Using Topology for Data Analysis II

In this second part 1, we use Topological Data Analysis (TDA) on a dataset consisting on spatial information related to traffic. We’ll compare to usual “DBSCAN” method from Machine Learning.

DBSCAN is a method for finding clusters in data. It means Density-Based Spatial Clustering of Applications with Noise. It usually requires two parameters and the data: a radius, known as eps, and the minimum number of points required to form a cluster, that is the “density” part.

In any case, the parameters are unknown a priori. TDA in this case can help giving connected components as initial election of clusters and also, being robust against noise, these clusters will persist.

Using Topology for Data Analysis

When researching data we want to find features that help us understand the information. We look for insight in areas like Machine Learning or other fields in Mathematics and Artificial Intelligence. I want to present here a tool initially coming from Mathematics that can be used for exploratory data analysis and give some geometric insight before applying more sophisticated algorithms.

The tool I want to describe is Persistent Homology, member of a set of algorithms known as Topological Data Analysis. In this post I will describe the basic methodology when facing a common data analysis scenario: clustering.