Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions

Mixtures of multivariate contaminated shifted asymmetric Laplace distributions are developed for handling asymmetric clusters in the presence of outliers (also referred to as bad points herein). In addition to the parameters of the related non-contaminated mixture, for each (asymmetric) cluster, our model has one parameter controlling the proportion of outliers and one specifying the degree of contamination. Crucially, these parameters do not have to be specified a priori, adding a flexibility to our approach that is absent from other approaches such as trimming. Moreover, each observation is given a posterior probability of belonging to a particular cluster, and of being an outlier or not; advantageously, this allows for the automatic detection of outliers. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. The behaviour of the proposed model is investigated, and compared with well-established finite mixtures, on artificial and real data.

• Publication year

  2014

• Venue

  Computational Statistics & Data Analysis

• Publication date

  2014-02-26

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.csda.2018.12.001arXiv 1402.6744
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Mixtures of multivariate contaminated normal regression models

  2020cited by this paper
• Fitting insurance and economic data with outliers: a flexible approach based on finite mixtures of contaminated gamma distributions

  2018cited by this paper
• Robust mixtures of factor analysis models using the restricted multivariate skew-t distribution

  2018cited by this paper
• Mixtures of restricted skew-t factor analyzers with common factor loadings

  2018cited by this paper
• The Skew-Normal and Related Families

  2018cited by this paper
• Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering

  2017cited by this paper
• Three skewed matrix variate distributions

  2017cited by this paper
• A Mixture of Variance-Gamma Factor Analyzers

  2017cited by this paper
• Mixtures of generalized hyperbolic distributions and mixtures of skew-t distributions for model-based clustering with incomplete data

  2017cited by this paper
• Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers

  2017cited by this paper
• Compound unimodal distributions for insurance losses

  2017cited by this paper
• The multivariate leptokurtic‐normal distribution and its application in model‐based clustering

  2017cited by this paper
• Robust skew-t factor analysis models for handling missing data

  2017cited by this paper
• Flexible clustering of high‐dimensional data via mixtures of joint generalized hyperbolic distributions

  2017cited by this paper
• A matrix variate skew‐t distribution

  2017cited by this paper
• A new look at the inverse Gaussian distribution with applications to insurance and economic data

  2017cited by this paper
• mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models

  2016cited by this paper
• Flexible clustering via extended mixtures of common t-factor analyzers

  2016cited by this paper
• Mixture Model-Based Classification

  2016influential reference
• Model-Based Clustering

  2016influential reference
• ContaminatedMixt: An R Package for Fitting Parsimonious Mixtures of Multivariate Contaminated Normal Distributions

  2016cited by this paper
• Clustering Multivariate Longitudinal Observations: The Contaminated Gaussian Hidden Markov Model

  2016cited by this paper
• Clustering with the multivariate normal inverse Gaussian distribution

  2016cited by this paper
• Hypothesis Testing for Mixture Model Selection

  2016cited by this paper
• Mixtures of multivariate power exponential distributions

  2015cited by this paper
• Cluster-weighted t\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t$$\end{document}-factor analyzers for robust model-

  2015cited by this paper
• Advances in Data Analysis and Classification

  2015cited by this paper
• Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models

  2014cited by this paper
• Multivariate skew-normal/independent distributions: properties and inference

  2014cited by this paper
• R: A language and environment for statistical computing.

  2014cited by this paper
• Learning from incomplete data via parameterized t mixture models through eigenvalue decomposition

  2014cited by this paper
• Finite mixtures of multivariate skew t-distributions: some recent and new results

  2014cited by this paper
• Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model

  2014cited by this paper
• Robust High-Dimensional Modeling with the Contaminated Gaussian Distribution

  2014cited by this paper
• Parsimonious skew mixture models for model-based clustering and classification

  2013cited by this paper
• mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions

  2013cited by this paper
• Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions

  2013cited by this paper
• A mixture of SDB skew-t factor analyzers

  2013cited by this paper
• Parsimonious mixtures of multivariate contaminated normal distributions

  2013cited by this paper
• Mixtures of skew-t factor analyzers

  2013cited by this paper
• A mixture of generalized hyperbolic distributions

  2013cited by this paper
• Clustering and classification via cluster-weighted factor analyzers

