Segmentation of clusters by template rotation expectation maximization

Gaussian Mixture Models (GMMs) are widely used in unsupervised learning for their ability to model complex, multimodal data distributions. However, conventional GMMs ignore spatial dependencies, making them poorly suited for satellite image segmentation where spatial continuity and contextual coherence are essential. In this paper, we propose a novel Spatially-Aware Gaussian Mixture Model (SA-GMM) that integrates spatial regularization directly into the Expectation-Maximization (EM) framework. By encouraging neighboring pixels to share similar cluster assignments through edge-aware spatial priors, the proposed method achieves smoother and more accurate segmentations while preserving important land cover boundaries.We evaluate SA-GMM on multispectral satellite imagery from Sentinel-2 (EuroSAT) and Landsat 8, comparing it against standard GMM and K-Means baselines. Experimental results show that SA-GMM improves Calinski-Harabasz score by 2.5× (794.4 vs. 316.0) over classical GMM and increases edge preservation accuracy by 18.3%, confirming the model’s effectiveness in capturing spatial structure. These findings highlight the benefit of incorporating spatial context into probabilistic clustering and establish SA-GMM as a robust tool for unsupervised land cover mapping in remote sensing.

Gaussian-input Gaussian mixture model for representing density maps and atomic models.

The traditional Expectation-Maximization (EM) training of Gaussian Mixture Model (GMM) is essentially a batch mode procedure which requires the multiple data samples with the sufficient size to update the model parameters. This severely limits the deployment and adaptation of GMM in many real-time online systems since the newly observed data samples are expected to be incorporated into the system upon available via retraining the model. This paper presents a new online incremental EM training procedure of GMM, which aims to perform the EM training incrementally and so can adapt GMM online sample by sample. The proposed method is extended on two kinds of EM algorithms for GMM, namely, Split-and-Merge EM and the traditional EM. Experiments on both the synthetic data and a speech processing task show the advantages and efficiency of the new method.

The expectation maximisation (EM) algorithm is an iterative maximum likelihood procedure often used for estimating the parameters of a mixture model. Theoretically, increases in the likelihood function are guaranteed as the algorithm iteratively improves upon previously derived parameter estimates. The algorithm is considered to converge when all parameter estimates become stable and no further improvements can be made to the likelihood value. However, to reduce computational time, it is often common practice for the algorithm to be stopped before complete convergence using heuristic approaches. In this paper, we consider various stopping criteria and evaluate their effect on fitting Gaussian mixture models (GMMs) to patient length of stay (LOS) data. Although the GMM can be successfully fitted to positively skewed data such as LOS, the fitting procedure often requires many iterations of the EM algorithm. To our knowledge, no previous study has evaluated the effect of different stopping criteria on fitting GMMs to skewed distributions. Hence, the aim of this paper is to evaluate the effect of various stopping criteria in order to select and justify their use within a patient spell classification methodology. Results illustrate that criteria based on the difference in the likelihood value and on the GMM parameters may not always be a good indicator for stopping the algorithm. In fact we show that the values of the difference in the variance parameters should be used instead, as these parameters are the last to stabilise. In addition, we also specify threshold values for the other stopping criteria.

The accurate modeling of uncertain variables, such as wind power and load uncertainty, is an essential foundation for the planning operation and scheduling decisions in power systems. Currently, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are the primary techniques used to characterize uncertainties in power systems, which are commonly solved by expectation-maximization (EM) algorithm. However, for the massive data of uncertain variables, the algorithm encounters challenges in accurately obtaining GMM and DPMM with a lower time consumption. To address this issue, we propose a method for GMM uncertainty modeling in power systems considering the mutual assistance of latent variables. Specifically, the GMM of uncertain variables is first constructed, and the conditional probability is employed to characterize the mutual assistance of latent variables. Then, an improved EM algorithm is developed to obtain the optimal GMM parameters, in which the expectation step (E-step) and maximization step (M-step) of the algorithm are revised using the conditional probability. Importantly, the closed-form solutions for GMM parameters are rederived in the revised E-step and M-step. Finally, the proposed uncertainty modeling method is compared with the traditional GMM and DPMM on actual wind power and load data from Australia. The proposed method performs the efficiency and accuracy in characterizing uncertainty.

