Earticle

그동안 차두시간분포를 나타내는 확률분포로 음지수분포, Erlang 분포, 정규분포 등 다양한 단일확률분포들이 사용되어져 왔다. 그러나, 실제 도로에서 차두시간분포의 조사결과는 단일 확률분포로서 설명하기 어려운 경우가 있었다. 본 연구는 차량의 차두시간에 대해 두 개의 정 규분포가 일정한 관련성을 가지고 결합된 복합확률분포의 파라메타에 대해 최우추정법 중 하 나인 EM 알고리즘을 이용하여 추정하는 접근방법을 시도하였다. 이에 대한 분석결과 기존에 알려진 단일확률분포로서 잘 설명되기 어려웠던 차량도착 차두시간 분포를 EM 알고리즘을 이 용하여 복합확률분포의 파라메타를 추정하여 설명하였다. χ2 test 적합도 검정결과, 유의수준 1%에서 통계학적으로 유의성이 확보되어 EM 알고리즘을 이용한 복합확률분포의 파라메타 추 정의 신뢰성이 입증되는 것으로 분석되었다

Various single probability distributions have been used to represent time headway distributions. However, it has often been difficult to explain the time headway distribution as a single probability distribution on site. This study used the EM algorithm, which is one of the maximum likelihood estimations, for the parameters of combined mixture distributions with a certain relationship between two normal distributions for the time headway of vehicles. The time headway distribution of vehicle arrival is difficult to represent well with previously known single probability distributions. But as a result of this analysis, it can be represented by estimating the parameters of the mixture probability distribution using the EM algorithm. The result of a goodness-of-fit test was statistically significant at a significance level of 1%, which proves the reliability of parameter estimation of the mixture probability distribution using the EM algorithm.

This thesis studies two imputation methods, the MCMC method and the EM algorithm, that take care of the problem. The performance of the two methods for the linear (or quadratic) discriminant analysis are evaluated under various types of incomplete observations. Based on simulated experiments, the effect of the imputation using the EM algorithm and the MCMC method are evaluated and compared in terms of the probability of misclassification and the RMSE. This is done for the various cases of incomplete observations. The cases are differentiated by missing rates, sample sizes, and distances between two classification groups. The studies show that the probability of misclassification and the RMSE of the EM algorithm method is lower than the MCMC method. Therefore the imputation using the EM algorithm is more efficient than the MCMC method. And the probability of misclassification of the method that all vectors of observations with missing values are omitted from analysis is lower than the EM algorithm and the MCMC method when the samples size is small and the rate of missing values is extremely big.

In this paper, a specific type of incomplete data in Wi-Fi fingerprinting based indoor positioning systems (WF-IPS) is presented: censored and dropped mixture data. For fitting this type of data, a censored and dropped Gaussian Mixture Model (CD-GMM) was proposed. Further, an extended version of the Expectation-Maximization (EM) algorithm is developed for estimating parameters of this model. Simulation results demonstrate the effectiveness of the proposed method for parameter estimation.

The question of how to analyze unbalanced hierarchical data generated from structural equation models has been a common problem for researchers and analysts. Among difficulties plaguing statistical modeling are removing estimation bias due to measurement error and incorporating variability associated with the social milieu in which individuals are situated. This paper presents empirical Bayes estimation by means of the EM algorithm in the context of unbalanced sampling designs. The EM algorithm is particularly useful when the analytic expressions exist for the conditional expectations of the missing data given complete data and for the maximum likelihood estimators (MLE) of the model parameters. The accuracy of the algorithm was tested using a set of artificial data. The numerical results suggest that this new methodology is a useful mean for studying hypothesized relations among latent variables varying at two levels of hierarchy.

In data mining applications, there are various kinds of missing values in experimental datasets. Non-substitution or inappropriate treatment of missing values has a high probability to cause a lot of warnings or errors. Besides, many classification algorithms are very sensitive to the missing values. Because of these, handling the missing values is an important phase in many classification or data mining task. This paper introduces traditional EM algorithm and disadvantage of the EM algorithm. We propose a new method to implement the missing values based on EM algorithm, which uses Naive Bayesian to improve the accuracy. We conclude by classifying seeds dataset and vertebral columns dataset and comparing the results to those obtained by applying two other missing value handling methods: the traditional EM algorithm and the non-substitution method. The experimental results prove a stable algorithm for improving the data classification accuracy on large datasets, which contain a lot of missing values.