  2012cited by this paper
• Mixtures of Shifted AsymmetricLaplace Distributions

  2012influential reference
• The influence function of the TCLUST robust clustering procedure

  2012cited by this paper
• Initializing the EM algorithm in Gaussian mixture models with an unknown number of components

  2012cited by this paper
• Finite mixtures of unimodal beta and gamma densities and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{d

  2012cited by this paper
• Analytic calculations for the EM algorithm for multivariate skew-t mixture models

  2012cited by this paper
• Multivariate mixture modeling using skew-normal independent distributions

  2012influential reference
• Análise do perfil do cliente Recheio e desenvolvimento de um sistema promocional

  2011cited by this paper
• Extending mixtures of multivariate t-factor analyzers

  2011cited by this paper
• Skew scale mixtures of normal distributions: Properties and estimation

  2011cited by this paper
• Model-based clustering, classification, and discriminant analysis via mixtures of multivariate t-distributions

  2011cited by this paper
• Robust mixture modeling using multivariate skew t distributions

  2010cited by this paper
• LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS

  2010cited by this paper
• Robust Clustering Using Exponential Power Mixtures

  2010cited by this paper
• Flexible mixture modeling via the multivariate t distribution with the Box-Cox transformation: an alternative to the skew-t distribution

  2010cited by this paper
• Robust mixture modeling based on scale mixtures of skew-normal distributions

  2010cited by this paper
• Serial and parallel implementations of model-based clustering via parsimonious Gaussian mixture models

  2010cited by this paper
• Computationally efficient learning of multivariate t mixture models with missing information

  2009cited by this paper
• Model-based clustering with non-elliptically contoured distributions

  2009cited by this paper
• Multivariate Skew t Mixture Models: Applications to Fluorescence-Activated Cell Sorting Data

  2009cited by this paper
• Automated high-dimensional flow cytometric data analysis

  2009cited by this paper
• Maximum likelihood estimation for multivariate skew normal mixture models

  2009cited by this paper
• Parsimonious Gaussian mixture models

  2008cited by this paper
• Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution

  2007cited by this paper
• Finite mixture modelling using the skew normal distribution

  2007cited by this paper
• On fast supervised learning for normal mixture models with missing information

  2006cited by this paper
• The Skew‐normal Distribution and Related Multivariate Families *

  2005influential reference
• Properties of the Hubert-Arabie adjusted Rand index.

  2004cited by this paper
• Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models

  2003cited by this paper
• Choosing initial values for the EM algorithm for finite mixtures

  2003cited by this paper
• Modelling high-dimensional data by mixtures of factor analyzers

  2003cited by this paper
• Model-Based Clustering, Discriminant Analysis, and Density Estimation

  2002cited by this paper
• The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering, and Finance

  2001influential reference
• Robust mixture modelling using the t distribution

  2000cited by this paper
• Finite Mixture Models

  2000cited by this paper
• Detecting features in spatial point processes with clutter via model-based clustering

  1998cited by this paper
• The EM algorithm and extensions

  1996cited by this paper
• Bayes factors

  1995cited by this paper
• Bayesian Model Selection in Social Research

  1995cited by this paper
• Gaussian parsimonious clustering models

  1995cited by this paper
• Analysis of tomato root initiation using a normal mixture distribution.

  1995cited by this paper
• The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family

  1994cited by this paper
• Model-based Gaussian and non-Gaussian clustering

  1993cited by this paper
• Maximum likelihood estimation via the ECM algorithm: A general framework

  1993cited by this paper
• Unimodality, convexity, and applications

  1989cited by this paper
• Mixture models : inference and applications to clustering

  1989cited by this paper
• Skewness and mixtures of normal distributions

  1988cited by this paper
• Estimation of Contamination Parameters and Identification of Outliers in Multivariate Data

  1988cited by this paper
• Robust Bayes and Empirical Bayes Analysis with $_\epsilon$-Contaminated Priors

  1986cited by this paper
• Statistical analysis of finite mixture distributions

  1986cited by this paper
• Comparing partitions

  1985cited by this paper
• Bimodal grain size distribution and secondary thickening in air-fall ash layers

  1983cited by this paper
• Mixture Models, Outliers, and the EM Algorithm

  1980cited by this paper
• Estimating the Dimension of a Model

  1978cited by this paper
• Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper

  1977influential reference
• FINANCIAL RATIOS, DISCRIMINANT ANALYSIS AND THE PREDICTION OF CORPORATE BANKRUPTCY

  1968cited by this paper
• One cause? Many causes?

