation of competing procedures (e.g., factor analysis and principal component analysis) are provided. In addition to the Supreme Court analysis, we analyze several data sets often used to test cluster analysis procedures, including Fisher's Iris data, Agresti's Crab data, and a data set on glass fragments. Finally, discussion is provided to help determine when the proposed procedure will be the most beneficial to the researcher. [ABSTRACT FROM AUTHOR]

Clusterwise p* models are developed to detect differentially functioning network models as a function of the subset of observations being considered. These models allow the identification of subgroups (i.e., clusters) of individuals who are 'structurally' different from each other. These clusters are different from those produced by standard blockmodeling of social interactions in that the goal is not necessarily to find dense subregions of the network; rather, the focus is finding subregions that are functionally different in terms of graph structure. Furthermore, the clusterwise p* approach allows for local estimation of network regions, avoiding some of the common degeneracy problems that are rampant in p* (e.g., exponential random graph) models. © 2011 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 4: 487-496, 2011 [ABSTRACT FROM AUTHOR]

Steinley (2007) provided a lower bound for the sum-of-squares error criterion function used in K-means clustering. In this article, on the basis of the lower bound, the authors propose a method to distinguish between 1 cluster (i.e., a single distribution) versus more than 1 cluster. Additionally, conditional on indicating there are multiple clusters, the procedure is extended to determine the number of clusters. Through a series of simulations, the proposed methodology is shown to outperlbrm several other commonly used procedures for determining both the presence of clusters and their number. [ABSTRACT FROM AUTHOR]

McLachlan (2011) and Vermunt (2011) each provided thoughtful replies to our original article (Steinley & Brusco, 2011). This response serves to incorporate some of their comments while simultaneously clarifying our position. We argue that greater caution against overparamaterization must be taken when assuming that clusters ,are highly elliptical in nature. Specifically, users of mixture model clustering techniques should be wary of overreliance on fit indices, and the importance of cross-validation is highlighted. Additionally, we note that K-means clustering is part of a larger family of discrete partitioning algorithms, many of which are designed to solve problems identical to those for which mixture modeling approaches are often touted. [ABSTRACT FROM AUTHOR]

This article provides a large-scale investigation into several of the properties of mixture-model clustering techniques (also referred to as latent class cluster analysis, latent profile analysis, model-based clustering, probabilistic clustering, Bayesian classification, unsupervised learning, and finite mixture models; see Vermunt & Magdison, 2002). Focus is given to the multivariate normal distribution, and 9 separate decompositions (i.e., class structures) of the covariance matrix are investigated. To provide a link to the current literature, comparisons are made with K-means clustering in 3 detailed Monte Carlo studies. The findings have implications for applied researchers in that mixture-model clustering techniques performed best when the covariance structure and number of clusters were known. However, as the information about the shape and number of clusters became unknown, degraded performance was observed for both K-means clustering and mixture-model clustering. [ABSTRACT FROM AUTHOR]

The p-median clustering model represents a combinatorial approach to partition data sets into disjoint, nonhierarchical groups. Object classes are constructed around exemplars, that is, manifest objects in the data set, with the remaining instances assigned to their closest cluster centers. Effective, state-of-the-art implementations of p-median clustering are virtually unavailable in the popular social and behavioral science statistical software packages. We present p-median clustering, including a detailed description of its mechanics and a discussion of available software programs and their capabilities. Application to a complex structured data set on the perception of food items illustrates p-median clustering. [ABSTRACT FROM AUTHOR]

The implementation of multiobjective programming methods in combinatorial data analysis is an emergent area of study with a variety of pragmatic applications in the behavioural sciences. Most notably, multiobjective programming provides a tool for analysts to model trade offs among competing criteria in clustering, seriation, and unidimensional scaling tasks. Although multiobjective programming has considerable promise, the technique can produce numerically appealing results that lack empirical validity. With this issue in mind, the purpose of this paper is to briefly review viable areas of application for multiobjective programming and, more importantly, to outline the importance of cross-validation when using this method in cluster analysis. [ABSTRACT FROM AUTHOR]

