Search Results for author:
Found 4 papers, 4 papers with code
$k$-Means Clustering for Persistent Homology
Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram; it has recently gained much popularity from its myriad successful applications to many domains.
Approximating Persistent Homology for Large Datasets
We show that the mean of the persistence diagrams of subsamples -- taken as a mean persistence measure computed from the subsamples -- is a valid approximation of the true persistent homology of the larger dataset.
Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measures
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in a hierarchy-preserving manner using a variety of metrics.
Efficient Weingarten Map and Curvature Estimation on Manifolds
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space.
