Two Setups in TDA

While there are several different approaches in topological data analysis, our first step is to turn our data into a continuous function. To be more precise, we associate a continuous function \(f\) to a real world phenomenon, that we seek to understand, and then we capture some data to which we associate a continuous function \(g\) approximating \(f\). We start by loosely describing two different setups of a real world phenomenon, the type of data we capture, and how we obtain the continuous function \(g\) from this data.