This paper develops a new procedure, called stability analysis, for K-means clustering. Instead of ignoring local optima and only considering the best solution found, this procedure takes advantage of additional information from a K-means cluster analysis. The information from the locally optimal solutions is collected in an object by object co-occurrence matrix. The co-occurrence matrix is clustered and subsequently reordered by a steepest ascent quadratic assignment procedure to aid visual interpretation of the multidimensional cluster structure. Subsequently, measures are developed to determine the overall structure of a data set, the number of clusters and the multidimensional relationships between the clusters. [ABSTRACT FROM AUTHOR]

Eight different variable selection techniques for model-based and non-model-based clustering are evaluated across a wide range of cluster structures. It is shown that several methods have difficulties when non-informative variables (i.e., random noise) are included in the model. Furthermore, the distribution of the random noise greatly impacts the performance of nearly all of the variable selection procedures. Overall, a variable selection technique based on a variance-to-range weighting procedure coupled with the largest decreases in within-cluster sums of squares error performed the best. On the other hand, variable selection methods used in conjunction with finite mixture models performed the worst. [ABSTRACT FROM AUTHOR]

A variance-to-range ratio variable weighting procedure is proposed. We show how this weighting method is theoretically grounded in the inherent variability found in data exhibiting cluster structure. In addition, a variable selection procedure is proposed to operate in conjunction with the variable weighting technique. The performances of these procedures are demonstrated in a simulation study, showing favorable results when compared with existing standardization methods. A detailed demonstration of the weighting and selection procedure is provided for the well-known Fisher Iris data and several synthetic data sets. [ABSTRACT FROM AUTHOR]

Given that a minor condition holds (e.g., the number of variables is greater than the number of clusters), a nontrivial lower bound for the sum of squares error criterion in K -means clustering is derived. By calculating the lower bound for several different situations, a method is developed to determine the adequacy of cluster solution based on the observed sum-of squares error as compared to the minimum sum-of-squares error. [ABSTRACT FROM AUTHOR]

Using the cluster generation procedure proposed by D. Steinley and R. Henson (2005), the author investigated the performance of K-means clustering under the following scenarios: (a) different probabilities of cluster overlap; (b) different types of cluster overlap; (c) varying samples sizes, clusters, and dimensions; (d) different multivariate distributions of clusters; and (e) various multidimensional data structures. The results are evaluated in terms of the Hubert--Arabie adjusted Rand index, and several observations concerning the performance of K-means clustering are made. Finally, the article concludes with the proposal of a diagnostic technique indicating when the partitioning given by a K-means cluster analysis can be trusted. By combining the information from several observable characteristics of the data (number of clusters, number of variables, sample size, etc.) with the prevalence of unique local optima in several thousand implementations of the K-means algorithm, the author provides a method capable of guiding key data-analysis decisions. [ABSTRACT FROM AUTHOR]

The primary method for validating cluster analysis techniques is through Monte Carlo simulations that rely on generating data with known cluster structure (e.g., Milligan 1996). This paper defines two kinds of data generation mechanisms with cluster overlap, marginal and joint; current cluster generation methods are framed within these definitions. An algorithm generating overlapping clusters based on shared densities from several different multivariate distributions is proposed and shown to lead to an easily understandable notion of cluster overlap. Besides outlining the advantages of generating clusters within this framework, a discussion is given of how the proposed data generation technique can be used to augment research into current classification techniques such as finite mixture modeling, classification algorithm robustness, and latent profile analysis. [ABSTRACT FROM AUTHOR]

This article provides an investigation of cluster validation indices that relates 4 of the indices to the L. Hubert and P. Arabie (1985) adjusted Rand index--the cluster validation measure of choice (G. W. Milligan & M. C. Cooper, 1986). It is shown how these other indices can be "roughly" transformed into the same scale as the adjusted Rand index. Furthermore, in-depth explanations are given of why classification rates should not be used in cluster validation research. The article concludes by summarizing several properties of the adjusted Rand index across many conditions and provides a method for testing the significance of observed adjusted Rand indices. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including the fractionally-supervised classification method for unsupervised and supervised learning, semi-definite programming (SDP) method for anlyzing data, and exact algorithm for clustering.