What Is Topological Data Analysis?

Topological data analysis is a concept found in applied mathematics. This approach uses a general framework to explore information from datasets, even when it is incomplete, high-dimensional, or noisy.

It inherits functoriality from its topological nature, allowing it to adapt to new mathematical tools. 

In other words, topological data analysis augments other analysis forms, such as geometric approaches. That’s why it is useful to data scientists who need a better understanding of what their information contains. 

What Is the Basic Theory of Topological Data Analysis?

Topological data analysis is based on the idea that data shapes contain relevant information. Since actual high-dimensional info is sparse and tends to have low-dimensional features, this technique delivers a precise characterization of the facts.

With topological data analysis, users also get the tools need to detect and quantify recurrent motion within different equations.

Think of it as a type of math that concerns itself with continuous objects. It doesn’t care about shapes or sizes – only continuity. You’re focusing on how things connect to explore where gaps could be present. 

Imagine that you’re putting up Christmas lights on your home. You’d think about the logistics of doing the work, the geometric shape of the installation, or the utility statistics to know how much it’ll cost. 

Topological data analysis ignores the spatial features of the lights, such as the distance between bulbs, to focus on the connectivity. That information lets us have a greater understanding of what could be missing from an equation.

This introductory video covers the basics of this concept nicely.