A deeper dive into the “shape of the data”
The concept of shape in topological data analysis is quite different from how we traditionally understand shapes in geometry. Instead of focusing on rigid properties such as lengths, angles, and areas, the shape in topology refers to the broader, more flexible structure of data. It looks at how data points relate to each other and form a larger pattern or structure.
Imagine that you have a cluster of data points. At the simplest level, you could look at the points individually. However, this wouldn’t provide much insight beyond each point’s specific characteristics. In contrast, topological data analysis allows you to take a step back and view the dataset as a whole.
To visualize this concept, let’s consider a simple example. Suppose you have a dataset comprising various species of animals recorded from different habitats. The data includes attributes such as size, diet, habitat type, and other traits...
