Estimation and selection for the latent block model on categorical data

Keribin, Christine; Brault, Vincent; Celeux, Gilles; Govaert, Gérard

doi:10.1007/s11222-014-9472-2

Cited by 96 publications

(98 citation statements)

References 20 publications

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“…In particular, Keribin et al . () detailed how to express ICL‐BIC for the general case of categorical data and Jacques and Biernacki () for the specific case of ordinal data by using the BOS model. In the present work, ICL‐BIC is therefore adapted for the constrained latent block model:

\begin{matrix} ICL‐BIC (G, H_{1}, \dots, H_{D}) = & log {p false(\overset{x}{true}, \overset{v}{true}, {\overset{false^}{boldw}}^{1}, \dots, {\overset{false^}{boldw}}^{D}; \overset{θ}{true} false)} \\ - \frac{G - 1}{2} log false(N false) - \underset{d}{false\sum} \frac{H_{d} - 1}{2} log false(J_{d} false) - \underset{d}{false\sum} \frac{G H_{d}}{2} log false(N J_{d} false), \end{matrix}

where

\overset{false^}{boldv}, {\overset{w}{true}}^{1}, \dots, {\overset{w}{true}}^{D}

are the row and column partitions that are discovered by the SEM algorithm, and

\overset{θ}{true}

is the corresponding estimated model parameter.…”

Section: Methodsmentioning

confidence: 99%

“…The key point is that the dependence structure vanishes as the ICL relies on the complete latent block information .v, w/, instead of integrating it out as is the case for the BIC. In particular, Keribin et al (2015) detailed how to express ICL-BIC for the general case of categorical data and Jacques and Biernacki (2018) for the specific case of ordinal data by using the BOS model. In the present work, ICL-BIC is therefore adapted for the constrained latent block model: ICL-BIC.G, H 1 , : : : , H D / = log{p.x,v,ŵ 1 , : : :…”

Section: Model Selectionmentioning

confidence: 99%

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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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\begin{matrix} ICL‐BIC (G, H_{1}, \dots, H_{D}) = & log {p false(\overset{x}{true}, \overset{v}{true}, {\overset{false^}{boldw}}^{1}, \dots, {\overset{false^}{boldw}}^{D}; \overset{θ}{true} false)} \\ - \frac{G - 1}{2} log false(N false) - \underset{d}{false\sum} \frac{H_{d} - 1}{2} log false(J_{d} false) - \underset{d}{false\sum} \frac{G H_{d}}{2} log false(N J_{d} false), \end{matrix}

where

\overset{false^}{boldv}, {\overset{w}{true}}^{1}, \dots, {\overset{w}{true}}^{D}

are the row and column partitions that are discovered by the SEM algorithm, and

\overset{θ}{true}

is the corresponding estimated model parameter.…”

Section: Methodsmentioning

confidence: 99%

Section: Model Selectionmentioning

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

View full text Add to dashboard Cite

show abstract

“…Alternatively, the E-step can be replaced by a S-step by using a SEM algorithm instead of EM (see details on SEM in Section 2.1). In the S-step, random couples (z, w) (conditionnally to x) are drawn sequentially by the following two-step Gibbs algorithm (see more details in [26]): Z|x, w; θ and W|x, z; θ. Estimating the block membership designed by the pair (z, w) can then be performed by a SE algorithm similar to this one described in Section 2.1.…”

Section: Model-based Co-clusteringmentioning

confidence: 99%

“…Estimation of the block number In addition, a specific expression of the ICL criterion (3) can be invoked for selecting the pair (K, L) (see [32] and [26] which provide ICL expressions for the Gaussian situation and for the Bernoulli/multinomial case, respectively).…”

Section: Model-based Co-clusteringmentioning

confidence: 99%

“…We fix two individual clusters (K = 2) and five variable clusters (L = 5), only units u being to be estimated. Obviously, the couple (K, L) could be also estimated by a model selection process [26], but it would add here some useless complexity on the model collection, whereas we have already many models in competition just by introducing flexibility in units. We involve the r BlockCluster package [6], available on the CRAN, for performing estimations associated to all competing units.…”

Section: A Binary Data Set With Natural Initial Unitsmentioning

confidence: 99%

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Unifying data units and models in (co-)clustering

Biernacki

Lourme

2018

Adv Data Anal Classif

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Statisticians are already aware that any modelling process issue (exploration, prediction) is wholly data unit dependent, to the extend that it should be impossible to provide a statistical outcome without specifying the couple (unit,model). In this work, this general principle is formalized with a particular focus in model-based clustering and co-clustering in the case of possibly mixed data types (continuous and/or categorical and/or counting features), being also the opportunity to revisit what the related data units are. Such a formalization allows to raise three important spots: (i) the couple (unit,model) is not identifiable so that different interpretations unit/model of the same whole modelling process are always possible; (ii) combining different "classical" units with different "classical" models should be an interesting opportunity for a cheap, wide and meaningful enlarging of the whole modelling process family designed by the couple (unit,model); (iii) if necessary, this couple, up to the non identifiability property, could be selected by any traditional model selection criterion. Some experiments on real data sets illustrate in detail practical benefits from the previous three spots.

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