A Weighted Spatially Constrained Finite Mixture Model for Image Segmentation

Spatially Constrained Mixture Model(SCMM)is an image segmentation model that works over the framework of maximum a-posteriori and Markov Random Field(MAP-MRF).It developed its own maximization step to be used within this framework.This research has proposed an improvement in the SCMM’s maximization step for segmenting simulated brain Magnetic Resonance Images(MRIs).The improved model is named as the Weighted Spatially Constrained Finite Mixture Model(WSCFMM).To compare the performance of SCMM and WSCFMM,simulated T1-Weighted normal MRIs were segmented.A region of interest(ROI)was extracted from segmented images.The similarity level between the extracted ROI and the ground truth(GT)was found by using the Jaccard and Dice similarity measuring method.According to the Jaccard similarity measuring method,WSCFMM showed an overall improvement of 4.72%,whereas the Dice similarity measuring method provided an overall improvement of 2.65%against the SCMM.Besides,WSCFMM signicantly stabilized and reduced the execution time by showing an improvement of 83.71%.The study concludes that WSCFMM is a stable model and performs better as compared to the SCMM in noisy and noise-free environments.

A Finite Mixture of Generalised Inverse Gaussian with Indexes -1/2 and -3/2 as Mixing Distribution for Normal Variance Mean Mixture with Application

Mixture models have become more popular in modelling compared to standard distributions. The mixing distributions play a role in capturing the variability of the random variable in the conditional distribution. Studies have lately focused on finite mixture models as mixing distributions in the mixing mechanism. In the present work, we consider a Normal Variance Mean mixture model. The mixing distribution is a finite mixture of two special cases of Generalised Inverse Gaussian distribution with indexes -1/2 and -3/2. The parameters of the mixed model are obtained via the Expectation-Maximization (EM) algorithm. The iterative scheme is based on a presentation of the normal equations. An application to some financial data has been done.

Predicting carbon storage of mixed broadleaf forests based on the finite mixture model incorporating stand factors,site quality,and aridity index

The diameter distribution function(DDF)is a crucial tool for accurately predicting stand carbon storage(CS).The current key issue,however,is how to construct a high-precision DDF based on stand factors,site quality,and aridity index to predict stand CS in multi-species mixed forests with complex structures.This study used data from70 survey plots for mixed broadleaf Populus davidiana and Betula platyphylla forests in the Mulan Rangeland State Forest,Hebei Province,China,to construct the DDF based on maximum likelihood estimation and finite mixture model(FMM).Ordinary least squares(OLS),linear seemingly unrelated regression(LSUR),and back propagation neural network(BPNN)were used to investigate the influences of stand factors,site quality,and aridity index on the shape and scale parameters of DDF and predicted stand CS of mixed broadleaf forests.The results showed that FMM accurately described the stand-level diameter distribution of the mixed P.davidiana and B.platyphylla forests;whereas the Weibull function constructed by MLE was more accurate in describing species-level diameter distribution.The combined variable of quadratic mean diameter(Dq),stand basal area(BA),and site quality improved the accuracy of the shape parameter models of FMM;the combined variable of Dq,BA,and De Martonne aridity index improved the accuracy of the scale parameter models.Compared to OLS and LSUR,the BPNN had higher accuracy in the re-parameterization process of FMM.OLS,LSUR,and BPNN overestimated the CS of P.davidiana but underestimated the CS of B.platyphylla in the large diameter classes(DBH≥18 cm).BPNN accurately estimated stand-and species-level CS,but it was more suitable for estimating stand-level CS compared to species-level CS,thereby providing a scientific basis for the optimization of stand structure and assessment of carbon sequestration capacity in mixed broadleaf forests.

Log-cumulants of the finite mixture model and their application to statistical analysis of fully polarimetric UAVSAR data

Since its first flight in 2007,the UAVSAR instrument of NASA has acquired a large number of fully Polarimetric SAR(PolSAR)data in very high spatial resolution.It is possible to observe small spatial features in this type of data,offering the opportunity to explore structures in the images.In general,the structured scenes would present multimodal or spiky histograms.The finite mixture model has great advantages in modeling data with irregular histograms.In this paper,a type of important statistics called log-cumulants,which could be used to design parameter estimator or goodness-of-fit tests,are derived for the finite mixture model.They are compared with logcumulants of the texture models.The results are adopted to UAVSAR data analysis to determine which model is better for different land types.

Modeling Cyber Loss Severity Using a Spliced Regression Distribution with Mixture Components

Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.

