Mixture Model-Based Classification

McNicholas, Paul D.

doi:10.1201/9781315373577

Cited by 143 publications

(129 citation statements)

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“…The author is grateful to Chapman & Hall/CRC Press for allowing some text and figures from his monograph (McNicholas 2016) to be used in this review paper. The author is thankful for the helpful comments of an anonymous reviewer and the Editor.…”

Section: Defining a Clustermentioning

confidence: 99%

“…As McNicholas (2016) explains, a driving force behind the work of Tiedeman (1955) is to encourage work on what we now know as clustering. Because the idea of defining a cluster in terms of a component in a mixture model goes back to Tiedeman (1955), it is worth noting how he formulated the problem:…”

Section: Defining a Clustermentioning

confidence: 99%

“…The oldest citation given pertaining to mixture models and clustering is usually the thesis by Wolfe (1963). McNicholas (2016) explains that while Wolfe (1963) uses the idea of a mixture model to define a cluster, he does not use a mixture model to perform clustering. More specifically, the clustering procedures developed by Wolfe (1963) are not based on maximiz-…”

Section: Defining a Clustermentioning

confidence: 99%

“…McNicholas 2016, Section 7.6). The unimodal requirement in the definition of McNicholas (2016) is important because if the component is not unimodal, then one of two things is almost certainly happening: the wrong mixture distribution is being fit-ted or not enough components are being used. An example of the formerspecifically, multiple Gaussian components being used to model one skewed cluster-is given in Section 4.2.…”

Section: Defining a Clustermentioning

confidence: 99%

“…McNicholas (2016) explains that an "appropriate" mixture model here is one that is appropriate in light of the data under consideration. What does it mean for a mixture model to be "appropriate" in light of the data?…”

Section: Defining a Clustermentioning

confidence: 99%

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Model-Based Clustering

McNicholas

2016

J Classif

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185

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Abstract:The notion of defining a cluster as a component in a mixture model was put forth by Tiedeman in 1955; since then, the use of mixture models for clustering has grown into an important subfield of classification. Considering the volume of work within this field over the past decade, which seems equal to all of that which went before, a review of work to date is timely. First, the definition of a cluster is discussed and some historical context for model-based clustering is provided. Then, starting with Gaussian mixtures, the evolution of model-based clustering is traced, from the famous paper by Wolfe in 1965 to work that is currently available only in preprint form. This review ends with a look ahead to the next decade or so.

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Section: Defining a Clustermentioning

confidence: 99%

Section: Defining a Clustermentioning

confidence: 99%

Section: Defining a Clustermentioning

confidence: 99%

Section: Defining a Clustermentioning

confidence: 99%

Section: Defining a Clustermentioning

confidence: 99%

See 3 more Smart Citations

Model-Based Clustering

McNicholas

2016

J Classif

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185

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Dimension Reduction in Clustering

Marbac

McNicholas

2016

Wiley StatsRef: Statistics Reference Online

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Similar to many other statistical methods, clustering approaches can fail when data dimensionality increases. This so‐called curse of dimensionality has led statisticians to develop specific models for dealing with higher dimensional data. Broadly, this review covers two frameworks for dimension reduction in model‐based clustering: methods based on variable transformation and methods based on variable selection.

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Mixture ratio modeling of dynamic systems

KárnýMiroslav

Ruman

2021

Adaptive Control & Signal

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Summary Any knowledge extraction relies (possibly implicitly) on a hypothesis about the modelled‐data dependence. The extracted knowledge ultimately serves to a decision‐making (DM). DM always faces uncertainty and this makes probabilistic modelling adequate. The inspected black‐box modeling deals with “universal” approximators of the relevant probabilistic model. Finite mixtures with components in the exponential family are often exploited. Their attractiveness stems from their flexibility, the cluster interpretability of components and the existence of algorithms for processing high‐dimensional data streams. They are even used in dynamic cases with mutually dependent data records while regression and auto‐regression mixture components serve to the dependence modeling. These dynamic models, however, mostly assume data‐independent component weights, that is, memoryless transitions between dynamic mixture components. Such mixtures are not universal approximators of dynamic probabilistic models. Formally, this follows from the fact that the set of finite probabilistic mixtures is not closed with respect to the conditioning, which is the key estimation and predictive operation. The paper overcomes this drawback by using ratios of finite mixtures as universally approximating dynamic parametric models. The paper motivates them, elaborates their approximate Bayesian recursive estimation and reveals their application potential.

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Mixture Model-Based Classification

Cited by 143 publications

References 0 publications

Model-Based Clustering

Model-Based Clustering

Dimension Reduction in Clustering

Mixture ratio modeling of dynamic systems

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