## Nerves and Towers I: Introduction

Fundamental concepts of Mapper and Multiscale Mapper.

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…