Learning about topological data analysis
Topological Data Analysis (TDA) is a rather novel technique that's used to extract features that quantify the shape of the data. The idea of this approach is that by observing how datapoints are organized in a certain space, we can reveal some important information about the process that generated it.
The main tool for applying TDA is persistent homology. The math behind this method is quite advanced, so let's introduce this concept through an example. Suppose you have a set of data points distributed on a space, and let's suppose you are "observing" them over time. Points are static (they do not move across the space); thus, you will observe those independent points forever. However, let's imagine we can create associations between these data points by connecting them together through some well-defined rules. In particular, let's imagine a sphere expanding from these points through time. Each point will...
