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Found 5 papers, 1 papers with code
Statistical learning on measures: an application to persistence diagrams
We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$.
Topologically penalized regression on manifolds
We study a regression problem on a compact manifold M. In order to take advantage of the underlying geometry and topology of the data, the regression task is performed on the basis of the first several eigenfunctions of the Laplace-Beltrami operator of the manifold, that are regularized with topological penalties.
ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks.
Robust Bregman Clustering
Using a trimming approach, we investigate a k-means type method based on Bregman divergences for clustering data possibly corrupted with clutter noise.
Stability and Minimax Optimality of Tangential Delaunay Complexes for Manifold Reconstruction
A similar result is also derived in a model with outliers.
Statistics Theory Statistics Theory I.3.5; G.1.2; G.3