One effective iterative method for estimating parameters in latent variable probabilistic models is the Expectation-Maximization (EM) algorithm, which finds extensive use in classification issues. A versatile probabilistic framework for modeling data from multiple Gaussian distributions, Gaussian Mixture Models (GMMs) employ EM for parameter estimation, which is explored in this article. Problems with class membership estimation (including means, covariances, and mixing coefficients) are the primary focus of this study. Starting with initial parameter estimations, estimating posterior probabilities in the E-step, and repeatedly updating model parameters in the M-step until convergence, the technique entails applying the EM algorithm on both synthetic and real-world datasets. In order to measure performance, we compare it to K-means and other baseline classifiers using measures like classification accuracy, Adjusted Rand Index (ARI), and log-likelihood progression. When data is distributed according to a multimodal Gaussian distribution, the findings show that EM-GMM provides better parameter estimation and better classification accuracy. Initialization procedures have a substantial effect on performance, as convergence study further shows. In addition to reiterating the EM algorithm's usefulness for probabilistic classification, this paper also describes its advantages and disadvantages and offers suggestions for improving its performance in settings with high-dimensional data and noise.

In a distribution power network, the load model has no certain pattern or predicted behaviour due to large range of data and changes in energy consumption for end-user consumers. Thus, a powerful analysis based on probabilistic structure is required. For this paper Gaussian Mixture Model (GMM) has been used. GMM is a powerful probability model that allows different types of load distributions to be presented as a combination of several Gaussian distributions. The parameters of GMM is unknown for large random data such as real load data and these parameters can be identified by Expectation Maximization (EM) algorithm. This paper presents a method to evaluate probabilistic load data concerning the time-evolution of any type of distribution load for any duration of time. The proposed method is explained through generated load data of 100 residential houses for duration of one year.

Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. This has a significant impact on the delay, power dissipation, and area of the final circuit. The gate sizing methods previously proposed suffer from problems that make them difficult to apply on real-life large circuits. This paper presents GS, a gate sizing based general purpose optimization algorithm, which has the following characteristics: it can optimize the power or/and area under some delay constraints, or the delay under some power or/and area constraints; it can take into account user defined or library dependent design rules; as opposed to greedy approaches, it addresses non-linear, non-unimodal, constrained optimization, in order to handle complex cost models (e.g., delay and power); it can be applied on large circuits within a reasonable CPU time, e.g., 10000 nodes in 2 hours for power optimization under delay constraints.

This article proposes the distribution similarity measure–based Gaussian mixtures model for the contact-state (CS) modelling in force-guided robotic assembly processes of flexible rubber parts. The wrench (Cartesian force and torque) signals of the manipulated object are captured for different states of the given assembly process. The distribution similarity measure–based Gaussian mixtures model CS modelling scheme is employed in modelling the captured wrench signals for different CSs. The proposed distribution similarity measure–based Gaussian mixtures model CS modelling scheme uses the Gaussian mixtures model in modelling the captured signals. The parameters of the Gaussian mixtures models are computed using expectation maximisation. The optimal number of Gaussian mixtures model components for each CS model is determined by considering the classification success rate as an index for the similarity measure between the distribution of the captured signals and the developed models. The optimal number of Gaussian mixtures model components corresponds to the highest classification success rate; hence, object elasticity variation would be accommodated by properly choosing the optimal number of Gaussian mixtures model components. The performance of the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy is evaluated by a test stand composed of a KUKA lightweight robot doing peg-in-hole assembly processes for flexible rubber objects. Two rubber objects with different elasticity are considered for two experiments; in the first experiment, an elastic peg of 30 Shore A hardness is considered and that of the second experiment has hardness of 6 Shore A which is even softer than the one used in experiment 1. Employing the proposed distribution similarity measure–based Gaussian mixtures model CS modelling strategy excellent classification success rate was obtained for both experiments. However, more Gaussian mixtures model components are required for the softer one that gives a strong impression of the non-stationarity behaviour increment for softer materials. Comparison is performed with the available CS modelling schemes and the distribution similarity measure–based Gaussian mixtures model is shown to provide the best classification success rate performance with a reduced computational time.

To model manipulation tasks, we propose a novel method for learning manipulation skills based on the degree of motion granularity. Even though manipulation tasks usually consist of a mixture of fine-grained and coarse-grained movements, to the best of our knowledge, manipulation skills have so far been modeled without considering their motion granularity. To model such a manipulation skill, Gaussian mixture models (GMMs) have been represented using several well-known techniques such as principal component analysis, k-means, Bayesian information criterion, and expectation-maximization (EM) algorithms. However, in this GMM, there is a problem in that when a mixture of fine-grained and coarse-grained movements is modeled as a GMM, fine-grained movements tend to be poorly represented. To resolve this issue, we measure a continuous degree of motion granularity for every time step of a manipulation task from a GMM. Then, we remodel the GMM by weighting a conventional k-means algorithm with motion granularity. Finally, we also estimate the parameters of the GMM by weighting the conventional EM with motion granularity. To validate our proposed method, we evaluate the GMM estimated using our proposed method by comparing it with those estimated by different GMMs in terms of inference, regression, and generalization using a robot arm that performs two daily tasks, namely decorating a very small area and passing through a narrow tunnel.

