Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skew<i>t</i>-Distribution

Azzalini, Adelchi; Capitanio, Antonella

doi:10.1111/1467-9868.00391

Cited by 1,205 publications

(947 citation statements)

References 30 publications

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“…where fh(y; h, ⌺h, Dh, h) is the multivariate skew t pdf for the hth component with location vector h, scale matrix ⌺h, skew parameter Dh and degrees of freedom h. The multivariate skew t distribution is defined by introducing skewness in a multivariate elliptically symmetric t distribution (26) f͑y;…”

Section: Methodsmentioning

confidence: 99%

Automated High-Dimensional Flow Cytometric Data Analysis

Pyne

Wang

et al. 2010

Lecture Notes in Computer Science

114

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Flow cytometric analysis allows rapid single cell interrogation of surface and intracellular determinants by measuring fluorescence intensity of fluorophore-conjugated reagents. The availability of new platforms, allowing detection of increasing numbers of cell surface markers, has challenged the traditional technique of identifying cell populations by manual gating and resulted in a growing need for the development of automated, high-dimensional analytical methods. We present a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation. We demonstrate its ability to detect rare populations, to model robustly in the presence of outliers and skew, and to perform the critical task of matching cell populations across samples that enables downstream analysis. This advance will facilitate the application of flow cytometry to new, complex biological and clinical problems.finite mixture model ͉ flow cytometry ͉ multivariate skew distribution F low cytometry transformed clinical immunology and hematology over 2 decades ago by allowing the rapid interrogation of cell surface determinants and, more recently, by enabling the analysis of intracellular events using fluorophore-conjugated antibodies or markers. Although flow cytometry initially allowed the investigation of only a single fluorophore, recent advances allow close to 20 parallel channels for monitoring different determinants (1-4). These advances have now surpassed our ability to interpret manually the resulting high-dimensional data and have led to growing interest and recent activity in the development of new computational tools and approaches (5-8).The difficulty in data analysis arises from the traditional technique of identifying discrete cell populations by manual gating, which is a labor-intensive process and varies by user experience. The initial computational packages for flow cytometric analyses focused largely on different preprocessing tasks such as data acquisition, normalization, and live cell gating. Besides visualization and transformation of flow cytometric data, useful tools such as Flowjo (www.flowjo.com) and the packages in BioConductor (www.bioconductor.org) (such as prada, flowCore, flowViz, flowUtils, and rflowcyt) allow some form of software-assisted gating and extraction of populations of interest. The operator subjectively demarcates a cell population while moving through successive 2-or 3-dimensional projections of the data. This process limits the reproducibility of data processing. A more fundamental problem is that this lower dimensional visualization hinders the identification of higher-dimensional features. Furthermore, current methods extract only a limited number of sample parameters, such as the mean fluorescence intensity of a cell population, which can lead to loss of critical information in defining the properties of a cell population....

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Section: Methodsmentioning

confidence: 99%

Automated High-Dimensional Flow Cytometric Data Analysis

Pyne

Wang

et al. 2010

Lecture Notes in Computer Science

114

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“…One of these skew-normal formulations is given by Azzalini and Valle (1996) and examined further by Azzalini and Capitanio (1999) and others. Branco and Dey (2001) and Azzalini and Capitanio (2003) introduce an analogous skewt distribution. The other formulation is given by Sahu, Dey, and Branco (2003), for both skew-normal and skew-t distributions.…”

Section: Mixtures Of Asymmetric Componentsmentioning

confidence: 99%

Model-Based Clustering

McNicholas

2016

J Classif

187

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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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“…4 and used in Ref. 23. The estimation of the parameters of a mixture model can be carried out using the expectation-maximization (EM) algorithm.…”

Section: The Jcm Algorithmmentioning

confidence: 99%

Modeling of inter‐sample variation in flow cytometric data with the joint clustering and matching procedure

2015

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We present an algorithm for modeling flow cytometry data in the presence of large inter-sample variation. Large-scale cytometry datasets often exhibit some within-class variation due to technical effects such as instrumental differences and variations in data acquisition, as well as subtle biological heterogeneity within the class of samples. Failure to account for such variations in the model may lead to inaccurate matching of populations across a batch of samples and poor performance in classification of unlabeled samples. In this paper, we describe the Joint Clustering and Matching (JCM) procedure for simultaneous segmentation and alignment of cell populations across multiple samples. Under the JCM framework, a multivariate mixture distribution is used to model the distribution of the expressions of a fixed set of markers for each cell in a sample such that the components in the mixture model may correspond to the various populations of cells, which have similar expressions of markers (that is, clusters), in the composition of the sample. For each class of samples, an overall class template is formed by the adoption of random-effects terms to model the inter-sample variation within a class. The construction of a parametric template for each class allows for direct quantification of the differences between the template and each sample, and also between each pair of samples, both within or between classes. The classification of a new unclassified sample is then undertaken by assigning the unclassified sample to the class that minimizes the distance between its fitted mixture density and each class density as provided by the class templates. For illustration, we use a symmetric form of the Kullback-Leibler divergence as a distance measure between two densities, but other distance measures can also be applied. We show and demonstrate on four real datasets how the JCM procedure can be used to carry out the tasks of automated clustering and alignment of cell populations, and supervised classification of samples. V C 2015International Society for Advancement of Cytometry Key terms flow cytometry; classification; class template; inter-sample variation; clustering; matching; skew mixture models; EM algorithm; JCM FLOW cytometry (FCM) is a powerful tool in clinical diagnosis of health disorders, in particular, immunological diseases. It offers rapid high-throughput measurements of multiple characteristics on every cell in a sample, enabling biologists to study a variety of biological processes at the cellular level. A critical component in the pipeline of FCM data analysis is the identification of cell populations from the multidimensional FCM dataset, currently performed manually by visually separating regions or gates of interest on a series of sequential bivariate projections of the data, a process known as gating. However, this approach has many problems and limitations, including variability between different analysts, non-standardization and nonreproducibility of results, an unrealistic assumption that bi...

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Distributions Generated by Perturbation of Symmetry with Emphasis on a Multivariate Skewt-Distribution

Cited by 1,205 publications

References 30 publications

Automated High-Dimensional Flow Cytometric Data Analysis

Automated High-Dimensional Flow Cytometric Data Analysis

Model-Based Clustering

Modeling of inter‐sample variation in flow cytometric data with the joint clustering and matching procedure

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