Clustering Ordinal Data via Latent Variable Models

McParland, Damien; Gormley, Isobel Claire

doi:10.1007/978-3-319-00035-0_12

Cited by 11 publications

(7 citation statements)

References 15 publications

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“…Recent contributions have defined clustering algorithms that are specific to ordinal data. Several contributions use Gaussian latent variables to model the data: in McParland and Gormley (), the observed data are viewed as discrete versions of an underlying latent Gaussian variable. In Ranalli and Rocci (), the observed categorical variables are considered as a discretization of an underlying finite mixture of Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

Analysing a Quality-of-Life Survey by Using a Coclustering Model for Ordinal Data and Some Dynamic Implications

Selosse

Jacques

Biernacki

et al. 2019

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary The data set that motivated this work is a psychological survey on women affected by a breast tumour. Patients replied at different stages of their treatment to questionnaires with answers on an ordinal scale. The questions relate to aspects of their life referred to as ‘dimensions’. To assist psychologists in analysing the results, it is useful to highlight the structure of the data set. The clustering method achieves this by creating groups of individuals that are depicted by a representative of the group. From a psychological position, it is also useful to observe how questions may be clustered. The simultaneous clustering of both patients and questions is called ‘coclustering’. However, placing questions in the same group when they are not related to the same dimension does not make sense from a psychological perspective. Therefore, constrained coclustering was performed to prevent questions of different dimensions from being placed in the same column cluster. The evolution of coclusters over time was then investigated. The method uses a constrained latent block model embedding a probability distribution for ordinal data. Parameter estimation relies on a stochastic expectation–maximization algorithm associated with a Gibbs sampler, and the integrated completed likelihood–Bayesian information criterion is used to select the number of coclusters.

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Section: Introductionmentioning

confidence: 99%

Analysing a Quality-of-Life Survey by Using a Coclustering Model for Ordinal Data and Some Dynamic Implications

Selosse

Jacques

Biernacki

et al. 2019

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…McNicholas, ; ). They can be used to cluster various types of data, such as continuous (Banfield & Raftery, ; McNicholas & Murphy, ; Andrews & McNicholas, ), categorical (Goodman, ); Gollini & Murphy, ; Marbac, Biernacki, & Vandewalle, ), ordinal (Jollois & Nadif, ; McParland & Gormley, ; Biernacki & Jacques, ), mixed (Browne & McNicholas, ; Hennig & Liao, ; Kosmidis & Karlis, ; McParland & Gormley, ), and other data types. Because of their flexibility, mixture models are employed in functional data clustering.…”

Section: Introductionmentioning

confidence: 99%

Model‐based clustering for spatiotemporal data on air quality monitoring

2017

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Data extracted from air quality monitoring can require spatiotemporal clustering techniques. Of late, many clustering techniques are based on mixture models; however, there is a shortage of model‐based approaches for spatiotemporal data. A new mixture to cluster spatiotemporal data, named STM, is introduced, and generic identifiability is proved. The resulting model defines each mixture component as a mixture of autoregressive polynomial regressions in which the weights consider the spatial and temporal information with logistic links. Under the maximum likelihood framework, parameter estimation is carried out via an expectation–maximization algorithm while classical information criteria can be used for model selection. The proposed model is applied to air quality monitoring data from the periphery of Paris considering one of the critical pollutants, nitrogen dioxide, at different times during the day. The STM model is implemented in the R package SpaTimeClust.

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“…Finite mixture models (McLachlan and Peel, 2004;McNicholas, 2016) allows assessment of this unknown partition among observations. They permit dealing with continuous (Banfield and Raftery, 1993;Celeux and Govaert, 1995;Morris and McNicholas, 2016), categorical (Meila and Jordan, 2001;McParland and Gormley, 2013;, integer (Karlis and Meligkotsidou, 2007) or mixed data (Browne and McNicholas, 2012;Kosmidis and Karlis, 2015;Marbac et al, 2015). When observations are described by many variables, the within components independence permits achievement of the clustering goal, by limiting the number of parameters (Goodman, 1974;Hand and Yu, 2001;Moustaki and Papageorgiou, 2005).…”

Section: Introductionmentioning

confidence: 99%

Variable selection for mixed data clustering: a model-based approach

Marbac¹,

Sedki²

2017

Preprint

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We propose two approaches for selecting variables in latent class analysis (i.e., mixture model assuming within component independence), which is the common model-based clustering method for mixed data. The first approach consists in optimizing the BIC with a modified version of the EM algorithm. This approach simultaneously performs both model selection and parameter inference. The second approach consists in maximizing the MICL, which considers the clustering task, with an algorithm of alternate optimization. This approach performs model selection without requiring the maximum likelihood estimates for model comparison, then parameter inference is done for the unique selected model. Thus, the benefits of both approaches is to avoid the computation of the maximum likelihood estimates for each model comparison. Moreover, they also avoid the use of the standard algorithms for variable selection which are often suboptimal (e.g. stepwise method) and computationally expensive. The case of data with missing values is also discussed. The interest of both proposed criteria is shown on simulated and real data.

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Clustering Ordinal Data via Latent Variable Models

Cited by 11 publications

References 15 publications

Analysing a Quality-of-Life Survey by Using a Coclustering Model for Ordinal Data and Some Dynamic Implications

Analysing a Quality-of-Life Survey by Using a Coclustering Model for Ordinal Data and Some Dynamic Implications

Model‐based clustering for spatiotemporal data on air quality monitoring

Variable selection for mixed data clustering: a model-based approach

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