A Special Weight for Inverse Gaussian Mixing Distribution in Normal Variance Mean Mixture with Application

Normal Variance-Mean Mixture (NVMM) provides a general framework for deriving models with desirable properties for modelling financial market variables such as exchange rates, equity prices, and interest rates measured over short time intervals, i.e. daily or weekly. Such data sets are characterized by non-normality and are usually skewed, fat-tailed and exhibit excess kurtosis. The Generalised Hyperbolic distribution (GHD) introduced by Barndorff-Nielsen (1977) which act as Normal variance-mean mixtures with Generalised Inverse Gaussian (GIG) mixing distribution nest a number of special and limiting case distributions. The Normal Inverse Gaussian (NIG) distribution is obtained when the Inverse Gaussian is the mixing distribution, i.e., the index parameter of the GIG is . The NIG is very popular because of its analytical tractability. In the mixing mechanism, the mixing distribution characterizes the prior information of the random variable of the conditional distribution. Therefore, considering finite mixture models is one way of extending the work. The GIG is a three parameter distribution denoted by and nest several special and limiting cases. When , we have which is called an Inverse Gaussian (IG) distribution. When , , , we have , and distributions respectively. These distributions are related to and are called weighted inverse Gaussian distributions. In this work, we consider a finite mixture of and and show that the mixture is also a weighted Inverse Gaussian distribution and use it to construct a NVMM. Due to the complexity of the likelihood, direct maximization is difficult. An EM type algorithm is provided for the Maximum Likelihood estimation of the parameters of the proposed model. We adopt an iterative scheme which is not based on explicit solution to the normal equations. This subtle approach reduces the computational difficulty of solving the complicated quantities involved directly to designing an iterative scheme based on a representation of the normal equation. The algorithm is easily programmable and we obtained a monotonic convergence for the data sets used.

EXPLICIT EXPRESSIONS FOR SOME DISTRIBUTIONS RELATED TO RUIN PROBLEMS

The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.

A Normal Weighted Inverse Gaussian Distribution for Skewed and Heavy-Tailed Data

High frequency financial data is characterized by non-normality: asymmetric, leptokurtic and fat-tailed behaviour. The normal distribution is therefore inadequate in capturing these characteristics. To this end, various flexible distributions have been proposed. It is well known that mixture distributions produce flexible models with good statistical and probabilistic properties. In this work, a finite mixture of two special cases of Generalized Inverse Gaussian distribution has been constructed. Using this finite mixture as a mixing distribution to the Normal Variance Mean Mixture we get a Normal Weighted Inverse Gaussian (NWIG) distribution. The second objective, therefore, is to construct and obtain properties of the NWIG distribution. The maximum likelihood parameter estimates of the proposed model are estimated via EM algorithm and three data sets are used for application. The result shows that the proposed model is flexible and fits the data well.

Local component based principal component analysis model for multimode process monitoring

For plant-wide processes with multiple operating conditions,the multimode feature imposes some challenges to conventional monitoring techniques.Hence,to solve this problem,this paper provides a novel local component based principal component analysis(LCPCA)approach for monitoring the status of a multimode process.In LCPCA,the process prior knowledge of mode division is not required and it purely based on the process data.Firstly,LCPCA divides the processes data into multiple local components using finite Gaussian mixture model mixture(FGMM).Then,calculating the posterior probability is applied to determine each sample belonging to which local component.After that,the local component information(such as mean and standard deviation)is used to standardize each sample of local component.Finally,the standardized samples of each local component are combined to train PCA monitoring model.Based on the PCA monitoring model,two monitoring statistics T^(2) and SPE are used for monitoring multimode processes.Through a numerical example and the Tennessee Eastman(TE)process,the monitoring result demonstrates that LCPCA outperformed conventional PCA and LNS-PCA in the fault detection rate.

Performance monitoring of non-gaussian chemical processes with modes-switching using globality-locality preserving projection

In this paper, we propose a novel performance monitoring and fault detection method, which is based on modified structure analysis and globality and locality preserving （MSAGL） projection, for non-Gaussian processes with multiple operation conditions. By using locality preserving projection to analyze the embedding geometrical manifold and extracting the non-Gaussian features by independent component analysis, MSAGL preserves both the global and local structures of the data simultaneously. Furthermore, the tradeoff parameter of MSAGL is tuned adaptively in order to find the projection direction optimal for revealing the hidden structural information. The validity and effectiveness of this approach are illustrated by applying the proposed technique to the Tennessee Eastman process simulation under multiple operation conditions. The results demonstrate the advantages of the proposed method over conventional eigendecomposition-based monitoring methotis.