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Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent
Mathieu Carrière, Seunghyun Kim, Woojin Kim
The generalized persistence diagram (GPD) is a natural extension of the classical persistence barcode to the setting of multi-parameter persistence and beyond. The GPD is defined a…
Diffeomorphic interpolation for efficient persistence-based topological optimization
Mathieu Carriere, Marc Theveneau, Théo Lacombe
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functio…
Differentiable Mapper For Topological Optimization Of Data Representation
Ziyad Oulhaj, Mathieu Carrière, Bertrand Michel
Unsupervised data representation and visualization using tools from topology is an active and growing field of Topological Data Analysis (TDA) and data science. Its most prominent…