Principle Component Analysis
This course has mostly covered small networks and single neurons because these are the easiest to understand. However, most neurons in the brain are impossible to understand on their own
Massive neural networks in the brain are often indecipherable, but methods like PCA can help reduce the high amount of information in order to find patterns
To distinguish neurons, spikes detected by electrodes can be represented as high-dimensional points, where each dimension is a time-bin around the spike. Then PCA can separate these spikes if they belong to different neurons
Furthermore, PCA can be used to separate neurons according to firing rate, in order to find correlations
PCA essentially involves projecting all points onto a lower dimensional space in a way that minimizes information loss
Steps,
- Center the data by subtracting the mean
- Calculate the covariance matrix of the centered data
- Find the eigenvectors of the covariance matrix with their eigenvalues
- Sort the eigenvectors by eigenvalue; the eigenvalues are proportional to the relative amount of variance