This paper addresses the problem of initialization of the expectation-maximization (EM) algorithm for maximum likelihood estimation of Gaussian mixture models. In order to avoid local maxima of the likelihood function, a genetic algorithm (GA) which searches for best initial conditions of the EM algorithm is proposed. In the GA, a chromosome represents a set of initial conditions, in which initial mean vectors of mixture components are feature vectors chosen from the training set. The chromosome also encodes variances of initial spherical covariance matrices of mixture components. To evaluate each chromosome in the GA we run the EM algorithm until convergence and use the obtained log likelihood as the fitness. In computational experiments our approach was applied to clustering problem and tested on two datasets from the image processing domain. The results indicate that our method outperforms the standard multiple restart EM algorithm and is at least comparable to the state-of-the art random swap EM method.

In this paper we apply generative modeling to Gaussian Mixture Models (GMM) as a solution to high dimensional novel event detection and analysis on radio frequency (RF) power generators. A family of Denoising and β-Disentangling Variational Autoencoders β-DVAE) is used to encode datasets into lower and more salient dimensions. The reduced feature sets are modeled using GMMs where model parameters are learned using the Expectation Maximization (EM) algorithm. The data is obtained from two different generator models operating under normal as well as known not-normal conditions. This approach is also tested on standard classification sets. Robust testing is reported to achieve a target class accuracy of 98.16% for the target RF generator. Additionally, the GMM parameters are decoded by the generative model to the original data space for calculating per-variable fitness in order to provide an initial novel event analysis for engineers and technicians. This per-variable fitness is very critical for determining each variable's contribution to a novelty so that engineers can perform informed trouble shooting and maintenance of the RF generators.

Gaussian mixture model based parameter estimation and classification has recently received great attention in modelling and processin g data. Gaussian Mixture Model (GMM) is the probabilistic model for representing the presence of subpopulations and it works well with the classification and parameter estimation strategy. Here in this work Maximum Likelihood Estimation (MLE) based on Expectation Maximization (EM) is being used for the parameter estimation approach and the estimated parameters are being used for the training and the testing of the images for their normality and the abnormality. With the mean and the covariance calculated as the parameters they are used in the Gaussian Mixture Model (GMM) based training of the classifier. Support Vector Machine a discriminative classifier and the Gaussian Mixture Model a generative model classifier are the two most popular techniques. The performance of the classification strategy of both the classifiers used has a better proficiency when compared to the other classifiers. By combining the SVM and GMM we co uld be able to classify at a better level since estimating the parameters through the GMM has a very few amount of features and hence it is not needed to use any of the feature reduction techniques. In this the GMM classifier and the SVM classifier are trained usin g the parameters and they are to be compared.

How to use historical data of public smart card to predict user behaviour attracts a lot of attention. This paper aims at modelling travel patterns and predicting future travel behaviour of metro system smart card holders. We apply Gaussian mixture model (GMM) on time series to model user behaviour. We propose a new method based on the perplexity for finite GMM and use expectation-maximisation (EM) algorithm to estimate parameters of GMM. In order to predict the future travel behaviour, we introduce the Gaussian process regression (GPR) to define distributions over GMM, which can not only tell the probability of travelling at a certain moment but also tell the reliability of the prediction. Experimental results show that our whole system in the centre of GMM and GPR can effectively mine the hidden knowledge of historical data of smart card, and thus model the travel patterns and predict future travel behaviour.

The expectation-maximization (EM) algorithm is a popular approach for parameter estimation of finite mixture model (FMM). A drawback of this approach is that the number of components of the finite mixture model is not known in advance, nevertheless, it is a key issue for EM algorithms. In this paper, a penalized minimum matching distance-guided EM algorithm is discussed. Under the framework of Greedy EM, a fast and accurate algorithm for estimating the number of components of the Gaussian mixture model (GMM) is proposed. The performance of this algorithm is validated via simulative experiments of univariate and bivariate Gaussian mixture models.