Topology in Real-World Machine Learning and Data Analysis

About this Research Topic

Background

Topological Data Analysis (TDA) and Topological Machine Learning (TML) comprise a set of powerful techniques whose ability to extract robust geometric information has led to novel insights in the analysis of complex data.

Topology is concerned with understanding the global shape and structure of objects. When applied to data, topological methods provide a natural complement to conventional machine learning approaches, which tend to rely on local properties of the data. The main strengths of TDA/TML include their robustness to noise and ability to succinctly capture multi-scale behaviour.

Topological techniques have found great success in domains ranging from network science to drug and materials design, visualisation and dimensionality reduction, neuroscience, and time series analysis. Recently, connections between topology and deep learning have been explored, revealing promising avenues into regularization, interpretability, and protection from adversarial attacks.

This Article Collection builds on speakers' and organizers' contributions from the "AI & Topology" track at the Applied Machine Learning Days conference, held in Lausanne, Switzerland, from January 25-29, 2020. The track provided an accessible introduction to the use of topology in data science and machine learning and, via a selection of use cases from experts in the field, showcased the benefits of integrating TDA and TML into traditional data science workflows.

Expected manuscripts will cover algorithms or computational techniques based on ideas in topology, as well as their applications to data problems of high relevance to industry, research or the public sector.

Keywords: topological data analysis, computational topology, machine learning, algebraic topology, nonlinear dimensionality reduction

Important note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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