  1964cited by this paper
• XXV.—On Bernoulli's Numerical Solution of Algebraic Equations

  year unknowninfluential reference

• A contaminated regression model for count health data

  2025cites this paper
• Model-Based Clustering of Multivariate Rating Data Accounting for Feeling and Uncertainty

  2025cites this paper
• On the Use of Contaminated Normal Distributions for Modeling Data Groups with Heavy Tails and Outliers

  2025cites this paper
• Discrete-Continuous Dual Families, Reciprocal Laws, Random Summation, and Mixtures of Gaussian Distributions

  2025cites this paper
• Handling skewness and directional tails in model-based clustering

  2025cites this paper
• Mixtures of multivariate linear asymmetric Laplace regressions with multiple asymmetric Laplace covariates

  2025cites this paper
• Finite Mixtures of Multivariate Contaminated Normal Censored Regression Models

  2025cites this paper
• Robust Recursive Identification of Time-Delay Systems With Skewed Measurement Noise

  2025cites this paper
• Unsupervised Classification with a Family of Parsimonious Contaminated Shifted Asymmetric Laplace Mixtures

  2024influential citation
• Heckman selection-contaminated normal model

  2024cites this paper
• Alternative skew Laplace scale mixtures for modeling data exhibiting high-peaked and heavy-tailed traits

  2024influential citation
• A Laplace-based model with flexible tail behavior

  2024cites this paper
• Clustering asymmetrical data with outliers: Parsimonious mixtures of contaminated mean-mixture of normal distributions

  2023cites this paper
• Tackling the infinite likelihood problem when fitting mixtures of shifted asymmetric Laplace distributions

  2023cites this paper
• The generalized hyperbolic family and automatic model selection through the multiple‐choice LASSO

  2023cites this paper
• Clustering Three-Way Data with Outliers

  2023cites this paper
• On Model-Based Clustering of Directional Data with Heavy Tails

  2023cites this paper
• Contamination transformation matrix mixture modeling for skewed data groups with heavy tails and scatter

  2023cites this paper
• Parsimony and parameter estimation for mixtures of multivariate leptokurtic-normal distributions

  2023cites this paper
• Missing Values and Directional Outlier Detection in Model-Based Clustering

  2023cites this paper
• Asymmetric Laplace scale mixtures for the distribution of cryptocurrency returns

  2022cites this paper
• Dimension-wise scaled normal mixtures with application to finance and biometry

  2022cites this paper
• Mixtures of Matrix-Variate Contaminated Normal Distributions

  2021cites this paper
• Outlier detection in multivariate functional data through a contaminated mixture model

  2021cites this paper
• The multivariate tail-inflated normal distribution and its application in finance

  2020cites this paper
• Transformation mixture modeling for skewed data groups with heavy tails and scatter

  2020cites this paper
• Robust fitting of mixture models using weighted complete estimating equations

  2020cites this paper
• Robust Mixture Modeling using Weighted Complete Estimating Equations

  2020cites this paper
• Issues in Gaussian Model-Based Clustering

  2020cites this paper
• Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions

  2020cites this paper
• Editorial for the 4th Special Issue on advances in mixture models

  2019cites this paper
• Multiple scaled contaminated normal distribution and its application in clustering

  2018cites this paper
• An Evolutionary Algorithm with Crossover and Mutation for Model-Based Clustering

  2018cites this paper
• Modeling Household Income with Contaminated Unimodal Distributions

  2017cites this paper
• High-dimensional unsupervised classification via parsimonious contaminated mixtures

  2014cites this paper
• A Variational Approximations-DIC Rubric for Parameter Estimation and Mixture Model Selection Within a Family Setting

  2013cites this paper