Two new matrix-variate distributions with application in model-based clustering

Tomarchio, Salvatore D.; Punzo, Antonio; Bagnato, Luca

doi:10.1016/j.csda.2020.107050

Cited by 23 publications

(11 citation statements)

References 18 publications

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“…To further increase the parsimony of our model, constrained parameterizations of the covariance matrices can be employed, by following the approaches of Sarkar et al (2020), Subedi et al (2013), Punzo and Ingrassia (2015), and Mazza et al (2018). Furthermore, to accommodate skewness or mild outliers in the data, skewed or heavy tailed matrix-variate distributions could also be considered for the mixing components of the model (e.g., Melnykov and Zhu 2018;Gallaugher and McNicholas 2018;Tomarchio et al 2020).…”

Section: Discussionmentioning

confidence: 99%

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Matrix Normal Cluster-Weighted Models

2021

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Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal with regression data. However, they assume assignment independence, i.e., the allocation of data points to the clusters is made independently of the distribution of the covariates. To take into account the latter aspect, finite mixtures of regressions with random covariates, also known as cluster-weighted models (CWMs), have been proposed in the univariate and multivariate literature. In this paper, the CWM is extended to matrix data, e.g., those data where a set of variables are simultaneously observed at different time points or locations. Specifically, the cluster-specific marginal distribution of the covariates and the cluster-specific conditional distribution of the responses given the covariates are assumed to be matrix normal. Maximum likelihood parameter estimates are derived using an expectation-conditional maximization algorithm. Parameter recovery, classification assessment, and the capability of the Bayesian information criterion to detect the underlying groups are investigated using simulated data. Finally, two real data applications concerning educational indicators and the Italian non-life insurance market are presented.

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Section: Discussionmentioning

confidence: 99%

“…In the following, by adopting the notation used in Tomarchio et al (2020), the quantities marked with one dot correspond to the updates at the previous iteration and those marked with two dots represent the updates at the current iteration.…”

Section: Parameter Estimationmentioning

confidence: 99%

Matrix Normal Cluster-Weighted Models

2021

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“…In this paper, we propose a new Bayesian model for network data with matrix-variate t errors which accounts for heavy tails (Tomarchio et al, 2020 ). The inferential procedure is based on data augmentation and conjugate prior distributions that allow for an efficient posterior sampling scheme.…”

Section: Introductionmentioning

confidence: 99%

A Matrix-Variate t Model for Networks

Billio

Casarin

Costola

et al. 2021

Front. Artif. Intell.

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Networks represent a useful tool to describe relationships among financial firms and network analysis has been extensively used in recent years to study financial connectedness. An aspect, which is often neglected, is that network observations come with errors from different sources, such as estimation and measurement errors, thus a proper statistical treatment of the data is needed before network analysis can be performed. We show that node centrality measures can be heavily affected by random errors and propose a flexible model based on the matrix-variate t distribution and a Bayesian inference procedure to de-noise the data. We provide an application to a network among European financial institutions.

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“…Recently, the matrix mixture model was extended for various non-normal matrix data: Refs. [6,7] proposed finite mixture of matrix skewed distributions, and [8] introduced two matrix-variate distributions-both elliptical heavy-tailed generalizations of the matrix-variate normal distribution that are used in a finite mixture model. Ref.…”

Section: Introductionmentioning

confidence: 99%

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

Heo

Baek

2021

Entropy

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Along with advances in technology, matrix data, such as medical/industrial images, have emerged in many practical fields. These data usually have high dimensions and are not easy to cluster due to their intrinsic correlated structure among rows and columns. Most approaches convert matrix data to multi dimensional vectors and apply conventional clustering methods to them, and thus, suffer from an extreme high-dimensionality problem as well as a lack of interpretability of the correlated structure among row/column variables. Recently, a regularized model was proposed for clustering matrix-valued data by imposing a sparsity structure for the mean signal of each cluster. We extend their approach by regularizing further on the covariance to cope better with the curse of dimensionality for large size images. A penalized matrix normal mixture model with lasso-type penalty terms in both mean and covariance matrices is proposed, and then an expectation maximization algorithm is developed to estimate the parameters. The proposed method has the competence of both parsimonious modeling and reflecting the proper conditional correlation structure. The estimators are consistent, and their limiting distributions are derived. We applied the proposed method to simulated data as well as real datasets and measured its clustering performance with the clustering accuracy (ACC) and the adjusted rand index (ARI). The experiment results show that the proposed method performed better with higher ACC and ARI than those of conventional methods.

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Two new matrix-variate distributions with application in model-based clustering

Cited by 23 publications

References 18 publications

Matrix Normal Cluster-Weighted Models

Matrix Normal Cluster-Weighted Models

A Matrix-Variate t Model for Networks

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

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