In unsupervised learning, one of the main questions we want to answer is *what type of structure does this set or shape have?* The field of algebraic topology supplies a few tools to help answer this question. We can ask topological questions about the data, such as *how many clusters or connected components are there?* or *are there gaps, holes, or voids in the data?*. These question can be easy to answer if the shape is well defined, but in practice, we instead have data sampled from that shape. If we can construct a representation of the underlying shape, maybe we can estimate these properties instead. These questions and methods to answer them are central to the field of Topological Data Analysis (TDA).

More …
This post will define the nerve we eluded to in the previous post and then introduce how we build mapper.

More …
This post will build out the definition and intuition of towers. Once we understand the **tower**, we will show that it plays nice with all of the other definitions we have constructed so far and how it allows us to naturally define a multiscale mapper.

More …
As one of the main tools from the field of Topological Data Analysis, **mapper** has been shown to be particularly useful for exploring high dimensional point cloud data.This post will walk through the mapper construction from an intuitive perspective and demonstrate its use on a toy example.

More …
The traditional process of the scientific method is to create a hypothesis, design an experiment, collect specific data, and then analyze the results. With modern advances, data collection has become so cheap that it is often collected before we even know what to look for. The scientific method is being flipped on end.Data is being Now, the hard part in the process is sifting through the piles of data and figuring out what to questions to ask. New methods of analysis are emerging to help us explore these troves of data and to eek out insights.

More …