Studying crime trends in the USA over the years 2000–2012

Melnykov, Volodymyr; Zhu, Xuwen

doi:10.1007/s11634-018-0326-1

Cited by 38 publications

(17 citation statements)

References 29 publications

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“…They are reported in Fig. 1, for the full 5-year data, as done by Melnykov and Zhu (2019). The bimodality in all these histograms seems to suggest the presence of two groups in the data, validating the findings of Millo and Carmeci (2011).…”

Section: Insurance Datasupporting

confidence: 76%

“…Indeed, for a MN distribution, ⊗ = * ⊗ * if * = a and * = a −1 . As a result, and are identifiable up to a multiplicative constant a (Melnykov and Zhu 2019). According to McNicholas (2017, 2018) a way to obtain a unique solution is to fix the first diagonal element of the row covariance matrix to 1.…”

Section: Matrix Normal Cwmmentioning

confidence: 99%

“…For example, Leisch (2004) and Dang and McNicholas (2015) impose a minimum size for the clusters by forcing π g ≥ 0.05. Melnykov and Zhu (2019) tackle this issue by excluding all the solutions that involved clusters consisting of fewer than five points. Herein, we deal with this problem by removing the solutions that included clusters with estimated π g ≈ 0.05 or less, and with eigenvalues close to 0, in one or more of its estimated covariance matrices.…”

Section: Spurious Clustersmentioning

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: Insurance Datasupporting

confidence: 76%

Section: Matrix Normal Cwmmentioning

confidence: 99%

Section: Spurious Clustersmentioning

confidence: 99%

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Matrix Normal Cluster-Weighted Models

2021

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“…Specifically, important insight can be gained if the variables can be split into response and covariate variables as well as by accounting for a linear relationship among them. Such a requirement is the basis for the introduction in the literature of finite mixture of regression (FMR) models (see DeSarbo & Cron 1988, Frühwirth-Schnatter 2006 for examples), that in a matrix-variate setting have been recently presented by Melnykov & Zhu (2019). The FMR models are also termed as fixed covariates approaches, given that they do not explicitly use the distribution of the covariates for clustering.…”

Section: Introductionmentioning

confidence: 99%

Model-based clustering via skewed matrix-variate cluster-weighted models

Gallaugher¹,

Tomarchio²,

McNicholas³

et al. 2021

Preprint

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Cluster-weighted models (CWMs) extend finite mixtures of regressions (FMRs) in order to allow the distribution of covariates to contribute to the clustering process. In a matrix-variate framework, the matrix-variate normal CWM has been recently introduced. However, problems may be encountered when data exhibit skewness or other deviations from normality in the responses, covariates or both. Thus, we introduce a family of 24 matrix-variate CWMs which are obtained by allowing both the responses and covariates to be modelled by using one of four existing skewed matrix-variate distributions or the matrix-variate normal distribution. Endowed with a greater flexibility, our matrix-variate CWMs are able to handle this kind of data in a more suitable manner. As a by-product, the four skewed matrix-variate FMRs are also introduced.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. Lastly, our matrix-variate CWMs, along with the matrix- * *

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“…Gaussian mixture models for matrix or three‐way data have been proposed and extensively studied by Viroli (, , ). Recently, mixtures capable of modelling nonnormal matrix data groups have been proposed by Dogru et al (), Gallaugher and McNicholas (), Melnykov and Zhu (, ), and Sarkar et al ().…”

Section: Introductionmentioning

confidence: 99%

On variable selection in matrix mixture modelling

Wang

Melnykov

2020

Stat

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SummaryFinite mixture models are widely used for cluster analysis, including clustering matrix data. Nowadays, high‐dimensional matrix observations arise in a variety of fields. It is known that irrelevant variables can severely affect the performance of clustering procedures. Therefore, it is important to develop algorithms capable of excluding irrelevant variables and focusing on informative attributes in order to achieve good clustering results. Several variable selection approaches have been proposed in the multivariate framework. We introduce and study a variable selection procedure that can be applied in the matrix‐variate context. The methodological developments are supported by several simulation studies and application to real‐life data sets, with good results.

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Studying crime trends in the USA over the years 2000–2012

Cited by 38 publications

References 29 publications

Matrix Normal Cluster-Weighted Models

Matrix Normal Cluster-Weighted Models

Model-based clustering via skewed matrix-variate cluster-weighted models

On variable selection in matrix mixture modelling

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