5 citations · 20 across the 15 of their papers we have counts for
15 papers
Stable Density Ridges: Consistency and Convergence of Subspace Constrained Mean Shift
Wanli Qiao
The Subspace Constrained Mean Shift (SCMS) algorithm is a popular nonparametric method for extracting density ridges, which serve as a low-dimensional representation of high-dimens…
Embedding Functional Data: Multidimensional Scaling and Manifold Learning
Ery Arias-Castro, Wanli Qiao
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional settin…
Clustering by Hill-Climbing: Consistency Results
Ery Arias-Castro, Wanli Qiao
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's. We study both continuous-space and discrete-space (i.e., medoid) v…
An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree
Ery Arias-Castro, Wanli Qiao
Two important nonparametric approaches to clustering emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartigan, and clustering by gradient lines or gr…
Moving Up the Cluster Tree with the Gradient Flow
Ery Arias-Castro, Wanli Qiao
The paper establishes a strong correspondence between two important clustering approaches that emerged in the 1970's: clustering by level sets or cluster tree as proposed by Hartig…
Space Partitioning and Regression Mode Seeking via a Mean-Shift-Inspired Algorithm
Wanli Qiao, Amarda Shehu
The mean shift (MS) algorithm is a nonparametric method used to cluster sample points and find the local modes of kernel density estimates, using an idea based on iterative gradien…
Estimation of the Global Mode of a Density: Minimaxity, Adaptation, and Computational Complexity
Ery Arias-Castro, Wanli Qiao, Lin Zheng
We consider the estimation of the global mode of a density under some decay rate condition around the global mode. We show that the maximum of a histogram, with proper choice of ba…
Algorithms for ridge estimation with convergence guarantees
Wanli Qiao, Wolfgang Polonik
The extraction of filamentary structure from a point cloud is discussed. The filaments are modeled as ridge lines or higher dimensional ridges of an underlying density. We propose…
Extremes of locally stationary Gaussian and chi fields on manifolds
Wanli Qiao
Depending on a parameter , let , be a class of centered Gaussian fields indexed by compact manifolds .…
Asymptotic Confidence Regions for Density Ridges
Wanli Qiao
We develop large sample theory including nonparametric confidence regions for -dimensional ridges of probability density functions on , where . We view…
Nonparametric Confidence Regions for Level Sets: Statistical Properties and Geometry
Wanli Qiao, Wolfgang Polonik
This paper studies and critically discusses the construction of nonparametric confidence regions for density level sets. Methodologies based on both vertical variation and horizont…
Nonparametric Estimation of Surface Integrals on Level Sets
Wanli Qiao
Surface integrals on density level sets often appear in asymptotic results in nonparametric level set estimation (such as for confidence regions and bandwidth selection). Also surf…
Asymptotics and Optimal Bandwidth for Nonparametric Estimation of Density Level Sets
Wanli Qiao
Bandwidth selection is crucial in the kernel estimation of density level sets. A risk based on the symmetric difference between the estimated and true level sets is usually used to…
Theoretical Analysis of Nonparametric Filament Estimation
Wanli Qiao, Wolfgang Polonik
This paper provides a rigorous study of the nonparametric estimation of filaments or ridge lines of a probability density . Points on the filament are considered as local extrem…
Extrema of locally stationary Gaussian fields on growing manifolds
Wanli Qiao, Wolfgang Polonik
We consider a class of non-homogeneous, continuous, centered Gaussian random fields where denotes a rescaled smooth manifo…