Robust Gaussian Mixture Model Research Articles

Forecast of NOx Emissions for a 660MW Coal-Fired Boiler with Multilayered Gradient Boosting Decision Tree Considering Multiple Operating Modes.

Nitrogen oxides (NOx) are among the primary pollutants emitted by coal-fired power plants. Accurate prediction of NOx concentrations at the boiler outlet is crucial for optimizing unit control and reducing emissions. This study introduces a data-driven NOx emissions prediction methodology based on a multilayered Gradient Boosting Decision Tree (mGBDT) framework. Initially, Kernel Independent Component Analysis (KICA) is employed to eliminate nonlinear correlation among collected auxiliary variables. Subsequently, high-quality variables, grounded in physical mechanisms, are integrated with the extracted independent features. The robust Gaussian Mixture Model (RGMM) is then applied to capture the intrinsic multimode operational characteristics from these integrated features. Finally, local mGBDT-based NOx emissions prediction models are developed for each identified mode. The optimal hyperparameters for each local model are determined using Particle Swarm Optimization (PSO) and 10-fold cross-validation techniques. Utilizing historical measurements from the studied boiler, the proposed framework achieved a square of correlation coefficient (R 2) of 0.947, a root-mean-square error (RMSE) of 6.09 mg/m3, and a mean absolute error (MAE) of 4.009 mg/m3, outperforming five comparison models.

Dimensionality reducing Gaussian mixture‐based reconstruction for fault detection in multimode processes

AbstractModern industrial processes increasingly prioritize demands for safety and reliability, spurring substantial research on process monitoring models. Among existing research subjects, concurrent multimode operating conditions are vital for effective process monitoring. This work proposes an efficient dimensionality‐reducing Gaussian mixture‐based reconstruction approach for multimode industrial process monitoring. The t‐SNE method is first employed to transform high‐dimensional data into a lower‐dimensional space that retains critical operational information. Using these reduced dimensions, a robust Gaussian mixture model is established to partition the operation data into different modes. Furthermore, the original data are assigned to the corresponding operating modes, and local variational autoencoder (VAE) reconstruction models are established, respectively. For each VAE model, two statistics are designed, termed and , to detect abnormalities. The proposed method is applied to a three‐phase flow facility, and the superiority over the comparison methods is proved.

Joint unsupervised contrastive learning and robust GMM for text clustering

Text clustering aims to organize a vast collection of documents into meaningful and coherent clusters, thereby facilitating the extraction of valuable insights. While current frameworks for text clustering try to minimize the anisotropy of pre-trained language models through contrastive learning of text embeddings, the approach of treating in-batch samples as negatives is suboptimal. The K-means algorithm offers a way to sample both hard negatives and false negatives. However, relying solely on a single measure of semantic similarity between distributions and using coarse-grained weighting for negative pairs may potentially limit performance. Furthermore, considering the very similar distribution in text clusters due to rich semantics, the Mahalanobis distance-based Gaussian Mixture Model (GMM) is prone to falling into local optima due to one Gaussian model, having a smaller weight, may gradually merging into another during the parameter evaluation by the EM algorithm. To tackle these challenges, we propose a model named JourTC: Joint unsupervised contrastive learning and robust GMM for Text Clustering. In the contrastive learning phase, hard negatives, potential false negatives, and their corresponding global similarity-aware weights are determined through posterior probabilities derived from a Robust GMM (RGMM). This RGMM utilizes the entropy of each individual Gaussian model as a metric and adaptively adjusts the posterior probabilities of samples based on the Gaussian models with both maximum and minimum entropy to diminish the influence of low-entropy Gaussian models. Extensive experiments have shown that JourTC can be seamlessly integrated into existing text clustering frameworks, leading to a notable improvement in accuracy. Our code is publicly available.11http://github.com/nickhcx/JourTC.

Robust Human Upper-Limbs Trajectory Prediction Based on Gaussian Mixture Prediction

Accurate prediction of human motion trajectory can improve the security of human-robot cooperation. Due to the unstructured nature of collaborative workspace and the uncertainty of sensor sensing data, the trajectory prediction accuracy of traditional prediction algorithms is low, and the uncertainty is difficult to estimate. Aiming at the complex characteristics of human upper limb movement patterns, this paper proposes a robust upper limb end trajectory prediction algorithm. The robust Gaussian mixture model was used to model the trajectory of human upper limb movement, and the statistical values of the future trajectory were obtained by combining Gaussian mixture regression. The advantage of this algorithm is that the prediction result is not only the predicted value of the position, but also the probability distribution of all possible future motion trajectories of the upper limb. The position prediction information in a specific motion mode can be obtained by using probability and statistical distribution characteristics. The algorithm is tested on both public and private datasets. Experimental results show that this method can predict human trajectories well.

