Homology
Recall that I mentioned TDA’s strength lies in its persistence homology – a tool that identifies and quantifies topological features at various scales. Persistence homology is one of the most powerful tools in the TDA toolbox. To explain it simply, let’s use the analogy of taking photographs of a mountain range at different altitudes.
Imagine you’re in a helicopter, ascending from the base to the peak of a mountain range. As you ascend, you take a series of photographs. At the base, you capture individual mountains. As you rise higher, you start to see groups of mountains and then entire sections of the mountain range. By the time you’re at the peak, you have a complete, bird’s-eye view of the range.
In this analogy, each photograph you take represents a scale. Just like how different scales reveal different details about the mountain range, persistence homology explores data at different scales to uncover various topological...
