This paper presents a new finite mixture model based on the multivariate normal mean variance mixture of Birnbaum-Saunders (NMVBS) distribution. We develop a computationally analytical em algorithm for model fitting. ...
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This paper presents a new finite mixture model based on the multivariate normal mean variance mixture of Birnbaum-Saunders (NMVBS) distribution. We develop a computationally analytical em algorithm for model fitting. Due to the dependence of this algorithm on initial values and the number of mixing components, a learning-based em algorithm and an extended variant are proposed. Numerical simulations show that the proposed algorithms allow for better clustering performance and classification accuracy than some competing approaches. The effectiveness and prominence of the proposed methodology are also shown through an application to an extrasolar planet dataset. (C) 2018 Elsevier Inc. All rights reserved.
Organizing groups is a critical process in implementing cooperative learning. The grouping strategy based on the degree of complementarity is a popular grouping strategy at present. However, the existing collaborative...
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ISBN:
(纸本)9783030357580;9783030357573
Organizing groups is a critical process in implementing cooperative learning. The grouping strategy based on the degree of complementarity is a popular grouping strategy at present. However, the existing collaborative learning grouping strategy based on the degree of complementarity has disadvantages such as insufficient modeling accuracy for students' ability and lack of rationality for the reasons of regrouping. This paper proposes a collaborative learning grouping strategy with early warning function based on the degree of complementary mastery of knowledge points. First, we take knowledge points as the minimum unit, and use linear regression and expectation maximization algorithm to accurately model each student's mastery of each knowledge point. Then we use the inverse clustering algorithm based on knowledge points to classify students. Finally, we use LSTM neural network to predict the scores of each group in the next week, and early warning was given to the groups with significantly reduced predicted scores, and targeted suggestions were put forward for them according to the types of the warned groups. Experimental results show that the grouping strategy proposed in this paper can effectively improve the learning effect of students. The average precision and average recall of LSTM based group early warning were 30.1% and 27.6% higher than that based on linear regression, respectively.
In biomedical studies, a difference or deviation is usually measured and only the magnitude is recorded but the algebraic sign of the data is irretrievably lost, the resulting observed variable no longer follows a nor...
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In biomedical studies, a difference or deviation is usually measured and only the magnitude is recorded but the algebraic sign of the data is irretrievably lost, the resulting observed variable no longer follows a normal distribution, rather it follows a folded normal (FN) distribution. More importantly, the FN distribution could be used to fit data sets with the following two characteristics: (i) The density curve is similar to the normal density but truncated somewhere;(ii) The density curve of the truncated side is significantly higher than that of the other side. There are several issues on the statistical inferences with the FN distribution which are not (well) addressed in the existing literature. In this paper, starting from the stochastic representation, we develop a new expectation-maximization (em) algorithm to calculate the maximum likelihood estimates of parameters in both FN distribution and the FN regression models. The em structure can also facilitate the Bayesian inferences about the FN distribution and the FN regression models. Extensions to the generalized FN distribution are provided. Simulation studies are conducted to assess the estimation performances for the FN distribution and the FN regression model. Two real data sets are analyzed to illustrate the proposed methods. (C) 2020 Published by Elsevier B.V.
In semi-supervised learning, we have sample data of features that are from different classes, and only a small part of data have class labels. To predict class labels for unlabelled data, one approach is to model the ...
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In semi-supervised learning, we have sample data of features that are from different classes, and only a small part of data have class labels. To predict class labels for unlabelled data, one approach is to model the data in each class using a mixture normal distribution, estimate the parameters using maximum likelihood estimation via em algorithm, and predict class labels based on estimated probabilities. To implement the maximum likelihood approach, we provide an algorithm to determine initial values for the em algorithm and refer this method as the ML-em method. We conducted some simulation experiments to check the prediction performance of the ML-em method and six other methods. According to our simulation results, the ML-em method outperforms the six methods in some challenging cases based on average ARI values. However, in a simple case where data points from different classes are well separated, sometimes the ML-em method can be outperformed by some of the six methods. To improve the prediction performance of the ML-em method, we propose the ML-em II method, a modified version of the ML-em method. Simulation results show that the ML-em II method performs better than the ML-em method.
Arctic sea ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing temporal trend over the past 20 years. In this article, we propose a hierarchical spatio-temporal gen...
