The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

García-Escudero, Luis Ángel; Gordaliza, Alfonso; Greselin, Francesca; Ingrassia, Salvatore; Mayo-Íscar, Agustín

doi:10.1016/j.csda.2016.01.005

Cited by 17 publications

(18 citation statements)

References 37 publications

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“…Class recovery accuracy Adjusted Rand index Partition entropy [19] 0.977 -Mixture of generalized Dirichlet [2] 0.978 -Neural gas [5] 0.954 -Random Forest predictors [20] -0.93 Parsimonious Gaussian mixture [16] 0.927 0.79 Robust MFA [8] 0.994 0.98…”

Section: Performance Metric Methodologymentioning

confidence: 99%

“…To cope with this second issue, Common/Isotropic noise matrices/patterned covariances [1] and a mild constrained estimation [9] have been considered. The methodology considered here employs model estimation, complemented with trimming and constrained estimation, to provide robustness, to exclude singularities, and to reduce spurious solutions, along the lines of [8]. Therefore, with this approach, we overcome both previously mentioned issues.…”

Section: Mixtures Of Gaussian Factors Analyzersmentioning

confidence: 99%

“…For a fair comparison of the performance of the algorithms, we consider 3 clusters for pam, Mclust, and pgmm; whereas we consider only 2 clusters for AECM, because in this approach the adulterated group should ideally be captured by the trimmed units. A value of c = 20 allows to discard singularities and to reduce spurious solutions [8]. The effects of the trimming procedure are shown in Fig.…”

Section: Simulation Studymentioning

confidence: 99%

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Detecting Wine Adulterations Employing Robust Mixture of Factor Analyzers

Cappozzo

Greselin

2019

Statistical Learning of Complex Data

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An authentic food is one that is what it claims to be. Nowadays, more and more attention is devoted to the food market: stakeholders, throughout the value chain, need to receive exact information about the specific product they are commercing with. To ascertain varietal genuineness and distinguish potentially doctored food, in this paper we propose to employ a robust mixture estimation method. Particularly, in a wine authenticity framework with unobserved heterogeneity, we jointly perform genuine wine classification and contamination detection. Our methodology models the data as arising from a mixture of Gaussian factors and depicts the observations with the lowest contributions to the overall likelihood as illegal samples. The advantage of using robust estimation on a real wine dataset is shown, in comparison with many other classification approaches. Moreover, the simulation results confirm the effectiveness of our approach in dealing with an adulterated dataset.

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Section: Performance Metric Methodologymentioning

confidence: 99%

Section: Mixtures Of Gaussian Factors Analyzersmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

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Detecting Wine Adulterations Employing Robust Mixture of Factor Analyzers

Cappozzo

Greselin

2019

Statistical Learning of Complex Data

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“…Details are given in Greselin and Ingrassia (2015). Finally, we observe that only constraints on Ψ g are needed to discard singularities and to reduce spurious maximizers, as it has been done in a robust approach for estimating Mixtures of Gaussian factors in García-Escudero et al (2016).…”

Section: Model Id Loading Matrix λG Error Variance ψGmentioning

confidence: 99%

Eigenvalues and constraints in mixture modeling: geometric and computational issues

García-Escudero

Gordaliza

Greselin

et al. 2017

Adv Data Anal Classif

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This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. These restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned review of the constraints and their applications, along the contributions of many authors, spanning the literature of the last thirty years.Keywords Mixture Model · EM algorithm · Eigenvalues · Model-based clustering IntroductionFinite mixture distributions play a central role in statistical modelling, as they combine much of the flexibility of non parametric models with nice analytical properties of parametric models, see e.g.

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“…This leads to the so called Trimmed Cluster Weighted Restricted Model (TCWRM), where a Gaussian specification is generally assumed (the model, by García-Escudero et al 2016, is illustrated in Sect. 2).…”

Section: Introductionmentioning

confidence: 99%

Assessing trimming methodologies for clustering linear regression data

Torti

Perrotta

Riani

et al. 2018

Adv Data Anal Classif

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We assess the performance of state-of-the-art robust clustering tools for regression structures under a variety of different data configurations. We focus on two methodologies that use trimming and restrictions on group scatters as their main ingredients. We also give particular care to the data generation process through the development of a flexible simulation tool for mixtures of regressions, where the user can control the degree of overlap between the groups. Level of trimming and restriction factors are input parameters for which appropriate tuning is required. Since we find that incorrect specification of the second-level trimming in the Trimmed CLUSTering REGression model (TCLUST-REG) can deteriorate the performance of the method, we propose an improvement where the second-level trimming is not fixed in advance but is data dependent. We then compare our adaptive version of TCLUST-REG with the Trimmed Cluster Weighted Restricted Model (TCWRM) which provides a powerful extension of the robust clusterwise regression methodology. Our overall conclusion is that the two methods perform comparably, but with notable differences due to the inherent degree of modeling implied by them.

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The joint role of trimming and constraints in robust estimation for mixtures of Gaussian factor analyzers

Cited by 17 publications

References 37 publications

Detecting Wine Adulterations Employing Robust Mixture of Factor Analyzers

Detecting Wine Adulterations Employing Robust Mixture of Factor Analyzers

Eigenvalues and constraints in mixture modeling: geometric and computational issues

Assessing trimming methodologies for clustering linear regression data

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