Tracking Covert Spatial Attention using Linear and Non Linear Perceptrons

Basic Overview

Covert Visual attention can be tracked by alpha-band activity. [1] Inverted Encoding Models have been used before to track spatial attention.
We use Non Linear Perceptrons to do the same.

Channel Tuning Functions

For the experimental data presented in [1], we have 8 spatial locations called channels.
To each spatial location we associate a tuning function. The channel tuning function is

$$ \begin{aligned} R = sin^7(0.5(\theta - \theta_c + \pi)) \end{aligned} $$

where $\theta_c$ is the channel for which we are considering the TF.

Inverted Encoding Models (Forward Computation + Inversion of Weight Matrix) [1]

$B_1 \rightarrow$ Train EEG Matrix ($m$ electrodes $\times$ $n_1$ measurements)
$B_2 \rightarrow$ Test EEG Matrix ($m$ electrodes $\times$ $n_2$ measurements)
$W \rightarrow$ Weight Matrix ($m$ electrodes × $k$ channels)
$C_1 \rightarrow$ Channel Responses based on CTFs ($k$ channels $\times$ $n_1$ measurements)
$C_2 \rightarrow$ Predicted Channel Responses ($k$ channels $\times$ $n_2$ measurements)

$$ \begin{aligned} B_1 = WC_1 \\ \widehat{W} = B_1C_1^T(C_1C_1^T)^{-1} \\ \widehat{C_2} = (\widehat{W}^T\widehat{W})^{-1}\widehat{W}^TB_2 \end{aligned} $$

Non Linear Perceptrons (Forward Computation + Back Propogation to compute weights)

Directly compute mapping from EEG matrix to channel responses

Dependencies

python>=3.7
PyTorch
numpy
seaborn, matplotlib
Matlab R2023b + Signal Processing Toolbox

Downloading EEG and Behaviour Data

https://archive.org/details/osf-registrations-tuu4m-v1

How to use

To visualize spatial attention as heat maps

python run.py --model LinearPerceptron --numIterations 10 --startTime 0 --endTime 600 --verbose False --saveHeatMap "./trial.jpeg"

References

[1] Foster et al. (2017). Alpha-Band Oscillations Enable Spatially and Temporally Resolved Tracking of Covert Spatial Attention