The Directional Transform
Explore the innovative field of topological data analysis (TDA) and its application in measuring the shape of data through this insightful lecture. Delve into the concept of the directional transform, a powerful technique that allows for examining data from multiple perspectives simultaneously. Learn how this method combines ideas from algebraic topology, algorithms, statistics, and category theory to quantify the shape of various data types, from plant seeds to time series attractors. Discover the versatility of the directional transform in probing the shape of Euclidean space regions and its ability to generate comprehensive topological signatures. Gain insights into practical applications, including the analysis of X-Ray CT scans of barley seeds and the comparison of embedded graphs. Understand how this approach can enhance theoretical analysis and serve as valuable input for machine learning models, advancing the field of data shape analysis.