Email: [email protected]

！！！本库的所有文件，作者保留一切版权，在未经作者许可，请不要擅自使用或者发表！！！

• 主题
  • 抑郁症
  • 难治性癫痫

• Deep Learning for Time Series
  • 1 RNN Granger Causality
    • 1.1 Granger Causality Definition$^1$
    • 1.2 Simulation Model
    • 1.3 EEG Signals
    • 1.4 EEG64s Signals
    • 1.6 Network
  • Theory
  • Docs
  • Reference
  • Useful website
  • EEG 信号预处理
  • Info

Suppose $x$ is a stationary multivariate time series. Multivariate Granger causality analysis is estimated by fitting a vector autoregressive model (VAR) to the time series with time lag of $P$ :

$$ \tag{1}\vec x(t)=\sum_{p=1}^P A_p \vec x(t-p)+bias+\epsilon(t) $$

where $A$ is the coefficient matrix, $bias$ is a vector and $\epsilon(t)$ is Gaussian noise. A time series $x_i$ is a Granger cause of $x_j$, if $x_i$ is significantly contributed in prediction of $x_j$. To quantitatively measure the contribution, we fit another VAR as follows:

$$ \tag{2}\vec x_{\backslash x_i}(t)=\sum_{p^\star=1}^{P^\star} A_{p\star}^\star \vec x_{\backslash x_i}(t-p^\star)+bias^\star+\epsilon_{\backslash x_i}^\star(t) $$

where $A^\star$ is the model coefficients, $bias^\star$ is a vector, $\epsilon_{\backslash x_i}^\star(t)$ is Gaussian noise, and $\vec x_{\backslash x_i}(t)$ is a vector without containing $x_i$. Then we could define the Granger causality from $x_i$ to $x_j$ as:

$$ \tag{3}G_{x_i\rightarrow x_j}=\ln\frac{\text{var};{\epsilon_{x_j\backslash x_i}^\star(t)}}{\text{var};{\epsilon_{x_j}(t)}} $$

$$ \tag{4}G_{x_i\rightarrow x_j}=1-\frac{\text{var};{\epsilon_{x_j}(t)}}{\text{var};{\epsilon_{x_j\backslash x_i}^\star(t)}} $$

1. Linear model

   • formula

   

   • signals

   

   • Granger Causality Matrix

   

2. NonLinear model

   • formula

   

   • signals

   

   • Granger Causality Matrix

   

3. Long-lag NonLinear model

   • formula

   

   • signals

   

   • Granger Causality Matrix

   

• signals

• Granger Causality Matrix

1. Wang, Y., Lin, K., Qi, Y., Lian, Q., Feng, S., Wu, Z., & Pan, G. (2018). Estimating Brain Connectivity With Varying-Length Time Lags Using a Recurrent Neural Network. IEEE Transactions on Biomedical Engi-neering, 65, 1953-1963.
2. Montalto, A., Stramaglia, S., Faes, L., Tessitore, G., Prevete, R., & Marinazzo, D. (2015). Neural networks with non-uniform embedding and explicit validation phase to assess granger causality. Neural Net-works,71(C), 159-171.
3. Gómez-García J A, Godino-Llorente J I, Castellanos-Dominguez G. Non uniform Embedding based on Relevance Analysis with reduced computational complexity: Application to the detection of pathologies from biosignal recordings[J]. Neurocomputing, 2014, 132(7):148-158.
4. Smith, L. N. (2015). Cyclical learning rates for training neural networks. Computer Science, 464-472.
5. Loshchilov, I., & Hutter, F. (2016). Sgdr: stochastic gradient descent with warm restarts.

1. 深度学习在EEG数据的应用探索以及实验

1. RNN-GC
2. Deep Learning for Time Series Classification
3. LSTM-FCN: Codebase for the paper LSTM Fully Convolutional Networks for Time Series Classification
4. How to Normalize and Standardize Time Series Data in Python

• Notes

The code is for research use only. style based

1. explainshell.com - match command-line arguments to their help text
2. Documentation - Overleaf, Online LaTeX Editor
3. Supported Functions · KaTeX
4. Understanding and interpreting box plots | Wellbeing@School

1. EEG Data Processing and Classification with g.BSanalyze Under MATLAB - MATLAB & Simulink
2. EEG-Clean-Tools (PREP Pipeline)
3. EEGLAB
4. 介绍 · eeglab_cn
5. EEGLAB操作手册
6. Matlab之EEGLAB工具箱脑电数据预处理 - matlab教程
7. joramvd/eegpreproc: Preprocessing EEG data: Matlab code pipeline and pdf manual
8. [图文]ERP实验设计和数据分析 - 百度文库

$ cloc .
     117 text files.
     116 unique files.
      83 files ignored.

github.com/AlDanial/cloc v 1.80  T=0.50 s (124.0 files/s, 12766.0 lines/s)
-------------------------------------------------------------------------------
Language                     files          blank        comment           code
-------------------------------------------------------------------------------
Python                          32            867           1487           1542
MATLAB                          13             87            269            636
Markdown                        11            225              1            610
IPython Notebook                 1              0              0            312
JSON                             2              0              0            180
YAML                             2             15              4            145
Bourne Shell                     1              0              0              3
-------------------------------------------------------------------------------
SUM:                            62           1194           1761           3428
-------------------------------------------------------------------------------