Topological data analysis and clustering

With the advent of Big Data, algorithms that try to extract information from them are ubiquitous. Clustering algorithms are a subcategory of Machine Learning algorithms with a wide range of applications. Notions like closeness, distance and shape are central to clustering. It is then natural to try to use ideas and techniques from topology to improve clustering algorithms. This chapter examines some ways on how this could happen. In Section 2 a brief introduction to the clustering task is presented. In Subsection 2.1 a definition is presented along with notation.