Parameter Estimation Of Mixture Models Research Articles

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Retracted: Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

Offshore Wind Energy Assessment with a Clustering Approach to Mixture Model Parameter Estimation

In wind resource assessment research, mixture models are gaining importance due to the complex characteristics of wind data. The precision of parameter estimations for these models is paramount, as it directly affects the reliability of wind energy forecasts. Traditionally, the expectation–maximization (EM) algorithm has served as a primary tool for such estimations. However, challenges are often encountered with this method when handling complex probability distributions. Given these limitations, the objective of this study is to propose a new clustering algorithm, designed to transform mixture distribution models into simpler probability clusters. To validate its efficacy, a numerical experiment was conducted, and its outcomes were compared with those derived from the established EM algorithm. The results demonstrated a significant alignment between the new method and the traditional EM approach, indicating that comparable accuracy can be achieved without the need for solving complex nonlinear equations. Moreover, the new algorithm was utilized to examine the joint probabilistic structure of wind speed and air density in China’s coastal regions. Notably, the clustering algorithm demonstrated its robustness, with the root mean square error value being notably minimal and the coefficient of determination exceeding 0.9. The proposed approach is suggested as a compelling alternative for parameter estimation in mixture models, particularly when dealing with complex probability models.

Simulation of Tennis Match Scene Classification Algorithm Based on Adaptive Gaussian Mixture Model Parameter Estimation

This paper presents an in-depth analysis of tennis match scene classification using an adaptive Gaussian mixture model parameter estimation simulation algorithm. We divided the main components of semantic analysis into type of motion, distance of motion, speed of motion, and landing area of the tennis ball. Firstly, for the problem that both people and tennis balls in the video frames of tennis matches from the surveillance viewpoint are very small, we propose an adaptive Gaussian mixture model parameter estimation algorithm, which has good accuracy and speed on small targets. Secondly, in this paper, we design a sports player tracking algorithm based on role division and continuously lock the target player to be tracked and output the player region. At the same time, based on the displacement information of the key points of the player’s body and the system running time, the distance and speed of the player’s movement are obtained. Then, for the problem that tennis balls are small and difficult to capture in high-speed motion, this paper designs a prior knowledge-based algorithm for predicting tennis ball motion and landing area to derive the landing area of tennis balls. Finally, this paper implements a prototype system for semantic analysis of real-time video of tennis matches and tests and analyzes the performance indexes of the system, and the results show that the system has good performance in real-time, accuracy, and stability.

Optimizing the Estimation of a Histogram-Bin Width—Application to the Multivariate Mixture-Model Estimation

A maximum-likelihood estimation of a multivariate mixture model’s parameters is a difficult problem. One approach is to combine the REBMIX and EM algorithms. However, the REBMIX algorithm requires the use of histogram estimation, which is the most rudimentary approach to an empirical density estimation and has many drawbacks. Nevertheless, because of its simplicity, it is still one of the most commonly used techniques. The main problem is to estimate the optimum histogram-bin width, which is usually set by the number of non-overlapping, regularly spaced bins. For univariate problems it is usually denoted by an integer value; i.e., the number of bins. However, for multivariate problems, in order to obtain a histogram estimation, a regular grid must be formed. Thus, to obtain the optimum histogram estimation, an integer-optimization problem must be solved. The aim is therefore the estimation of optimum histogram binning, alone and in application to the mixture model parameter estimation with the REBMIX&EM strategy. As an estimator, the Knuth rule was used. For the optimization algorithm, a derivative based on the coordinate-descent optimization was composed. These proposals yielded promising results. The optimization algorithm was efficient and the results were accurate. When applied to the multivariate, Gaussian-mixture-model parameter estimation, the results were competitive. All the improvements were implemented in the rebmix R package.

Improved Initialization of the EM Algorithm for Mixture Model Parameter Estimation

A commonly used tool for estimating the parameters of a mixture model is the Expectation–Maximization (EM) algorithm, which is an iterative procedure that can serve as a maximum-likelihood estimator. The EM algorithm has well-documented drawbacks, such as the need for good initial values and the possibility of being trapped in local optima. Nevertheless, because of its appealing properties, EM plays an important role in estimating the parameters of mixture models. To overcome these initialization problems with EM, in this paper, we propose the Rough-Enhanced-Bayes mixture estimation (REBMIX) algorithm as a more effective initialization algorithm. Three different strategies are derived for dealing with the unknown number of components in the mixture model. These strategies are thoroughly tested on artificial datasets, density–estimation datasets and image–segmentation problems and compared with state-of-the-art initialization methods for the EM. Our proposal shows promising results in terms of clustering and density-estimation performance as well as in terms of computational efficiency. All the improvements are implemented in the rebmix R package.

Variable selection in finite mixture of generalized estimating equations

This paper develops a new method to estimate the parameters in mixture models. Traditionally, the parameter estimation in mixture models is performed from a likelihood point of view by exploiting the expectation maximization (EM) method. In this paper, however, we utilize the Least Square Principle. Based on this principle, we propose an iterative algorithm called Iterative Weighted least Square (IWLS) to estimate the parameters. Through comparative study, we demonstrate the superiority of our method compared to EM method. We show that IWLS method outperforms EM in both accuracy and the number of iterations required for convergence.

