An exploration of fMRI timeseries similarity metrics
In order to perform classification on a functional brain scan it first undergoes many preprocessing steps. One of these steps is the transformation from the timeseries output of the fMRI scan, transforming a m×nm{\times}n m × n (where mm m is the number of timepoints recorded and nn n is the number of brain regions used) to an n×nn{\times}n n × n matrix of similiarity values (called a connectome). This similarity value is a measure of the neural synchronization between the 2 regions.
So how do we quantify the similarity of 2 different timeseries? This blog post will explore the common ways of quantifying time series similarity in a neuroscientific setting. Before we get into the actual methods used to calculate time series similarity, we need to cover the corner stone of almost all of the methods we are about to explore - covariance.
In the case of fMRI, we have a multivariate random variable, allowing us to use Maximum Likelihood Estimation to estimate the covariance matrix. Below is a toy example of our estimated covariance matrix.
