A Bayesian Approach for Model-Based Clustering of Several Binary Dissimilarity Matrices: The dmbc Package in R

被引:1
|
作者
Venturini, Sergio [1 ]
Piccarreta, Raffaella [2 ]
机构
[1] Univ Cattolica Sacro Cuore, Dipartimento Sci Econ & Sociali, Via Bissolati 74, I-26100 Cremona, Italy
[2] Univ Commerciale L Bocconi, Dipartimento Sci Decis, Via Rontgen 1, I-20136 Milan, Italy
来源
JOURNAL OF STATISTICAL SOFTWARE | 2021年 / 100卷 / 16期
关键词
Bayesian data analysis; dissimilarity matrices; information criteria; multidimensional scaling; MCMC; MDS; mixture models; model-based clustering; three-way MDS; CHAIN MONTE-CARLO; EMPIRICAL PAIRWISE ORDERINGS; MAXIMUM-LIKELIHOOD METHOD; INDIVIDUAL-DIFFERENCES; MIXTURE;
D O I
10.18673/jss.v100.i16
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
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.
引用
收藏
页码:1 / 35
页数:35
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