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Explore the concept of stable volumes for persistent homology in this 54-minute conference talk by Ippei Obayashi. Delve into a new method designed to overcome the challenges of identifying homological structures in persistence diagrams. Learn about the mathematical formalization, algorithms, and properties of stable volumes, and see examples of their application to both synthetic and real-world data. Discover how this approach addresses issues of instability in homological optimization techniques, potentially leading to more accurate identification of minimal building blocks in input data. Gain insights into the implementation of this algorithm in HomCloud and explore its potential applications in characterizing data shape using topology.
