Abstract

Visualization techniques for complex data are a workhorse of modern scientific pursuits. The goal of visualization is to embed high-dimensional data in a low-dimensional space while preserving structure in the data relevant to exploratory data analysis such as clusters. However, existing visualization methods often either fail to separate clusters due to the crowding problem or can only separate clusters at a single resolution. Here, we develop a new approach to visualization, tree preserving embedding (TPE). Our approach uses the topological notion of connectedness to separate clusters at all resolutions. We provide a formal guarantee of cluster separation for our approach that holds for finite samples. Our approach requires no parameters and can handle general types of data, making it easy to use in practice.