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With the development of computer network bandwidth, packet classification algorithms which are able to deal with large-scale rule sets are in urgent need. Among the existing algorithms, researches on packet classification algorithms based on hierarchical trie have become an important packet classification research branch because of their widely practical use. Although hierarchical trie is beneficial to save large storage space, it has several shortcomings such as the existence of backtracking and empty nodes. This paper proposes a new packet classification algorithm, Hierarchical Trie Algorithm Based on Expectation-Maximization Clustering (HTEMC). Firstly, this paper uses the formalization method to deal with the packet classification problem by means of mapping the rules and data packets into a two-dimensional space. Secondly, this paper uses expectation-maximization algorithm to cluster the rules based on their aggregate characteristics, and thereby diversified clusters are formed. Thirdly, this paper proposes a hierarchical trie based on the results of expectation-maximization clustering. Finally, this paper respectively conducts simulation experiments and real-environment experiments to compare the performances of our algorithm with other typical algorithms, and analyzes the results of the experiments. The hierarchical trie structure in our algorithm not only adopts trie path compression to eliminate backtracking, but also solves the problem of low efficiency of trie updates, which greatly improves the performance of the algorithm. [ABSTRACT FROM AUTHOR]

A common problem in statistical modelling is to distinguish between finite mixture distribution and a homogeneous non-mixture distribution. Finite mixture models are widely used in practice and often mixtures of normal densities are indistinguishable from homogenous non-normal densities. This paper illustrates what happens when the EM algorithm for normal mixtures is applied to a distribution that is a homogeneous non-mixture distribution. In particular, a population-based EM algorithm for finite mixtures is introduced and applied directly to density functions instead of sample data. This algorithm is used to find finite mixture approximations to common homogeneous distributions. An example regarding the nature of a placebo response in drug treated depressed subjects is used to illustrate ideas. [ABSTRACT FROM AUTHOR]

In practice, many systems exhibit load‐sharing behavior, where the surviving components share the total load imposed on the system. Different from general systems, the components of load‐sharing systems are interdependent in nature, in such a way that when one component fails, the system load has to be shared by the remaining components, which increases the failure rate or degradation rate of the remaining components. Because of the load‐sharing mechanism among components, parameter estimation and reliability assessment are usually complicated for load‐sharing systems. Although load‐sharing systems with components subject to sudden failures have been intensely studied in literatures with detailed estimation and analysis approaches, those with components subject to degradation are rarely investigated. In this paper, we propose the parameter estimation method for load‐sharing systems subject to continuous degradation with a constant load. Likelihood function based on the degradation data of components is established as a first step. The maximum likelihood estimators for unknown parameters are deduced and obtained via expectation‐maximization (EM) algorithm considering the nonclosed form of the likelihood function. Numerical examples are used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider a class of degradation processes that can consist of distinct phases of behavior. In particular, the degradation rates could possibly increase or decrease in a non-smooth manner at some point in time when the underlying degradation process changes phase. To model the degradation path of a given device, we use an independent-increments stochastic process with a single unobserved change-point. Furthermore, we assume that the change-point varies randomly from device-to-device. The likelihood functions for such a model are analytically intractable, so in this paper we develop an EM algorithm for this model to obtain the maximum likelihood estimators efficiently. We demonstrate the applicability of the method using two different models, and present some computational results of our implementation. [ABSTRACT FROM AUTHOR]

It is common, even with new SPECT/CT systems, that the transmission data are truncated. This paper develops a method that obtains exact attenuation correction with truncated transmission data. The emission object (e.g., the heart) is assumed to have a finite, convex support, whose emission projections are not truncated. The transmission measurements over the support are available, but may be truncated outside the support (within the torso). A novel emission data reconstruction technique combines emission projections from conjugate views; a modified version of the ML-EM algorithm is used to reconstruct emission data. The attenuation map outside the support is not needed during reconstruction. The transmission measurements through the support are used to pre-scale the emission data and to reconstruct the attenuation map within the support. The attenuation map reconstruction within the support is an interior problem in which only a biased solution can be obtained using an iterative algorithm. The bias is then corrected by identifying a soft tissue region within the support and the known attenuation coefficient values of these pixels for the soft tissue. Proof of convergence of the new algorithm is provided. Computer simulations verify the accuracy of the new method. Conclusions: an exact attenuation map within the support can be obtained provided the attenuation coefficient is known at 1 pixel within the support. The method, which requires emission data over 360deg, provides a means to perform attenuation correction in SPECT with truncated transmission data. [ABSTRACT FROM AUTHOR]

Finite mixture models are a widely known method for modelling data that arise from a heterogeneous population. Within the family of mixtures of regression models, mixtures of linear mixed models have also been applied in different areas since, besides taking into consideration the heterogeneity in the population, they also allow to take into account the correlation between observations from the same individual. One of the main issues in mixture models concerns the estimation of the parameters. Maximum likelihood estimation is one of the most used methods in the estimation of the parameters for mixture models. However, the maximization of the log-likelihood function in mixture models is complex, producing in many cases infinite solutions whereby the maximum likelihood estimator may not exist, at least globally. For this reason, it is common to resort to iterative methods, in particular to the Expectation-Maximization (EM) algorithm. However, the slow convergence and the selection of initial values are two of biggest issues of the EM algorithm, the reason why some modified versions of this algorithm have been developed over the years. In this article we compare the performance of the EM, Classification EM (CEM) and Stochastic EM (SEM) algorithms in the estimation of the parameters for mixtures of linear mixed models. In order to evaluate their performance, we carry out a simulation study and a real data application. The results show that the CEM algorithm is the least computationally demanding algorithm, although the three algorithms provide similar maximum likelihood estimates for the parameters. [ABSTRACT FROM AUTHOR]

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data. [ABSTRACT FROM AUTHOR]