A Bayesian Approach for Model-Based Clustering of Several Binary Dissimilarity Matrices: The dmbc Package in R
Dublin Core
Title
A Bayesian Approach for Model-Based Clustering of Several Binary Dissimilarity Matrices: The dmbc Package in R
Subject
: Bayesian data analysis, dissimilarity matrices, information criteria, multidimensional scaling, MCMC, MDS, mixture models, model-based clustering, three-way MDS.
Description
We introduce the new package dmbc that implements a Bayesian algorithm for clustering a set of binary dissimilarity matrices within a model-based framework. Specifically, we
consider the case when S matrices are available, each describing the dissimilarities among
the same n objects, possibly expressed by S subjects (judges), or measured under different
experimental conditions, or with reference to different characteristics of the objects themselves. In particular, we focus on binary dissimilarities, taking values 0 or 1 depending on
whether or not two objects are deemed as dissimilar. We are interested in analyzing such
data using multidimensional scaling (MDS). Differently from standard MDS algorithms,
our goal is to cluster the dissimilarity matrices and, simultaneously, to extract an MDS
configuration specific for each cluster. To this end, we develop a fully Bayesian three-way
MDS approach, where the elements of each dissimilarity matrix are modeled as a mixture
of Bernoulli random vectors. The parameter estimates and the MDS configurations are
derived using a hybrid Metropolis-Gibbs Markov Chain Monte Carlo algorithm. We also
propose a BIC-like criterion for jointly selecting the optimal number of clusters and latent
space dimensions. We illustrate our approach referring both to synthetic data and to a
publicly available data set taken from the literature. For the sake of efficiency, the core
computations in the package are implemented in C/C++. The package also allows the
simulation of multiple chains through the support of the parallel package.
consider the case when S matrices are available, each describing the dissimilarities among
the same n objects, possibly expressed by S subjects (judges), or measured under different
experimental conditions, or with reference to different characteristics of the objects themselves. In particular, we focus on binary dissimilarities, taking values 0 or 1 depending on
whether or not two objects are deemed as dissimilar. We are interested in analyzing such
data using multidimensional scaling (MDS). Differently from standard MDS algorithms,
our goal is to cluster the dissimilarity matrices and, simultaneously, to extract an MDS
configuration specific for each cluster. To this end, we develop a fully Bayesian three-way
MDS approach, where the elements of each dissimilarity matrix are modeled as a mixture
of Bernoulli random vectors. The parameter estimates and the MDS configurations are
derived using a hybrid Metropolis-Gibbs Markov Chain Monte Carlo algorithm. We also
propose a BIC-like criterion for jointly selecting the optimal number of clusters and latent
space dimensions. We illustrate our approach referring both to synthetic data and to a
publicly available data set taken from the literature. For the sake of efficiency, the core
computations in the package are implemented in C/C++. The package also allows the
simulation of multiple chains through the support of the parallel package.
Creator
Sergio Venturini
Source
https://www.jstatsoft.org/article/view/v100i16
Publisher
Università Cattolica del Sacro Cuore
Date
November 2021
Contributor
Fajar bagus W
Format
PDF
Language
English
Type
Text
Files
Collection
Citation
Sergio Venturini, “A Bayesian Approach for Model-Based Clustering of Several Binary Dissimilarity Matrices: The dmbc Package in R,” Repository Horizon University Indonesia, accessed April 4, 2025, https://repository.horizon.ac.id/items/show/8229.