Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data

Vera, José Ramón Navarro; Macías, Rodrigo; Heiser, Willem J.

doi:10.1007/s00357-013-9144-5

Cited by 9 publications

(10 citation statements)

References 37 publications

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“…, the global MSCRU function can be conditionally minimized in terms of E by minimizing As noted in Vera et al (2013), minimizing 2 (E ) produces a partition equivalent to Kmeans clustering, considering the centring of both i and t . Each row e i of E , i = 1, …, N, is assigned to the cluster…”

Section: Assignment Step For Fixed Unfolding Parameter Estimatesmentioning

confidence: 99%

“…In our study, the model was implemented using MATLAB and its T A B L E 6 Estimated distances between centres of clusters and environmental issues in three dimensions. performance analysed in a Monte Carlo experiment, the results of which were compared with those obtained using the cluster difference scaling model of Vera et al (2013). In general, both the CDU and the MSCRU model obtained good results in terms of the estimated classification, with a slight advantage to the CDU model, but with greater CPU time.…”

Section: Conc Lusions a N D E X T Ensionsmentioning

confidence: 99%

“…For the unfolding model, Heiser (1993) formulated a least squares method for combining it with the clustering of individuals by using the well-known Kmeans loss function (Hartigan & Wong, 1979). In a follow-up study, Vera et al (2013) proposed a least squares procedure that performs clustering in both the rows and columns of a preference matrix while the cluster centres are represented in a lowdimensional Euclidean space. Given that the model considers a linear transformation with fixed slope, it does not suffer from the problem of degenerate solutions (Busing, 2010, Ch.…”

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confidence: 99%

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A cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals

Macías,

Vera,

Heiser

2024

Brit J Math & Statis

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Clustering and spatial representation methods are often used in combination, to analyse preference ratings when a large number of individuals and/or object is involved. When analysed under an unfolding model, row‐conditional linear transformations are usually most appropriate when the goal is to determine clusters of individuals with similar preferences. However, a significant problem with transformations that include both slope and intercept is the occurrence of degenerate solutions. In this paper, we propose a least squares unfolding method that performs clustering of individuals while simultaneously estimating the location of cluster centres and object locations in low‐dimensional space. The method is based on minimising the mean squared centred residuals of the preference ratings with respect to the distances between cluster centres and object locations. At the same time, the distances are row‐conditionally transformed with optimally estimated slope parameters. It is computationally efficient for large datasets, and does not suffer from the appearance of degenerate solutions. The performance of the method is analysed in an extensive Monte Carlo experiment. It is illustrated for a real data set and the results are compared with those obtained using a two‐step clustering and unfolding procedure.

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Section: Assignment Step For Fixed Unfolding Parameter Estimatesmentioning

confidence: 99%

Section: Conc Lusions a N D E X T Ensionsmentioning

confidence: 99%

mentioning

confidence: 99%

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A cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals

Macías,

Vera,

Heiser

2024

Brit J Math & Statis

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“…Here we combine suitable clustering methods for preference rankings with Multidimensional unfolding techniques. Our approach is similar to the Cluster Differences Unfolding (CDU) (Vera et al, 2013), which can be considered as the natural extension to Unfolding of the Cluster Difference Scaling (CDS) (Heiser, 1993). The main difference is that CDU, which is devoted to metric Unfolding, performs a cluster analysis over both the sets of individuals and objects, producing a configuration plot that shows the bari-centers of the sets retaining their preference relationship.…”

Section: Clustering Preference Datamentioning

confidence: 99%

Projection Clustering Unfolding: A New Algorithm for Clustering Individuals or Items In A Preference Matrix

2018

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In the framework of preference rankings, the interest can lie in clustering individuals or items in order to reduce the complexity of the preference space for an easier interpretation of collected data. The last years have seen a remarkable flowering of works about the use of decision tree for clustering preference vectors. As a matter of fact, decision trees are useful and intuitive, but they are very unstable: small perturbations bring big changes. This is the reason why it could be necessary to use more stable procedures in order to clustering ranking data. In this work, a Projection Clustering Unfolding (PCU) algorithm for preference data will be proposed in order to extract useful information in a low-dimensional subspace by starting from an high but mostly empty dimensional space. Comparison between unfolding configurations and PCU solutions will be carried out through Procrustes analysis. Keywords Projetion pursuit • Preference data • Clustering rankings Riassunto Nell'ambito delle classifiche di preferenza, uno degli obiettivi potrebbe consistere nel raggruppare gli individui o gli oggetti al fine di ridurre la complessità dello spazio di preferenza, per un'interpretazione più semplice dei dati raccolti. Gli ultimi anni hanno visto una notevole fioritura di articoli sull'uso degli alberi decisionali per il raggruppamento dei vettori

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“…Such a clustering reduces the number of objects in the graphical display and therefore makes the final result better interpretable. In a least squares unfolding framework, classification and representation methods have already been developed to enhance the interpretation of the solution and/or to obtain an adequate fit of the model when the number of elements is large (Vera et al, 2013). In a probabilistic context, mixture distribution formulations are the natural way to proceed.…”

Section: Introductionmentioning

confidence: 99%

A latent class distance association model for cross‐classified data with a categorical response variable

Vera

Rooij

Heiser

2014

Brit J Math & Statis

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In this paper we propose a latent class distance association model for clustering in the predictor space of large contingency tables with a categorical response variable. The rows of such a table are characterized as profiles of a set of explanatory variables, while the columns represent a single outcome variable. In many cases such tables are sparse, with many zero entries, which makes traditional models problematic. By clustering the row profiles into a few specific classes and representing these together with the categories of the response variable in a low-dimensional Euclidean space using a distance association model, a parsimonious prediction model can be obtained. A generalized EM algorithm is proposed to estimate the model parameters and the adjusted Bayesian information criterion statistic is employed to test the number of mixture components and the dimensionality of the representation. An empirical example highlighting the advantages of the new approach and comparing it with traditional approaches is presented.

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Cluster Differences Unfolding for Two-Way Two-Mode Preference Rating Data

Cited by 9 publications

References 37 publications

A cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals

A cluster differences unfolding method for large datasets of preference ratings on an interval scale: Minimizing the mean squared centred residuals

Projection Clustering Unfolding: A New Algorithm for Clustering Individuals or Items In A Preference Matrix

A latent class distance association model for cross‐classified data with a categorical response variable

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