주변 후방산란 통신 (Ambient Backsactter Communication, AmBC)은 주변의 RF 신호를 활용해 데이터를 전송하기 때문에 송신 전력이 제한되는 단점을 가지고 있다. 이를 위해, 송수신기 간 전송 효율을 높이 위한 방법으로 수신단에서 채널 상태를 추정할 수 있는 채널 추정기가 필요하다. 본 논문에서는 주변 후방산란 통신에서 기댓값-최대화 알고리즘(Expectation-Maximization Algorithm, EM algorithm) 기반의 채널 추정기의 성능 개선을 위해 K-means 알고리즘 도입 방안을 고려하였다. 모의실험은 제안한 채널 추정기의 성능 확인을 위해 성능 지표로 평균 제곱 오차 (Mean Square Error, MSE)를 사용한다. 모의실험을 통해 K-means을 통한 초깃값 설정 시, 기존 EM 알고 리즘을 통한 채널 추정 방식 대비 개선된 성능을 보인다.

Ambient backscatter communication has a drawback in which the transmission power is limited because the data is transmitted using the ambient RF signal. In order to improve transmission efficiency between transceiver, a channel estimator capable of estimating channel state at a receiver is needed. In this paper, we consider the K-means algorithm to improve the performance of the channel estimator based on EM algorithm. The simulation uses MSE as a performance parameter to verify the performance of the proposed channel estimator. The initial value setting through K-means shows improved performance compared to the channel estimation method using the general EM algorithm.

Aiming at the cuckoo search algorithm (CSA) with disadvantages of slow convergence speed, getting into local extremum easily and low accuracy, we put forward cuckoo search algorithm with cauchy mutation(CCSA). For Bayesian networks(BNs) structure learning with insufficient data, we propose data completion method and Bayesian network structure learning with insufficient data based on CCSA(BNSL-ID-CCSA). In BNSL-ID-CCSA, firstly, we adopt K2 metric as evaluation measure for learning Bayesian networks from data. Secondly, we use expectation maximization(EM) algorithm and CCSA to make BNSL-ID-CCSA quickly and accurately converge to the global optimal solution. The experimental results show that BNSL-ID-CCSA has strong learning ability and good stability.

For the personalized learning, a good testing method, which can effectively estimate a learner’s proficiency, is required. In this paper, we propose a novel testing method, Bayesian network-based approach to Computerized Adaptive Testing (CAT). Our novel approach can estimate proficiency of the examinee effectively and efficiently because it reflects complicated relationships between all items and their categories, and can estimate detailed proficiency about each specific category. In experimental results, we show that our approach can improve accuracy and speed of estimating examinee’s proficiency as compared with classical testing methods like paper-based test and conventional IRT-based CAT.

This paper considers an EM (expectation-maximization) based scheme for record value statistics (RVS) models in software reliability estimation. The RVS model provides one of the generalized modeling frameworks to unify several of existing software reliability models described as non-homogeneous Poisson processes (NHPPs). The proposed EM algorithm gives a numerically stable procedure to compute the maximum likelihood estimates of RVS models. In particular, this paper focuses on an RVS model based on a mixture of exponential distributions. As an illustrative example, we also derive a concrete EM algorithm for the wellknown Musa-Okumoto logarithmic Poisson execution time model by applying our result, and discusses the effectiveness of the EM-based scheme for RVS models with a simple numerical example.

Clustering is one of the main tasks used in pattern recognition and classification. Out of many methods that have been reported till date the most widely used methods are based on likelihood approach of mixture model. Among different mixture models, Expectation Maximization for Gaussian Mixture is most exploited and trusted algorithm for data clustering. However, it has some short comings such as initial parameters are to be given a-priori, convergence speed is slow and the results obtained are highly dependent upon the initial parameters. Many variations have been carried out in implementing EM algorithm but still there is ample scope for improvement. The proposed algorithm tries to overcome these shortcomings and provide more robust and efficient version of clustering algorithm. An improvement related to cluster partitioning is proposed in the existing algorithm resulting some advantages. The robustness and efficacy of the algorithm is demonstrated qualitatively as well as quantitatively with the help of some experiments.

