Efficient implementation of the EM algorithm for mammographic image texture analysis with multivariate Gaussian mixtures

Gallego-Ortiz, Nicolás; Femandez-Mc-Cann, David S.

doi:10.1109/ssp.2011.5967832

Cited by 2 publications

(1 citation statement)

References 7 publications

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“…In view of this analogy an arbitrarily weighted log-likelihood function (23) is maximized by the respective weighted sum (24), (cf. (8) and (9)), provided that the formula (22) is available (cf. Theorem 5.1 of Ref.…”

Section: Weighted Likelihood Estimatementioning

confidence: 99%

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Grim

2017

Int. J. Patt. Recogn. Artif. Intell.

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In literature the references to EM estimation of product mixtures are not very frequent. The simplifying assumption of product components, e.g. diagonal covariance matrices in case of Gaussian mixtures, is usually considered only as a compromise because of some computational constraints or limited dataset. We have found that the product mixtures are rarely used intentionally as a preferable approximating tool. Probably, most practitioners do not “trust” the product components because of their formal similarity to “naive Bayes models.” Another reason could be an unrecognized numerical instability of EM algorithm in multidimensional spaces. In this paper we recall that the product mixture model does not imply the assumption of independence of variables. It is even not restrictive if the number of components is large enough. In addition, the product components increase numerical stability of the standard EM algorithm, simplify the EM iterations and have some other important advantages. We discuss and explain the implementation details of EM algorithm and summarize our experience in estimating product mixtures. Finally we illustrate the wide applicability of product mixtures in pattern recognition and in other fields.

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Section: Weighted Likelihood Estimatementioning

confidence: 99%

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Grim

2017

Int. J. Patt. Recogn. Artif. Intell.

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Statistical Texture Model for mass Detection in Mammography

Gallego-Ortiz¹,

Fernández-McCann

2013

Revista de Ingeniería

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Palabras clavesAntracita, arena, configuración de medio filtrante, filtración, turbiedad. ResumenSe evaluó a escala piloto el efecto de la configuración del medio filtrante sobre el proceso de filtración del agua clarificada de la planta de potabilización Puerto Mallarino, Cali -Colombia. Se analizaron cuatro configuraciones, una con características similares a los filtros existentes y las restantes con diferente tamaño efectivo y espesor de antracita. Se analizó turbiedad, duración de carrera, producción de agua y pérdida de carga. La filtración fue más eficaz al reducir el tamaño efectivo e incrementar el espesor. La configuración que mostró un mejor desempeño incluso operando con turbiedades de agua clarificada mayores a 10,0 UTN, fue la del filtro con un espesor de 700 mm.

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Efficient implementation of the EM algorithm for mammographic image texture analysis with multivariate Gaussian mixtures

Cited by 2 publications

References 7 publications

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Statistical Texture Model for mass Detection in Mammography

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