Application of three-parameter Weibull mixture model for reliability assessment of NC machine tools: a case study

To analyse the reliability of numerical control (NC) machine tools, a three-parameter Weibull mixture model is proposed in this case study. Negative log-likelihood function is used as an optimal objective instead of solving complex system of equations; the problem of parameter estimation of mixture model is solved by a non-linear programming method. A comprehensive criteria, which include Akaike information criterion, Bayesian information criterion, and root mean squared error, is presented for selecting the number of components of mixture model. The field failure data of three NC machine tools are analysed and the results of reliability assessment, such as the reliability, maintainability, availability, etc., are all presented. The results show that the mixture model of three-parameter Weibull distribution, with advantages over other Weibull models, is suitable for modelling failure data of multiple NC machine tools with multiple failure modes and causes.

A Hybrid Algorithm with GA and DAEM

Although the expectation-maximization (EM) algorithm has been widely used for finding maximum likelihood estimation of parameters in probabilistic models, it has the problem of trapping by local maxima. To overcome this problem, the deterministic annealing EM (DAEM) algorithm was once proposed and had achieved better performance than EM algorithm, but it is not very effective at avoiding local maxima. In this paper, a solution is proposed by integrating GA and DAEM into one procedure to further improve the solution quality. The population based search of genetic algorithm will produce different solutions and thus can increase the search space of DAEM. Therefore, the proposed algorithm will reach better solution than just using DAEM. The algorithm retains the property of DAEM and gets the better solution by genetic operation. Experiment results on Gaussian mixture model parameter estimation demonstrate that the proposed algorithm can achieve better performance.

Multi-year drought frequency analysis at multiple sites by operational hydrology – A comparison of methods

This paper compares two generators of yearly water availabilities from sources located at multiple sites with regard to their ability to reproduce the characteristics of historical critical periods and to provide reliable results in terms of the return period of critical sequences of different length. The two models are a novel multi-site Markov mixture model explicitly accounting for drought occurrences and a multivariate ARMA. In the case of the multisite Markov mixture model parameter estimation is limited to a search in the parameter space guided by the value of parameter λ to show the sensitivity of the model to this parameter. Application to two of the longest time series of streamflows available in Sicily (Italy) shows that the models can provide quite different results in terms of estimated return periods of historic droughts, although they seem to perform more uniformly when it comes to simulate drought-related statistics such as drought length, severity and intensity. The role of parameter selection for the multisite Markov mixture model and of the marginal probability of generated flows in providing results consistent with the characteristics of the observed series is discussed. Both models are applied to the system of sources supplying the city of Palermo (Sicily) and its environs showing the applicability of the newly developed multisite Markov mixture model to medium-to-large scale water resources systems.

Competitive EM algorithm for finite mixture models

In this paper, we present a novel competitive EM (CEM) algorithm for finite mixture models to overcome the two main drawbacks of the EM algorithm: often getting trapped at local maxima and sometimes converging to the boundary of the parameter space. The proposed algorithm is capable of automatically choosing the clustering number and selecting the “split” or “merge” operations efficiently based on the new competitive mechanism we propose. It is insensitive to the initial configuration of the mixture component number and model parameters.Experiments on synthetic data show that our algorithm has very promising performance for the parameter estimation of mixture models. The algorithm is also applied to the structure analysis of complicated Chinese characters. The results show that the proposed algorithm performs much better than previous methods with slightly heavier computation burden.

Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models

Simple methods to choose sensible starting values for the EM algorithm to get maximum likelihood parameter estimation in mixture models are compared. They are based on random initialization, using a classification EM algorithm (CEM), a Stochastic EM algorithm (SEM) or previous short runs of EM itself. Those initializations are included in a search/run/select strategy which can be compounded by repeating the three steps. They are compared in the context of multivariate Gaussian mixtures on the basis of numerical experiments on both simulated and real data sets in a target number of iterations. The main conclusions of those numerical experiments are the following. The simple random initialization which is probably the most employed way of initiating EM is often outperformed by strategies using CEM, SEM or shorts runs of EM before running EM. Also, it appears that compounding is generally profitable since using a single run of EM can often lead to suboptimal solutions. Otherwise, none of the experimental strategies can be regarded as the best one and it is difficult to characterize situations where a particular strategy can be expected to outperform the other ones. However, the strategy initiating EM with short runs of EM can be recommended. This strategy, which as far as we know was not used before the present study, has some advantages. It is simple, performs well in a lot of situations presupposing no particular form of the mixture to be fitted to the data and seems little sensitive to noisy data.

Outliers in statistical pattern recognition and an application to automatic chromosome classification

We propose a heuristic method of parameter estimation in mixture models for data with outliers and design a Bayesian classifier for assignment of m objects to n ⩾ m classes under constraints. This method of outlier handling combined with the classifier is applied to the well-known problem of automatic, constrained classification of chromosomes into their biological classes. We show that it decreases the error rate relative to the classical, normal, model by more than 50%. When applied to the Edinburgh feature data of the large Copenhagen image data set Cpr our best classifier yields an error rate close to 1.3% relative to chromosomes; 4 out of 5 cells are correctly classified.