The Hotelling—Like $$T^2$$ T 2 Control Chart Modified for Detecting Changes in Images having the Matrix Normal Distribution

2019 ◽  
pp. 193-206 ◽  
Author(s):  
Ewaryst Rafajłowicz ◽  
Ansgar Steland
Keyword(s):  
Normal Distribution ◽  
Control Chart ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution

scholarly journals On n/p-Asymptotic Distribution Of Vector Of Weighted Traces Of Powers Of Wishart Matrices

2018 ◽  
Vol 33 ◽  
pp. 24-40 ◽  
Author(s):  
Jolanta Pielaszkiewicz ◽  
Dietrich Von Rosen ◽  
Martin Singull
Keyword(s):  
Normal Distribution ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Joint Distribution ◽  
Recursive Formula ◽  
Multivariate Normal ◽  
Wishart Matrices ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution

The joint distribution of standardized traces of $\frac{1}{n}XX'$ and of $\Big(\frac{1}{n}XX'\Big)^2$, where the matrix $X:p\times n$ follows a matrix normal distribution is proved asymptotically to be multivariate normal under condition $\frac{{n}}{p}\overset{n,p\rightarrow\infty}{\rightarrow}c>0$. Proof relies on calculations of asymptotic moments and cumulants obtained using a recursive formula derived in Pielaszkiewicz et al. (2015). The covariance matrix of the underlying vector is explicitely given as a function of $n$ and $p$.

scholarly journals A Bayesian Multiple-Trait and Multiple-Environment Model Using the Matrix Normal Distribution

2018 ◽  
Author(s):  
Osval A. Montesinos-López ◽  
Abelardo Montesinos-López ◽  
José Cricelio Montesinos-López ◽  
José Crossa ◽  
Francisco Javier Luna-Vázquez ◽  
...  
Keyword(s):  
Normal Distribution ◽  
Multiple Trait ◽  
Environment Model ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution

scholarly journals Dynamic Brain Connectivity Alternation Detection via Matrix-variate Differential Network Model

2018 ◽  
Author(s):  
Jiadong Ji ◽  
Yong He ◽  
Lei Xie
Keyword(s):  
Normal Distribution ◽  
Partial Correlation ◽  
Graphical Model ◽  
Brain Connectivity ◽  
Connectivity Analysis ◽  
Differential Network ◽  
The Matrix ◽  
Matrix Normal ◽  
Matrix Normal Distribution ◽  
The Brain

AbstractMotivationNowadays brain connectivity analysis has attracted tremendous attention and has been at the foreground of neuroscience research. Brain functional connectivity reveals the synchronization of brain systems through correlations in neurophysiological measures of brain activity. Growing evidence now suggests that the brain connectivity network experiences alternations with the presence of numerous neurological disorders, thus differential brain network analysis may provides new insights into disease pathologies. For the matrix-valued data in brain connectivity analysis, existing graphical model estimation methods assume a vector normal distribution that in essence requires the columns of the matrix data to be independent. It is obviously not true, they have limited applications. Among the few solutions on graphical model estimation under a matrix normal distribution, none of them tackle the estimation of differential graphs across different populations. This motivates us to consider the differential network for matrix-variate data to detect the brain connectivity alternation.ResultsThe primary interest is to detect spatial locations where the connectivity, in terms of the spatial partial correlation, differ across the two groups. To detect the brain connectivity alternation, we innovatively propose a Matrix-Variate Differential Network (MVDN) model. MVDN assumes that the matrix-variate data follows a matrix-normal distribution. We exploit the D-trace loss function and a Lasso-type penalty to directly estimate the spatial differential partial correlation matrix where the temporal information is fully excavated. We propose an ADMM algorithm for the Lasso penalized D-trace loss optimization problem. We investigate theoretical properties of the estimator. We show that under mild and regular conditions, the proposed method can identify all differential edges accurately with probability tending to 1 in high-dimensional setting where dimensions of matrix-valued data p, q and sample size n are all allowed to go to infinity. Simulation studies demonstrate that MVDN provides more accurate differential network estimation than that achieved by other state-of-the-art methods. We apply MVDN to Electroencephalography (EEG) dataset, which consists of 77 alcoholic individuals and 45 controls. The hub genes and differential interaction patterns identified are consistent with existing experimental [email protected] informationSupplementary data are available online.

