A variable‐selection control chart via penalized likelihood and Gaussian mixture model for multimodal and high‐dimensional processes

2019 ◽  
Vol 35 (4) ◽  
pp. 1263-1275 ◽  
Author(s):  
Dandan Yan ◽  
Shuai Zhang ◽  
Uk Jung
Keyword(s):  
Variable Selection ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Control Chart ◽  
Penalized Likelihood ◽  
Gaussian Mixture ◽  
High Dimensional

scholarly journals The Generalized Bayes Method for High-Dimensional Data Recognition with Applications to Audio Signal Recognition

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 19
Author(s):  
Hsiuying Wang
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Conventional Method ◽  
High Dimensional Data ◽  
Audio Signal ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Signal Recognition ◽  
Bayes Method ◽  
Generalized Bayes

High-dimensional data recognition problem based on the Gaussian Mixture model has useful applications in many area, such as audio signal recognition, image analysis, and biological evolution. The expectation-maximization algorithm is a popular approach to the derivation of the maximum likelihood estimators of the Gaussian mixture model (GMM). An alternative solution is to adopt a generalized Bayes estimator for parameter estimation. In this study, an estimator based on the generalized Bayes approach is established. A simulation study shows that the proposed approach has a performance competitive to that of the conventional method in high-dimensional Gaussian mixture model recognition. We use a musical data example to illustrate this recognition problem. Suppose that we have audio data of a piece of music and know that the music is from one of four compositions, but we do not know exactly which composition it comes from. The generalized Bayes method shows a higher average recognition rate than the conventional method. This result shows that the generalized Bayes method is a competitor to the conventional method in this real application.

scholarly journals A Method for Aero-Engine Gas Path Anomaly Detection Based on Markov Transition Field and Multi-LSTM

Aerospace ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 374
Author(s):  
Langfu Cui ◽  
Chaoqi Zhang ◽  
Qingzhen Zhang ◽  
Junle Wang ◽  
Yixuan Wang ◽  
...  
Keyword(s):  
Anomaly Detection ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Gaussian Mixture ◽  
High Accuracy ◽  
High Dimensional ◽  
True Value ◽  
Markov Transition ◽  
Aero Engine ◽  
Transition Field

There are some problems such as uncertain thresholds, high dimension of monitoring parameters and unclear parameter relationships in the anomaly detection of aero-engine gas path. These problems make it difficult for the high accuracy of anomaly detection. In order to improve the accuracy of aero-engine gas path anomaly detection, a method based on Markov Transition Field and LSTM is proposed in this paper. The correlation among high-dimensional QAR data is obtained based on Markov Transition Field and hierarchical clustering. According to the correlation analysis of high-dimensional QAR data, a multi-input and multi-output LSTM network is constructed to realize one-step rolling prediction. A Gaussian mixture model of the residuals between predicted value and true value is constructed. The three-sigma rule is applied to detect outliers based on the Gaussian mixture model of the residuals. The experimental results show that the proposed method has high accuracy for aero-engine gas path anomaly detection.

scholarly journals High-dimensional Probabilistic Fingerprinting in Wireless Sensor Networks based on a Multivariate Gaussian Mixture Model

2018 ◽  
Author(s):  
Yan Li ◽  
Simon Williams ◽  
Bill Moran ◽  
Allison Kealy ◽  
Guenther Retscher
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Low Cost ◽  
Classification Problem ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Mobile Users ◽  
Prototype Model ◽  
Location Awareness ◽  
Multivariate Gaussian

The extensive deployment of wireless infrastructure provides a low-cost way to track mobile users in indoor environment. This paper demonstrates a prototype model of an accurate and reliable room location awareness system in a real public environment, where three typical problems arise. First, a massive number of access points (APs) can be sensed leading to a high-dimensional classification problem. Second, heterogeneous devices record different received signal strength (RSS) levels due to the variations in chip-set and antenna attenuation. Third, APs are not necessarily visible in every scanning cycle leading to missing data. This paper presents a probabilistic Wi-Fi fingerprinting method in a hidden Markov model (HMM) framework for mobile user tracking. Considering the spatial correlation of the signal strengths from multiple APs, a Multivariate Gaussian Mixture Model (MVGMM) is fitted to model the probability distribution of RSS measurements in each cell. Furthermore, the unseen property of invisible AP has been investigated in this research, and demonstrated the efficiency of differentiation between cells. The proposed system is able to achieve comparable localization performance. The filed test results present a reliable 97% localization room level accuracy of multiple mobile users in a real university campus WiFi network without any prior knowledge of the environment.

