Model-based co-clustering for ordinal data

Jacques, Julien; Biernacki, Christophe

doi:10.1016/j.csda.2018.01.014

Cited by 53 publications

(21 citation statements)

References 23 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%

“…In a coclustering context, Jacques and Biernacki () defined a model‐based algorithm relying on the latent block model (Govaert and Nadif, ) embedding the BOS distribution. Nevertheless, the weakness of this model is its inability to treat variables with different numbers of levels.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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%

See 1 more Smart Citation

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bonzo and Hermosilla (2002) first introduced multivariate statistical methods into panel data analysis and used probabilistic connection functions to improve clustering analysis algorithms for panel data analysis [5]. Subsequent research involves fixed effect [6], time series [2,7], ordinal data [8], parameter estimation [9,10], etc. However, the statistical method performs cluster analysis, which has certain requirements on the number of samples.…”

Section: Introductionmentioning

confidence: 99%

A novel grey object matrix incidence clustering model for panel data and its application

Liu

2019

Scientia Iranica

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In order to fully excavate the information contained in the multi-index and small sample panel data, one take decision objects as the research object, and the development state matrix and the development speed matrix of the decision objects are defined by considering the cross-section information and time information of the decision objects, and then the distances among the objects over the indexes are given. Based on grey incidence analysis, the absolute difference and relative difference between the measured value matrices are used to characterize and measure the close degree of the development state matrix and the development level matrix of the decision objects, so that the grey object matrix absolute incidence analysis model is established. And then, according to the grey incidence degree between the objects, the objects can be clustered based on the hierarchical clustering algorithm. Finally, a clustering problem of regional patent research and development (R&D) efficiency is used to verify the validity and rationality of the proposed model.

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“…Thus, the large data matrix can be summarized by a reduced number of blocks of data (or co-clusters). If the earliest (and most cited) method is probably due to Hartigan (1972), model-based approaches have recently proved their efficiency either for continuous, binary, categorical or contingency data (Govaert and Nadif, 2013;Jacques and Biernacki, 2017). Those approaches rely on the latent block model (LBM) (Govaert and Nadif, 2013), which tackles combinatorial issues by assuming local independence, i.e.…”

Section: Introductionmentioning

confidence: 99%

The Functional Latent Block Model for the Co-Clustering of Electricity Consumption Curves

Bouveyron

Bozzi

Jacques

et al. 2018

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary.As a consequence of the recent policies for smart meter development, electricity operators are nowadays able to collect data on electricity consumption widely and with a high frequency. This is in particular the case in France where EDF will be able soon to remotely record the consumption of its 27 millions clients every 30 minutes. We propose in this work a new co-clustering methodology, based on the functional latent block model (funLBM), which allows to build "summaries" of these large consumption data through coclustering. The funLBM model extends the usual latent block model to the functional case by assuming that the curves of one block live in a low-dimensional functional subspace. Thus, funLBM is able to model and cluster large data set with high-frequency curves. An SEM-Gibbs algorithm is proposed for model inference. An ICL criterion is also derived to address the problem of choosing the number of row and column groups. Numerical experiments on simulated and original Linky data show the usefulness of the proposed methodology.

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Model-based co-clustering for ordinal data

Cited by 53 publications

References 23 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

A novel grey object matrix incidence clustering model for panel data and its application

The Functional Latent Block Model for the Co-Clustering of Electricity Consumption Curves

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