A mixture of mixture models for a classification problem: The unity measure error

Zio, Marco Di; Guarnera, Ugo; Rocci, Roberto

doi:10.1016/j.csda.2006.01.001

Cited by 27 publications

(10 citation statements)

References 9 publications

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“…As stated by Di Zio et al. (), in the absence of any constraint, a mixture of mixtures is not identifiable in general; this is essentially due to the possibility of interchanging component labels between the two levels of the model. In our case, the contaminated normal distribution

f (x; ϑ_{g})

in cluster g is elliptical, and sufficient conditions for identifiability of finite mixtures of elliptical distributions are given in Holzmann et al.…”

Section: Identifiabilitymentioning

confidence: 98%

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Parsimonious mixtures of multivariate contaminated normal distributions

Punzo

McNicholas

2016

Biometrical J

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A mixture of multivariate contaminated normal distributions is developed for model-based clustering. In addition to the parameters of the classical normal mixture, our contaminated mixture has, for each cluster, a parameter controlling the proportion of mild 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. Parsimony is introduced via eigen-decomposition of the component covariance matrices, and sufficient conditions for the identifiability of all the members of the resulting family are provided. An expectation-conditional maximization algorithm is outlined for parameter estimation and various implementation issues are discussed. Using a large-scale simulation study, the behavior of the proposed approach is investigated and comparison with well-established finite mixtures is provided. The performance of this novel family of models is also illustrated on artificial and real data.

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f (x; ϑ_{g})

in cluster g is elliptical, and sufficient conditions for identifiability of finite mixtures of elliptical distributions are given in Holzmann et al.…”

Section: Identifiabilitymentioning

confidence: 98%

“…Di Zio et al. (). Note that Condition , the fact that

η_{g 2} > η_{g 1}

(

η_{s 2} > η_{s 1}

), and the positivity of all the weights

π_{g}

and

α_{g h}

(

π_{s}

and

α_{s t}

) avoids nonidentifiability due to potential overfitting (a potential problem for identifiability first noted by Crawford, ).…”

Section: Identifiabilitymentioning

confidence: 99%

Parsimonious mixtures of multivariate contaminated normal distributions

Punzo

McNicholas

2016

Biometrical J

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“…They showed varying performance depending on the aspects of the model and the performance measure considered. The novelty of these tools, makes it difficult to compare to other existing tools that either do not consider point pattern process (Frame & Jammalamadaka, 2007; Frühwirth-Schnatter, 2006; Hui, 2016; Martinez, 2015; Melnykov & Maitra, 2010; Quost & Denœux, 2016), Poisson distributions (Figueirido & Jain, 2002; Hui et al , 2015; Scrucca et al , 2016; Woillez et al , 2012), count data (Benaglia et al , 2009; Iovleff, 2018; Leisch, 2004) or implementation of mixture (Witten, 2011; Wendel et al , 2015) or semi-supervised learning frameworks (Di Zio et al , 2007; Fraley & Raftery, 1998; Jeffries & Pfeiffer, 2001; Taddy & Kottas, 2012).…”

Section: Discussionmentioning

confidence: 99%

Classification of unlabeled observations in Species Distribution Modelling using Point Process Models

Guilbault¹,

Renner²,

Mahony³

et al. 2019

Preprint

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71 Abstract 8 1. Species distribution modelling, which allows users to predict the spatial distribution of species with the 9 use of environmental covariates, has become increasingly popular, with many software platforms providing 10 tools to fit species distribution models. However, the species observations used in species distribution 11 models can have varying levels of quality and can have incomplete information, such as uncertain species 12 identity. 13 2. In this paper, we develop two algorithms to reclassify observations with unknown species identities 14 which simultaneously predict different species distributions using spatial point processes. We compare the 15 performance of the different algorithms using different initializations and parameters with models fitted 16 using only the observations with known species identity through simulations. 17 3. We show that performance varies with differences in correlation among species distributions, species 18 abundance, and the proportion of observations with unknown species identities. Additionally, some of the 19 methods developed here outperformed the models that didn't use the misspecified data. 20 4. These models represent an helpful and promising tool for opportunistic surveys where misidentification 21 happens or for the distribution of species newly separated in their taxonomy. 22 23

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“…Recently, various improved FCM‐type clustering schemes [2–11] have been proposed by incorporating spatial constraints to reduce the effect of the noise. Krinidis and Chatzis [4] proposed an algorithm called fuzzy local information C ‐means (FLICM) by using a fuzzy local similarity measure to reduce the effect of the noise.…”

Section: Introductionmentioning

confidence: 99%

“…To obtain more robust results, the hierarchical strategy has been proposed to improve mixture models [7, 8]. The hierarchical mixture classifier can provide class conditional density estimates as flat mixtures.…”

Section: Introductionmentioning

confidence: 99%