Manifold learning (ML), also known as nonlinear dimension reduction, is a set of methods to
find the low-dimensional structure of data. Dimension reduction for large, high-dimensional …

Simplicial complexes can be viewed as high dimensional generalizations of graphs that
explicitly encode multi-way ordered relations between vertices at different resolutions, all at …

We propose principled Gaussian processes (GPs) for modeling functions defined over the
edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form …

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an
arbitrary point cloud based on their contribution to global topological features. TPCC …

Methods that learn graph topological representations are becoming the usual choice to
extract features to help solve machine learning tasks on graphs. In particular, low …

Techniques based on th order Hodge Laplacian operators are widely used to describe the
topology as well as the governing dynamics of high-order systems modeled as simplicial …

We consider the problem of classifying trajectories on a discrete or discretised 2-
dimensional manifold modelled by a simplicial complex. Previous works have proposed to …

Simplicial complexes are generalizations of classical graphs. Their homology groups are
widely used to characterize the structure and the topology of data in eg chemistry …

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order
information on the global shape of a data set or point cloud. Tools like Persistent Homology …

Simplicial complexes (SCs), a generalization of graph models for relational data that
account for higher-order relations between data items, have become a popular abstraction …