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Arctic sea ice extent has been of considerable interest to scientists in recent years, mainly due to its decreasing temporal trend over the past 20 years. In this article, we propose a hierarchical spatio-temporal generalized linear model for binary Arctic sea-ice-extent data, where statistical dependencies in the data are modeled through a latent spatio-temporal linear mixed effects model. By using a fixed number of spatial basis functions, the resulting model achieves both dimension reduction and non-stationarity for spatial fields at different time points. An em algorithm is proposed to estimate model parameters, and an empirical-hierarchical-modeling approach is applied to obtain the predictive distribution of the latent spatio-temporal process. We illustrate the accuracy of the parameter estimation through a simulation study. The hierarchical model is applied to spatial Arctic sea-ice-extent data in the month of September for 20 years in the recent past, where several posterior summaries are obtained to detect the changes of Arctic sea ice cover. In particular, we consider a time series of latent 2 x 2 tables to infer the spatial changes of Arctic sea ice over time.
In this paper we analyze a unified approach to study a family of lifetime distributions of a system consisting of random number of components in series and in parallel proposed by Chowdhury (2014). While the lifetimes...
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In this paper we analyze a unified approach to study a family of lifetime distributions of a system consisting of random number of components in series and in parallel proposed by Chowdhury (2014). While the lifetimes of the components are assumed to follow generalized (exponentiated) Weibull distribution, a zero-truncated Poisson is assigned to model the random number of components in the system. The resulting family of compounded distributions describes several well-known distributions as well as some new models. Bivariate extension of the proposed family of distribution is also introduced. Some important statistical and reliability properties of the family of distributions are investigated. The distribution is found to exhibit both monotone and non-monotone failure rates. Parameters of the proposed distributions are estimated by the expectation maximization (em) algorithm. Some numerical results are obtained through Monte-Carlo simulation. The asymptotic variance-covariance matrices of the estimators are also derived. Potential of the distribution is explored through two real data sets and compared with similar compounded distribution and the results demonstrate that the family of distributions can be considered as a suitable model under several real situations.
In this paper, we propose a matrix extension of the scale and shape mixtures of multivariate skew normal distributions and present some particular cases of this new class. We also present several formal properties of ...
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In this paper, we propose a matrix extension of the scale and shape mixtures of multivariate skew normal distributions and present some particular cases of this new class. We also present several formal properties of this class, such as the marginal distributions, the moment generating function, the distribution of linear and quadratic forms, and the selection and stochastic representations. In addition, we introduce the matrix variate tail conditional expectation measure and derive this risk measure for the scale and shape mixtures of matrix variate extended skew normal distributions. We present an efficient em-type algorithm for the computation of maximum likelihood estimates of parameters in some special cases of the proposed class. Finally, we conduct a small simulation study and fit various special cases of the new class to a real dataset. (C) 2020 Published by Elsevier Inc.
With the advancements in digital technology, multispectral images have found use in fields like forensics, remote sensing due to their ability to perceive things which were otherwise non-existent. They are used to obt...
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ISBN:
(纸本)9789811315923;9789811315916
With the advancements in digital technology, multispectral images have found use in fields like forensics, remote sensing due to their ability to perceive things which were otherwise non-existent. They are used to obtain more information about terrains, land cover and in forensics as certain things like blood stains are not visible in visible spectrum. But with newly developed photo-editing softwares, they can be easily manipulated without leaving any visible clue of manipulation, but will destroy the underlying correlation between different bands. Newly developed digital cameras employ a single sensor along with multispectral filter array (MSFA) and then interpolate the data at other locations, hence introducing a correlation between bands. In this paper, we have proposed an algorithm that can identify the lack of correlation at tampered locations in a multispectral image and can thus help in establishing the authenticity of the given multispectral image. We showthe efficiency of our approach with respect to the size of tampered regions in images interpolated with one the most common demosaicking algorithm-binary tree-based edge sensing (BTES).
Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has beco...
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Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely available. From sociological experiments involving cognitive social structures to fMRI scans revealing large-scale brain networks of groups of patients, there is a growing awareness that we urgently need tools to analyse populations of networks and particularly to model the variation between networks due to covariates. We propose a model-based clustering method based on mixtures of generalized linear (mixed) models that can be employed to describe the joint distribution of a populations of networks in a parsimonious manner and to identify subpopulations of networks that share certain topological properties of interest (degree distribution, community structure, effect of covariates on the presence of an edge, etc.). Maximum likelihood estimation for the proposed model can be efficiently carried out with an implementation of the em algorithm. We assess the performance of this method on simulated data and conclude with an example application on advice networks in a small business.
This article is concerned with the likelihood-based inference of vector autoregressive models with multivariate scaled t-distributed innovations by applying the em-based (ECM and ECME) algorithms. The ECM and ECME alg...
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This article is concerned with the likelihood-based inference of vector autoregressive models with multivariate scaled t-distributed innovations by applying the em-based (ECM and ECME) algorithms. The ECM and ECME algorithms, which are analytically quite simple to use, are applied to find the maximum likelihood estimates of the model parameters and then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ECME is efficient and usable in practice. We also show how the method can be applied to a multivariate dataset.
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