Reconstruction of Sentinel-2 derived time series using robust Gaussian mixture models — Application to the detection of anomalous crop development

Missing data is a recurrent problem in remote sensing, mainly due to cloud coverage for multispectral images and acquisition problems. This can be a critical issue for crop monitoring, especially for applications relying on machine learning techniques, which generally assume that the feature matrix does not have missing values. This paper proposes a Gaussian Mixture Model (GMM) for the reconstruction of parcel-level features extracted from multispectral images. A robust version of the GMM is also investigated, since datasets can be contaminated by inaccurate samples or features (e.g., wrong crop type reported, inaccurate boundaries, undetected clouds, etc). Additional features extracted from Synthetic Aperture Radar (SAR) images using Sentinel-1 data are also used to provide complementary information and improve the imputations. The robust GMM investigated in this work assigns reduced weights to the outliers during the estimation of the GMM parameters, which improves the final reconstruction. These weights are computed at each step of an Expectation–Maximization (EM) algorithm by using outlier scores provided by the isolation forest (IF) algorithm. Experimental validation is conducted on rapeseed and wheat parcels located in the Beauce region (France). Overall, we show that the GMM imputation method outperforms other reconstruction strategies. A mean absolute error (MAE) of 0.013 (resp. 0.019) is obtained for the imputation of the median Normalized Difference Index (NDVI) of the rapeseed (resp. wheat) parcels. Other indicators (e.g., Normalized Difference Water Index) and statistics (for instance the interquartile range, which captures heterogeneity among the parcel indicator) are reconstructed at the same time with good accuracy. In a dataset contaminated by irrelevant samples, using the robust GMM is recommended since the standard GMM imputation can lead to inaccurate imputed values. An application to the monitoring of anomalous crop development in the presence of missing data is finally considered. In this application, using the proposed method leads to the best detection results, especially when SAR data are used jointly with multispectral images. Exploiting the information contained in cloudy multispectral images instead of removing these images is beneficial for this application.

Robust GMM least square twin K-class support vector machine for urban water pipe leak recognition

Monitoring pipe operation status is very important in saving water resources and realizing sustainability of the water supply system. Currently, the support vector machine (SVM) and its improved algorithms have been used to detect leaks in pipe networks. Among them, the least square twin multi-class support vector machine (LST-KSVC) is a novel multi-classification method. However, LST-KSVC assigns same weights to leak samples, including outliers that affect it. In addition, through the quadratic loss function, LST-KSVC often misclassifies rest class. Therefore, to overcome these two drawbacks, we propose a weighted version of LST-KSVC, referred to as the GMM least square twin K-class support vector machine (GLT-KSVC). Based on the Gaussian mixture model (GMM) method, GLT-KSVC assigns larger weights to main leak samples, and assigns smaller weights to outliers, making it insensitive to outliers. Moreover, GLT-KSVC avoids the misclassification drawback for rest samples by using weighted least squares linear loss function. The leak recognition experiment revealed that GLT-KSVC is better than LST-KSVC in classification accuracy, and its calculation time is only slightly higher than that of LST-KSVC.

Weighted dimensionality reduction and robust Gaussian mixture model based cancer patient subtyping from gene expression data

