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DATASHAPE Research team

Understanding the Shape of Data

Team presentation

DataShape is a research project in Topological Data Analysis (TDA), a recent field whose aim is to uncover, understand and exploit the topological and geometric structure underlying complex and possibly high dimensional data. The DataShape project gathers a unique variety of expertise that allows it to embrace the mathematical, statistical, algorithmic and applied aspects of the field in a common framework ranging from fundamental theoretical studies to experimental research and software development.

The overall objective of the DataShape project is to settle the mathematical, statistical, algorithmic and software foundations of TDA and to disseminate and promote our results in the data science community.

The approach of DataShape relies on the conviction that it is necessary to combine statistical, topological/geometric and computational approaches in a common framework, in order to face the challenges of TDA. We are also convinced that these challenges need to be simultaneously addressed from the fundamental and application sides.
The expected output of DataShape is two-fold. First, we intend to set-up and develop the mathematical, statistical and algorithmic foundations of Topological and Geometric Data Analysis. Second, we intend to develop the Gudhi platform in order to provide an efficient state-of-the-art toolbox for the understanding of the topology and geometry of data.
The ultimate goal of DataShape is to develop and promote TDA as a new family of well founded methods to uncover and exploit the geometry of data. Our objective is also to provide efficient and flexible tools that could be used independently, complementarily or in combination with other classical data analysis and machine learning approaches.

Research themes

Algorithmic aspects of topological and geometric data analysis

Statistical aspects of topological and geometric data analysis

Topological approaches for multimodal data processing

Software

Transfer and applications

Keywords: Topological Data Analysis Computational Topology Computational Geometry Statistics Algorithms