This two day workshop will bring together researchers from the various subdisciplines of Geometric Data Analysis, such as manifold learning, topological data analysis, shape analysis, will showcase recent progress in this field and will establish directions for future research. The focus will be on high dimensional and big data, and on mathematically founded methodology.

Specific aims

One aim of this workshop is to build connections between Topological Data Analysis on one side and Manifold Learning on the other. This is starting to happen, after years of more or less separate evolution of the two fields. The moment has been reached when the mathematical, statistical and algorithmic foundations of both areas are mature enough -- it is now time to lay the foundations for joint topological and differential geometric understanding of data, and this workshop will expliecitly focus on this process.

The second aim is to bring GDA closer to real applications. We see the challenge of real problems and real data as a motivator for researchers to explore new research questions, to reframe and expand the existing theory, and to step out of their own sub-area. In particular, for people in GDA to see TDA and ML as one.

The impact of GDA in practice also depends on having scalable implementations of the most current results in theory. This workshop will showcase the GDA tools which achieve this and initiate a collective discussion about the tools that need to be built.

We intend this workshop to be a forum for researchers in all areas of Geometric Data Analysis. Trough the tutorials, we are reaching out to the wider NIPS audience, to the many potential users of of Geometric Data Analysis, to make them aware of the state of the art in GDA, and of the tools available. Last but not least, we hope that the scientists invited will bring these methods back to their communities.