Cover Learning for Topological Inference
The standard approach to Topological Inference is based on geometric complexes. Most commonly, geometric complexes scale cubically (and often worse) in the number of data points, which poses a big problem. Here I describe an alternative approach to Topological Inference.
Topological Inference and Unsupervised Learning
Fundamental problems in Unsupervised Learning, such as Clustering and Dimensionality Reduction, can be fruitfully interpreted from the point of view of Topological Inference. This is an introduction to this point of view.