It is well known that the maximum likelihood estimator(MLE) in normal mixture models with unequal variances does not fall in the interior of the parameter space. Recently, a doubly smoothed maximum likelihood estimator(DS-MLE) (Seo and Lindsay, 2010) was proposed as a general alternative to the ordinary maximum likelihood estimator. Although this method gives a natural modification to the ordinary MLE, its computation is cumbersome due to intractable integrations. In this paper, we derive an EM algorithm for the DS-MLE under normal mixture models and propose a fast computational tool using a local quadratic approximation. The accuracy and speed of the proposed method is then presented via some numerical studies.

For discrimination with binary variables, reformulated full and first order Bahadur model with incomplete observations are presented. This allows prior probabilities associated with multiple population to be estimated for the sample-based classification rule. The EM algorithm is adopted to provided the maximum likelihood estimates of the parameters of interest. Some experiences with the models are evaluated and discussed.

The EM algorithm is the most important tool to obtain the maximum likelihood estimator in finite mixture models due to its stability and simplicity. However, its convergence rate is often slow because the conventional EM algorithm is based on a large missing data space. Several techniques have been proposed in the literature to reduce the missing data space. In this paper, we review existing methods and propose a new EM algorithm for Gaussian mixtures, which reduces the missing data space while preserving the stability of the conventional EM algorithm. The performance of the proposed method is evaluated with other existing methods via simulation studies.

Due to the uniquely slow convergence speed of the EM algorithm, it suffers form a lot of processing time until the desired deconvolution image is obtained when the image is large. To cope with the problem, in this paper, an immediate solution of the EM algorithm is provided under the Gaussian image model. It is derived by finding the recurrent formular of the EM algorithm and then substituting the results repeatedly. In this paper, two types of immediate soultion of image deconboution by EM algorithm are provided, and both methods have been shown to work well. It is expected that it free the processing time of image deconvolution because it no longer requires an iterative process. Based on this, we can find the statistical properties of the restored image at specific iterates. We demonstrate the effectiveness of the proposed method through a simple experiment, and discuss future concerns.

This study proposes a fuzzy classification using EM algorithm. For cluster validation, this approach iteratively estimates the class-parameters in the fuzzy training for the sample classes and continuously computes the log-likelihood ratio of two consecutive class-numbers. The maximum ratio rule is applied to determine the optimal number of classes.

Many data sets obtained from surveys or medical trials often include missing observations. When these data sets are analyzed, it is general to use only complete cases. However, it is possible to have big biases or involve inefficiency. In this paper, we consider a method for estimating parameters in logistic linear models involving non-ignorable missing data mechanism. A binomial response and normal exploratory model for the missing data are used. We fit the model using the EM algorithm. The E-step is derived by Metropolis-hastings algorithm to generate a sample for missing data and Monte-carlo technique, and the M-step is by Newton-Raphson to maximize likelihood function. Asymptotic variances of the MLE's are derived and the standard error and estimates of parameters are compared.

A fuzzy approach using an EM algorithm for image classification is presented. In this study, a double compound stochastic image process is assumed to combine a discrete-valued field for region-class processes and a continuous random field for observed intensity processes. The Markov random field is employed to characterize the geophysical connectedness of a digital image structure. The fuzzy classification is an EM iterative approach based on mixture probability distribution. Under the assumption of the double compound process, given an initial class map, this approach iteratively computes the fuzzy membership vectors in the E-step and the estimates of class-related parameters in the M-step. In the experiments with remotely sensed data, the MRF-based method yielded a spatially smooth class-map with more distinctive configuration of the classes than the non-MRF approach.

Maximum likelihood estimates (MLEs) for recursive models of categorical variables are discussed under an EM framework. Since MLEs by EM often depend on the choice of the initial values for MLEs, we explore reasonable rules for selecting the initial values for EM. Simulation results strongly support the proposed rules.

This paper presents an object tracking with radical change of color. Conventional Mean Shift do not provide appropriate result when major color distribution disappear. Our tracking approach is based on Mean Shift as basic tracking method. However we propose tracking algorithm that shows good results for an object of radical variation. The key idea is iterative update previous color information of an object that shows different color by using EM algorithm. As experiment results, we show that our proposed algorithm is an effective approach in tracking for a real object include an object having radical change of color.