【VG、teVG、梯度下降的teVG及MarkoVG】基于马尔可夫先验的动态时空重构研究（Matlab代码实现）

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📋📋📋本文目录如下：🎁🎁🎁

目录

💥1 概述

📚2 运行结果

🎉3 参考文献

🌈4 Matlab代码实现

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💥1 概述

VG：马尔可夫先验是一种概率模型，用于描述随机过程中状态的转移概率。动态时空重构是指利用时间和空间信息对数据进行重建和分析的过程。基于马尔可夫先验的动态时空重构研究，可以利用马尔可夫先验来建模时空数据的转移概率，从而实现对动态时空数据的重构和分析。

teVG：梯度下降是一种优化算法，用于寻找函数的最小值。在动态时空重构中，梯度下降可以用来优化模型参数，从而实现对时空数据的重构和分析过程的优化。

teVG及MarkoVG：结合梯度下降和马尔可夫先验的动态时空重构研究，可以利用梯度下降算法来优化马尔可夫先验模型的参数，从而实现对动态时空数据的更精确的重构和分析。这种方法可以在时空数据分析领域中发挥重要作用，有助于更好地理解和预测时空数据的变化规律。

VG 参考:
[1]Hansen, S. T., Stahlhut, C., & Hansen, L. K. (2013).  Expansion of the variational garrote to a multiple measurement vectors model.  In 12th Scandinavian Conference on Artificial Intelligence (SCAI 2013) Scandinavian Conference on Artificial Intelligence (pp. 105-114).  IOS Press.

teVG with gradient descent参考:
[2]Hansen, S. T., & Hansen, L. K. (2015, April).  EEG source reconstruction performance as a function of skull conductance contrast.  In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on (pp. 827-831).  IEEE.

MarkoVG 参考:
[3]Hansen, S. T., & Hansen, L. K. (2017).  Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior.  NeuroImage, 148, 274-283.

📚2 运行结果

部分代码：

% original VG
Gammas = VG_cross(A,Y);
Vvg=NaN(size(X_true));Mvg=NaN(size(X_true));Xvg=NaN(size(X_true));
for t=1:25,[Vvg(:,t),Mvg(:,t),Xvg(:,t)] = VG(A,Y(:,t),Gammas(t));end
[F1measureVG(rep),TPVG(rep),FPVG(rep)] = calc_F1measure(Mvg,X_true);
[F1measureVG2(rep),TPVG2(rep),FPVG2(rep)] = calc_F1measure(sum(Mvg,2),S);

% teVG
[gamma_mean1,gamma_median] = teVGGD_wcross(A,Y); % find sparsity
[VteVG,mteVG,XteVG,Ffull] = teVGGD(A,Y,gamma_median);
[F1measureteVG(rep),TPteVG(rep),FPteVG(rep)] = calc_F1measure(repmat(mteVG,1,size(X_true,2)),X_true);
[F1measureteVG2(rep),TPteVG2(rep),FPteVG2(rep)] = calc_F1measure(mteVG,S);

% MarkoVG
tic;[q,q0,fCross] = MarkoVGGD_cross(A,Y);toc
[VmarkoVG,MmarkoVG,X,F] = MarkoVGGD(A,Y,q,q);
MarkoVGact = find(MmarkoVG>0.5);
[F1measureMarko(rep),TPMarko(rep),FPMarko(rep)] = calc_F1measure(MmarkoVG,X_true);
[F1measureMarko2(rep),TPMarko2(rep),FPMarko2(rep)] = calc_F1measure(sum(MmarkoVG,2),S);

figure,
subplot(1,4,1)
plot(X_true');title('True')
subplot(1,4,2)
plot(Vvg');title('VG')
subplot(1,4,3)
plot(VteVG'),title('teVG')
subplot(1,4,4)
plot(VmarkoVG'),title('MarkoVG')
drawnow

🎉3 参考文献

文章中一些内容引自网络，会注明出处或引用为参考文献，难免有未尽之处，如有不妥，请随时联系删除。

VG 参考:
[1]Hansen, S. T., Stahlhut, C., & Hansen, L. K. (2013).  Expansion of the variational garrote to a multiple measurement vectors model.  In 12th Scandinavian Conference on Artificial Intelligence (SCAI 2013) Scandinavian Conference on Artificial Intelligence (pp. 105-114).  IOS Press.

teVG with gradient descent参考:
[2]Hansen, S. T., & Hansen, L. K. (2015, April).  EEG source reconstruction performance as a function of skull conductance contrast.  In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on (pp. 827-831).  IEEE.

MarkoVG 参考:
[3]Hansen, S. T., & Hansen, L. K. (2017).  Spatio-temporal reconstruction of brain dynamics from EEG with a Markov prior.  NeuroImage, 148, 274-283.

🌈4 Matlab代码实现