Topological Data Analysis (TDA) combines ideas from topology and also algebra, geometry, with the objective of analyzing high dimensional data sets. Topology is a mathematical discipline that studies shapes, sets of points and their invariants under continuous deformations such as the number of connected components or holes. Topological Data Analysis (TDA) refers to the adaptation of this discipline to the analysis of very complex data. It is based on the philosophy that all data has a underlying form and that this form has a meaning. Some datasets are too small for standard data analysis and others are extremely large and data size reduction methods may be needed. One solution is to use topological data analysis to simplify and/or visualize data. The overall goal of topological data analysis is to be able to analyze the topological characteristics of datasets, often through calculations of topological properties such as homology. This workshop will include both tutorials and research talks on topological techniques for visualizing data.
Quantum machine learning is a relatively new field of machine learning that leverages the power of quantum computing to optimize new and existing machine learning models, including quantum neural networks, quantum annealing, and quantum network science algorithms. These algorithms are specially-designed to run on quantum computers and often provide a speed-up of run-time for combinatorial optimization problems. In the past few years, quantum algorithms have found use on initial real-world problems. The goal of this workshop is to introduce attendees to the use of topological techniques for data visualization, in addition to quantum algorithms in both research and real-world applications.