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Found 12 papers, 1 papers with code
Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Motivated by the challenge of sampling Gibbs measures with nonconvex potentials, we study a continuum birth-death dynamics.
Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applications
We introduce new estimators for the normal vector to the boundary, distance of a point to the boundary, and a test for whether a point lies within a boundary strip.
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algorithm with spectral clustering at discrete and continuum levels.
Rates of Convergence for Laplacian Semi-Supervised Learning with Low Labeling Rates
The proofs of our well-posedness results use the random walk interpretation of Laplacian learning and PDE arguments, while the proofs of the ill-posedness results use $\Gamma$-convergence tools from the calculus of variations.
Mumford-Shah functionals on graphs and their asymptotics
We consider adaptations of the Mumford-Shah functional to graphs.
Large Data and Zero Noise Limits of Graph-Based Semi-Supervised Learning Algorithms
Scalings in which the graph Laplacian approaches a differential operator in the large graph limit are used to develop understanding of a number of algorithms for semi-supervised learning; in particular the extension, to this graph setting, of the probit algorithm, level set and kriging methods, are studied.
Analysis of $p$-Laplacian Regularization in Semi-Supervised Learning
The task is to assign real-valued labels to a set of $n$ sample points, provided a small training subset of $N$ labeled points.
A Transportation $L^p$ Distance for Signal Analysis
Transport based distances, such as the Wasserstein distance and earth mover's distance, have been shown to be an effective tool in signal and image analysis.
Transport-based analysis, modeling, and learning from signal and data distributions
Transport-based techniques for signal and data analysis have received increased attention recently.
Multiple penalized principal curves: analysis and computation
We study the problem of finding the one-dimensional structure in a given data set.
A variational approach to the consistency of spectral clustering
We also show that the discrete clusters obtained via spectral clustering converge towards a continuum partition of the ground truth measure.
Continuum limit of total variation on point clouds
We consider point clouds obtained as random samples of a measure on a Euclidean domain.
