Learning Mixtures of Gaussians
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Vines and vineyards by updating persistence in linear time
Proceedings of the twenty-second annual symposium on Computational geometry
Stability of Persistence Diagrams
Discrete & Computational Geometry
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Towards persistence-based reconstruction in euclidean spaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
A Sampling Theory for Compact Sets in Euclidean Space
Discrete & Computational Geometry
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Information Processing Letters
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Distance function to a compact set plays a central role in several areas of computational geometry. Methods that rely on it are robust to the perturbations of the data by the Hausdorff noise, but fail in the presence of outliers. The recently introduced distance to a measure offers a solution by extending the distance function framework to reasoning about the geometry of probability measures, while maintaining theoretical guarantees about the quality of the inferred information. A combinatorial explosion hinders working with distance to a measure as an ordinary power distance function. In this paper, we analyze an approximation scheme that keeps the representation linear in the size of the input, while maintaining the guarantees on the inference quality close to those for the exact but costly representation.