Background:The heterogeneous nature of cancer necessitates subtyping of cancer patients into distinct and well separated subgroups. However, computational issues arise because gene expression data is noisy and contains outliers apart from being high dimensional. As such, an attempt to subtype cancer patients from gene expression data leads to highly overlapping Kaplan–Meier (KM) survival plots and thus clear distinction among the discovered subtypes becomes difficult. Here we attempt to achieve a greater separation among the subtypes through a robust clustering pipeline. Methods:We propose a robust framework to achieve a better separation among the discovered subtypes. Our framework is based on dimensionality reduction of a weighted gene expression matrix using t-distributed Stochastic Neighbor Embedding (t-SNE) and a robust Gaussian mixture model based clustering approach. Every gene is weighted according to the median absolute deviation (MAD) of the gene before dimensionality reduction. The results are quantified by measuring the minimum pairwise separation among the KM plots and minimum hazard ratio among the subtypes. We also introduce a novel method, called cumulative survival separation, to quantify the separation among the discovered subtypes. Results:To validate the proposed methodology we obtained five cancer gene expression datasets from The Cancer Genome Atlas (TCGA) and comparisons with Consensus Clustering (CC), Consensus non-negative matrix factorization (CNMF), fast density-aware spectral clustering (Spectrum) and Neighborhood based Multi-Omics clustering (NEMO) methodologies show that the proposed method is able to achieve a greater separation compared to the aforementioned methods in literature. For instance, the minimum pairwise life expectancy difference (in days) between the discovered subtypes for GBM is 61 days for the proposed methodology with MAD scores, whereas it is approximately 33, 19, 49 and 33 days only for CC, Spectrum, Nemo and CNMF respectively. Comparisons are also shown for the proposed framework with and without using the MAD scores and it is observed that MAD score significantly improves the subtype separation. Hazard ratio analysis also shows that the proposed methodology performs better. Furthermore, pathway over-representation analyses were carried to identify relevant genetic pathways which can be possible targets for treatment. Conclusion:The results suggest that the use of median absolute deviation and a robust clustering methodology are helpful in achieving greater separation among the subtypes with better statistical and clinical significance.

On-Manifold GMM Registration

This letter presents a robust Gaussian mixture model registration technique to enable mapping and navigation in dark, complex, unstructured domains such as caves and mines. Subterranean environments are often unmapped and challenged by low-lighting conditions and communication constraints. Prior works that leverage direct and image-based techniques with active illumination fail when taking tight turns due to sensor washout, dense methods are sensitive to initialization, and state-of-the-art registration methods that leverage probabilistic models are neither real-time viable nor thoroughly evaluated with real-world data. The proposed approach minimizes the squared L2 norm between two distributions through an on-manifold parameterization of the objective function. The contribution of this letter is a robust, real-time viable distribution-to-distribution registration methodology that considers all possible correspondences between mixture components. The approach is evaluated in a feature-scarce mine, unstructured cave, and on open-source data of an office environment with both light detection and ranging (LIDAR) and depth sensors. The results demonstrate superior performance as compared to the state of the art. Beyond cave and mine environments, the method readily extends to solving the problem of registration in cluttered domains.

Automatic Visual Detection System of Railway Surface Defects With Curvature Filter and Improved Gaussian Mixture Model

Rails are among the most important components of railway transportation, and real-time defects detection of the railway is an important and challenging task because of intensity inhomogeneity, low contrast, and noise. This paper presents an automatic railway visual detection system (RVDS) for surface defects and focuses on several key issues of RVDS. First, in view of challenges such as complex condition and orbital reflectance inequality, we put forward a region-of-interest detection region extraction algorithm by vertical projection and gray contrast algorithm. In addition, a curvature filter equipped with implicit computing and surface preserving power is studied to eliminate noise and keep only the details. Then, an improved fast and robust Gaussian mixture model based on Markov random field is established for accurate and rapid surface defect segmentation. Additionally, an expectation–maximization algorithm is applied to optimize the parameters. The experimental results demonstrate that the proposed method performs well with both noisy and railway images, which enables identification and segmentation of the defects from rail surface, achieving detection performance with 92% precision and 88.8% recall rate on average, and is robust compared with the related well-established approaches.

Root cause diagnosis of quality-related faults in industrial multimode processes using robust Gaussian mixture model and transfer entropy

Abstract Modern complex industrial processes often have multiple operating modes due to various factors, such as different manufacturing strategies, alterations of feedstock and compositions, etc. In this paper, a practical technology or solution of quality-related fault diagnosis is put forward for industrial multimode processes. Different from traditional data-based fault diagnosis methods, the alternative approach is focused more on root cause diagnosis. The new scheme addresses the quality-related fault detection issue with a developed robust Gaussian mixture model and modified Mahalanobis distance. Then, a Bayesian inference-based robust Gaussian mixture contribution index is designed to analyze the potential root-cause variables. Meanwhile, a combination of transfer entropy and direct transfer entropy-based cause and effect extraction methodologies is proposed for root cause diagnosis of quality-related faults. Finally, the whole proposed framework is applied to a real industrial multimode finishing mill process, where the performance and effectiveness are further demonstrated from real industrial data.