Hybrid fuzzy interface model of sports rehabilitation activities

2021 ◽  
pp. 1-10
Author(s):  
Wu Shoujiang
Keyword(s):  
Evaluation System ◽  
Clustering Algorithm ◽  
Mixed Model ◽  
Expectation Maximization Algorithm ◽  
Rehabilitation Training ◽  
Development Platform ◽  
Longitudinal Tracking ◽  
Database Structure ◽  
The Matrix ◽  
Matrix Normal

At present, the relevant test data and training indicators of athletes during rehabilitation training lack screening and analysis, so it is impossible to establish a long-term longitudinal tracking research system and evaluation system. In order to improve the practical effect of sports rehabilitation activities, this paper successively introduces the matrix normal mixed model and the fuzzy clustering algorithm based on the K-L information entropy regularization and the matrix normal mixed model. Moreover, this paper uses the expectation maximization algorithm to estimate the parameters of the model, discusses the framework, key technologies and core services of the development platform, and conducts certain research on the related technologies of the three-tier architecture. At the same time, according to the actual needs of sports rehabilitation training, this paper designs the functions required for exercise detection and prescription formulation. In addition, this paper analyzes and designs the database structure involved in each subsystem. Finally, this paper designs experiments to verify the performance of the model constructed in this paper. The research results show that the performance of the model constructed in this paper meets the expectations of model construction, so it can be applied to practice.

scholarly journals Model selection and estimation in the matrix normal graphical model

2012 ◽  
Vol 107 ◽  
pp. 119-140 ◽  
Author(s):  
Jianxin Yin ◽  
Hongzhe Li
Keyword(s):  
Model Selection ◽  
Graphical Model ◽  
The Matrix ◽  
Matrix Normal

The Empirical Distribution of the Singular Values of a Random Hankel Matrix

2015 ◽  
Vol 14 (03) ◽  
pp. 1550027 ◽  
Author(s):  
Mansi Ghodsi ◽  
Nader Alharbi ◽  
Hossein Hassani
Keyword(s):  
Normal Distribution ◽  
Random Matrix ◽  
Empirical Distribution ◽  
Hankel Matrix ◽  
Singular Values ◽  
Shape Parameters ◽  
The Matrix ◽  
Non Parametric

The empirical distribution of the eigenvalues of the matrix HHT divided by its trace is considered, where H is a Hankel random matrix. The normal distribution with different parameters are considered and the effect of scale and shape parameters are evaluated. The correlation among eigenvalues are assessed using parametric and non-parametric association criteria.

Probabilistic Damage Detection of Long-Span Bridges Using Measured Modal Frequencies and Temperature

2018 ◽  
Vol 18 (10) ◽  
pp. 1850126 ◽  
Author(s):  
Yang Deng ◽  
Aiqun Li ◽  
Dongming Feng
Keyword(s):  
Damage Detection ◽  
Normal Distribution ◽  
Control Chart ◽  
Temperature Effects ◽  
Suspension Bridge ◽  
Standard Normal Distribution ◽  
Long Span Bridges ◽  
Long Span ◽  
Standard Normal ◽  
Probabilistic Monitoring

This paper aims to develop a new probabilistic monitoring-based framework for damage detection of long-span bridges, by eliminating the temperature effects from the measured modal frequencies, probabilistic modeling of modal frequencies using kernel density estimate, and detection damage using the control chart. A methodology is presented to address the issue of modal frequencies' non-normal distribution, which has been neglected in the past studies using the control chart to detect the modal frequencies' abnormality caused by structural damages. The efficiency of the proposed framework is validated through a case study of long-term monitoring data of a long-span suspension bridge. The results show that after elimination of the temperature effects, the selected modal frequencies are not normally distributed, while the Q statistics transferred from the modal frequencies follow the standard normal distribution. The abnormality of modal frequencies can be detected when the data points of the Q statistics exceed the limits of the control chart. Further, the control chart has sufficient sensitivity and thus can be used to detect minor abnormalities of the prototype bridge's modal frequencies. It is concluded that the proposed probabilistic monitoring-based framework offers an effective technique for structural health monitoring of long-span bridges.

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