Biclustering of Gene Expression Data by an Extension of Mixtures of Factor Analyzers

Martella, Francesca; Alfó, Marco; Vichi, Maurizio

doi:10.2202/1557-4679.1078

Cited by 18 publications

(46 citation statements)

References 20 publications

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“…Our modelling framework is based on the biclustering approach proposed by Martella et al (2008), where the idea is to approximate the data density by a mixture of Gaussian distributions with an appropriate component-specific covariance structure. More precisely, we consider a partition of indicators by imposing a binary and row stochastic matrix representing column partition, whereas the traditional mixture approach is used to defined university clustering.…”

Section: Model-based Biclusteringmentioning

confidence: 99%

“…In Section 2, we describe the data, introduce the indicators and provide summary (descriptive) statistics. The model-based biclustering used for the analysis has been proposed by Martella et al (2008) and described in Section 3, along with computational details needed to obtain parameter estimates. Results are discussed in Section 4, whereas Section 5 provides conclusions and future development.…”

Section: Introductionmentioning

confidence: 99%

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A biclustering approach to university performances: an Italian case study

Raponi

Martella

Maruotti

2015

Journal of Applied Statistics

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University evaluation is a topic of increasing concern in Italy as well as in other countries. In empirical analysis, university activities and performances are generally measured by means of indicator variables, summarizing the available information under different perspectives. In this paper, we argue that the evaluation process is a complex issue that can not be addressed by a simple descriptive approach and thus association between indicators and similarities among the observed universities should be accounted for. Particularly, we examine faculty-level data collected from different sources, covering 55 Italian Economics faculties in the academic year 2009/2010. Making use of a clustering framework, we introduce a biclustering model that accounts for both homogeneity/heterogeneity among faculties and correlations between indicators.Our results show that there are two substantial different performances between universities which can be strictly related to the nature of the institutions, namely the Private and Public profiles . Each of the two groups has its own peculiar features and its own group-specific list of priorities, strengths and weaknesses. Thus, we suggest that caution should be used in interpreting standard university rankings as they generally * Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Roma, Italy † Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Roma, Italy ‡ Southampton Statistical Sciences Research Institute, Southampton, UK 1 do not account for the complex structure of the data.

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Section: Model-based Biclusteringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A biclustering approach to university performances: an Italian case study

Raponi

Martella

Maruotti

2015

Journal of Applied Statistics

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“…Classical joint clustering methods were based on a distance (Hartigan, 1972). The modern methods can be divided into two subcategories: (i) the frequentist approach where the statistical parameters of the model are treated as fixed unknowns, for example mixture models (Lazzeroni and Owen, 2002); and (ii) the Bayesian approach where a prior distribution is associated to the model parameters (Gu and Liu, 2008;Martella et al, 2008;Zhang, 2010), for a comprehensive review see Madeira and Oliveira (2004), Tanay et al (2005), and Busygin et al (2008). In modern joint clustering, observations in each joint cluster are supposed to be drawn independently of a parametric form (Sheng et al, 2003;Gan et al, 2008;van Uitert et al, 2008;Martella et al, 2008;Hochreiter et al, 2010).…”

Section: Figurementioning

confidence: 99%

“…Classical joint clustering methods were based on a distance (Hartigan, ). The modern methods can be divided into two subcategories: (i) the frequentist approach where the statistical parameters of the model are treated as fixed unknowns, for example mixture models (Lazzeroni and Owen, ); and (ii) the Bayesian approach where a prior distribution is associated to the model parameters (Gu and Liu, ; Martella et al., ; Zhang, ), for a comprehensive review see Madeira and Oliveira (), Tanay et al. (), and Busygin et al.…”

Section: Introductionmentioning

confidence: 99%

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Agglomerative joint clustering of metabolic data with spike at zero: A Bayesian perspective

Nia

Ghannad-Rezaie

2015

Biometrical J

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In many biological applications, for example high-dimensional metabolic data, the measurements consist of several continuous measurements of subjects or tissues over multiple attributes or metabolites. Measurement values are put in a matrix with subjects in rows and attributes in columns. The analysis of such data requires grouping subjects and attributes to provide a primitive guide toward data modeling. A common approach is to group subjects and attributes separately, and construct a two-dimensional dendrogram tree, once on rows and then on columns. This simple approach provides a grouping visualization through two separate trees, which is difficult to interpret jointly. When a joint grouping of rows and columns is of interest, it is more natural to partition the data matrix directly. Our suggestion is to build a dendrogram on the matrix directly, thus generalizing the two-dimensional dendrogram tree to a three-dimensional forest. The contribution of this research to the statistical analysis of metabolic data is threefold. First, a novel spike-and-slab model in various hierarchies is proposed to identify discriminant rows and columns. Second, an agglomerative approach is suggested to organize joint clusters. Third, a new visualization tool is invented to demonstrate the collection of joint clusters. The new method is motivated over gas chromatography mass spectrometry (GCMS) metabolic data, but can be applied to other continuous measurements with spike at zero property.

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A family of mixture models for biclustering

Subedi

2021

Statistical Analysis

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Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known a priori. It is being increasingly used in bioinformatics, text analytics, and so on. Previously, biclustering has been introduced in a model‐based clustering framework by utilizing a structure similar to a mixture of factor analyzers. In such models, observed variables X are modeled using a latent variable U that is assumed to be from Nfalse(0,Ifalse). Clustering of variables are introduced by imposing constraints on the entries of the factor loading matrix to be 0 and 1 that results in block diagonal covariance matrices. However, this approach is overly restrictive as off‐diagonal elements in the blocks of the covariance matrices can only be 1 which can lead to unsatisfactory model fit on complex data. Here, the latent variable U is assumed to be from a Nfalse(0,Tfalse) where T is a diagonal matrix. This ensures that the off‐diagonal terms in the block matrices within the covariance matrices are non‐zero and not restricted to be 1. This leads to a superior model fit on complex data. A family of models is developed by imposing constraints on the components of the covariance matrix. For parameter estimation, an alternating expectation conditional maximization (AECM) algorithm is used. Finally, the proposed method is illustrated using simulated and real datasets.

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Biclustering of Gene Expression Data by an Extension of Mixtures of Factor Analyzers

Cited by 18 publications

References 20 publications

A biclustering approach to university performances: an Italian case study

A biclustering approach to university performances: an Italian case study

Agglomerative joint clustering of metabolic data with spike at zero: A Bayesian perspective

A family of mixture models for biclustering

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