Topological Data Analysis for Data Professionals: Beyond Ayasdi

Real data can be messy, and, in many fields, it can include very few observations, making statistical analyses a challenge and pushing machine learning algorithms to their limit. Sometimes, data breaks the assumptions of most extant methods in statistics, complicating analysis and muddying the validity of results. However, recent developments in a field called topological data analysis (TDA) has provided a set of tools to wrangle messy and/or small data in a robust manner. TDA--and the approach of applying topological concepts to statistical problems--is subfield of analytics developed from ideas in algebraic and differential topology. Though the theory is rooted in graduate level mathematics, a basic understanding and a package implementation of the algorithms allow it to be more accessible to data miners, particularly those with a strong mathematical background.