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1

Estimation of parameters of Gaussian mixture models by a hybrid method combining a self-adaptive differential evolution with the EM algorithm

Kwedlo W.

Advances in Computer Science Research

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2014

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Nr 11

109--123

EN

In the paper the problem of learning of Gaussian mixture models (GMMs) is considered. A new approach based on hybridization of a self-adaptive version of differential evolution (DE) with the classical EM algorithm is described. In this approach, called DEEM, the EM algorithm is run until convergence to fine-tune each solution obtained by the mutation and crossover operators of DE. To avoid the problem with parameter representation and infeasible solutions we use a method in which the covariance matrices are encoded using their Cholesky factorizations. In a simulation study GMMs were used to cluster synthetic datasets differing by a degree of separation between clusters. The results of experiments indicate that DE-EM outperforms the standard multiple restart expectation-maximization algorithm (MREM). For datasets with high number of features it also outperforms the state of-the-art random swap EM (RSEM).

PL

W pracy poruszono problem uczenia modeli mieszanin rozkładów normalnych. Zaproponowano nowe podejście, nazwane DE-EM, oparte na hybrydyzacji samoadaptacyjnego algorytmu ewolucji różnicowej i klasycznego algorytmu EM. W nowej metodzie rozwiązanie otrzymane jako wynik operatorów mutacji i krzyżowania jest poddawane optymalizacji lokalnej, prowadzonej aż do momentu uzyskania zbieżności, przez algorytm EM. Aby uniknąć problemu z reprezentacją macierzy kowariancji i niedopuszczalności rozwiązań użyto metody, w której macierze kowariancji są kodowane przy pomocy dekompozycji Cholesky’ego. W badaniach symulacyjnych modele mieszanin rozkładów normalnych zastosowano do grupowania danych syntetycznych. Wyniki eksperymentów wskazują, że metoda DE-EM osiąga lepsze wyniki niż standardowa technika wielokrotnego startu algorytmu ˙ EM. Dla zbiorów danych z dużą liczbą cech, metoda osiąga lepsze wyniki niż technika losowej wymiany rozwiązań połączona z algorytmem EM.

2

Credibility assessment in an on-line car navigation system by means of the expectation maximization algorithm

Kubiak M.

Foundations of Computing and Decision Sciences

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2007

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Vol. 32, No. 4

275-293

EN

In an on-line car satellite navigation system users may communicate with the system's operator and send them information about some objects in a road network, e.g. dangerous places or safety cameras. The operator of such a system may publish this information for the benefit of other users, but firstly has to assess the credibility of the submitted information. The paper presents a probabilistic model of such a scenario- It investigates the possibility of estimating probabilities of objects' existence and users' credibilities based only on data provided by the users. This estimation is performed by the Expectation Maximization algorithm. The proposed approach is compared to a voting method in a simulation study, which is the first step required by an industrial partner toward a commercial application.

3

Novel statistical approach for segmentation of brain magnetic resonance imaging using an improved expectation maximization algorithm

Yang Y., Huang S.

Optica Applicata

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2006

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Vol. 36, nr 1

125-136

EN

In this paper, an improved expectation maximization (EM) algorithm called statistical histogram based expectation maximization (SHEM) algorithm is presented. The algorithm is put forward to overcome the drawback of standard EM algorithm, which is extremely computationally expensive for calculating the maximum likelihood (ML) parameters in the statistical segmentation. Combining the SHEM algorithm and the connected threshold region-growing algorithm that is used to provide a priori knowledge, a novel statistical approach for segmentation of brain magnetic resonance (MR) image data is thus proposed. The performance of our SHEM based method is compared with those of the EM based method and the commonly applied fuzzy C-means (FCM) segmentation. Experimental results show the proposed approach to be effective, robust and significantly faster than the conventional EM based method.

4

Fuzzy c-means clustering algorithm with a novel penalty term for image segmentation

Yang Y., Zheng C., Lin P.

Opto-Electronics Review

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2005

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Vol. 13, No. 4

309-315

EN

Fuzzy clustering techniques, especially fuzzy c-means (FCM) clustering algorithm, have been widely used in automated image segmentation. However, as the conventional FCM algorithm does not incorporate any information about spatial context, it is sensitive to noise. To overcome this drawback of FCM algorithm, a novel penalized fuzzy c-means (PFCM) algorithm for image segmentation is presented in this paper. The algorithm is formulated by incorporating the spatial neighbourhood information into the original FCM algorithm with a penalty term. The penalty term acts as a regularizer in this algorithm, which is inspired by the neighbourhood expectation maximization (NEM) algorithm and is modified in order to satisfy the criterion of the FCM algorithm. Experimental results on synthetic, simulated and real images indicate that the proposed algorithm is effective and more robust to noise and other artifacts than the standard FCM algorithm.

5

A Novel Statistical Approach for Segmentation of Single-Channel Brain MRI Using an Improved EM algorithm

Yang Y., Zheng Ch., Lin P.

Journal of Applied Computer Science

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2005

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Vol. 13, nr 1

113-125

EN

This paper presents a novel statistical method for segmentation of single-channel brain magnetic resonance (MR) image data. The method based on an improved expectation maximization (EM) algorithm proposed in this paper involves three steps. Firstly, after pre-processing the image with the curvature anisotropic diffusion filter, the background (BG) and brain masks of the image are obtained by applying a combination approach of thresholding with morphology. Secondly, the connected threshold region growing technique is employed to get the preliminary results of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) on a brain MRI. Finally, the previous results are served as the priori knowledge for the improved EM algorithm to segment the brain MRI. The performance of the proposed method is compared with that of the popular used fuzzy-C means (FCM) segmentation. Experimental results show our approach is effective, robust and significantly faster than the conventional EM based method.