Regularized Gaussian Mixture Model for High-Dimensional Clustering

2019 ◽  
Vol 49 (10) ◽  
pp. 3677-3688 ◽  
Author(s):  
Yang Zhao ◽  
Abhishek K. Shrivastava ◽  
Kwok Leung Tsui
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
High Dimensional Clustering

scholarly journals A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Applications

2017 ◽  
Vol 145 (7) ◽  
pp. 2763-2790 ◽  
Author(s):  
Tapovan Lolla ◽  
Pierre F. J. Lermusiaux
Keyword(s):  
Dynamical Systems ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
High Dimension ◽  
Gaussian Mixture ◽  
Sudden Expansion ◽  
High Dimensional ◽  
Diffusion Experiment ◽  
Stochastic Dynamical Systems ◽  
Observation Times

The nonlinear Gaussian Mixture Model Dynamically Orthogonal (GMM–DO) smoother for high-dimensional stochastic fields is exemplified and contrasted with other smoothers by applications to three dynamical systems, all of which admit far-from-Gaussian distributions. The capabilities of the smoother are first illustrated using a double-well stochastic diffusion experiment. Comparisons with the original and improved versions of the ensemble Kalman smoother explain the detailed mechanics of GMM–DO smoothing and show that its accuracy arises from the joint GMM distributions across successive observation times. Next, the smoother is validated using the advection of a passive stochastic tracer by a reversible shear flow. This example admits an exact smoothed solution, whose derivation is also provided. Results show that the GMM–DO smoother accurately captures the full smoothed distributions and not just the mean states. The final example showcases the smoother in more complex nonlinear fluid dynamics caused by a barotropic jet flowing through a sudden expansion and leading to variable jets and eddies. The accuracy of the GMM–DO smoother is compared to that of the Error Subspace Statistical Estimation smoother. It is shown that even when the dynamics result in only slightly multimodal joint distributions, Gaussian smoothing can lead to a severe loss of information. The three examples show that the backward inferences of the GMM–DO smoother are skillful and efficient. Accurate evaluation of Bayesian smoothers for nonlinear high-dimensional dynamical systems is challenging in itself. The present three examples—stochastic low dimension, reversible high dimension, and irreversible high dimension—provide complementary and effective benchmarks for such evaluation.

scholarly journals High-Dimensional Probabilistic Fingerprinting in Wireless Sensor Networks Based on a Multivariate Gaussian Mixture Model

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2602 ◽  
Author(s):  
Yan Li ◽  
Simon Williams ◽  
Bill Moran ◽  
Allison Kealy ◽  
Guenther Retscher
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Low Cost ◽  
Classification Problem ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Mobile Users ◽  
Prototype Model ◽  
Location Awareness ◽  
Multivariate Gaussian

The extensive deployment of wireless infrastructure provides a low-cost way to track mobile users in indoor environment. This paper demonstrates a prototype model of an accurate and reliable room location awareness system in a real public environment in which three typical problems arise. Firstly, a massive number of access points (APs) can be sensed leading to a high-dimensional classification problem. Secondly, heterogeneous devices record different received signal strength (RSS) levels because of the variations in chip-set and antenna attenuation. Thirdly, APs are not necessarily visible in every scanning cycle leading to missing data issue. This paper presents a probabilistic Wi-Fi fingerprinting method in a hidden Markov model (HMM) framework for mobile user tracking. To account for spatial correlation of the signal strengths from multiple APs, a Multivariate Gaussian Mixture Model (MVGMM) was fitted to model the probability distribution of RSS measurements in each cell. Furthermore, the unseen property of invisible AP was investigated in this research, and demonstrated the efficiency as a beneficial information to differentiate between cells. The proposed system is able to achieve comparable localisation performance. Filed test results achieve a reliable 97% localisation room level accuracy of multiple mobile users in a real university campus Wi-Fi network.

An Adaptive Gaussian Mixture Model Approach Based Framework for Solving Fokker-Planck Kolmogorov Equation Related to High Dimensional Dynamical Systems

2016 ◽  
Author(s):  
Arpan Mukherjee ◽  
Rahul Rai ◽  
Puneet Singla ◽  
Tarunraj Singh ◽  
Abani Patra
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
State Vector ◽  
Gaussian Mixture ◽  
The State ◽  
Kolmogorov Equation ◽  
High Dimensional ◽  
Dimensional System ◽  
Clustering Technique ◽  
Fokker Planck

Engineering systems are often modeled as a large dimensional random process with additive noise. The analysis of such system involves a solution to simultaneous system of Stochastic Differential Equations (SDE). The exact solution to the SDE is given by the evolution of the probability density function (pdf) of the state vector through the application of Stochastic Calculus. The Fokker-Planck-Kolmogorov Equation (FPKE) provides approximate solution to the SDE by giving the time evolution equation for the non-Gaussian pdf of the state vector. In this paper, we outline a computational framework that combines linearization, clustering technique and the Adaptive Gaussian Mixture Model (AGMM) methodology for solving the Fokker-Planck-Kolmogorov Equation (FPKE) related to a high dimensional system. The linearization and clustering technique facilitate easier decomposition of the overall high dimensional FPKE system into a finite number of much lower dimension FPKE systems. The decomposition enables the solution method to be faster. Numerical simulations test the efficacy of our developed framework.

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