Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Qiao, Wanli"'
We present a method for graph clustering that is analogous with gradient ascent methods previously proposed for clustering points in space. We show that, when applied to a random geometric graph with data iid from some density with Morse regularity,
Externí odkaz:
http://arxiv.org/abs/2411.18794
Autor:
Qiao, Wanli
Filamentary structures, also called ridges, generalize the concept of modes of density functions and provide low-dimensional representations of point clouds. Using kernel type plug-in estimators, we give asymptotic confidence regions for filamentary
Externí odkaz:
http://arxiv.org/abs/2311.17831
Autor:
Arias-Castro, Ery, Qiao, Wanli
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical methods th
Externí odkaz:
http://arxiv.org/abs/2208.14540
Autor:
Arias-Castro, Ery, Qiao, Wanli
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) variants and establish their consistency.
Externí odkaz:
http://arxiv.org/abs/2202.09023
Autor:
Arias-Castro, Ery, Qiao, Wanli
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 gradient flow as proposed by Fukunaga and Hosteler. In a recent paper, w
Externí odkaz:
http://arxiv.org/abs/2111.10298
Autor:
Arias-Castro, Ery, Qiao, Wanli
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 Hartigan and clustering by gradient lines or gradient flow as proposed by Fu
Externí odkaz:
http://arxiv.org/abs/2109.08362
Autor:
Qiao, Wanli, Polonik, Wolfgang
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 two novel algorithms, and provide theoretical guarantees for their con
Externí odkaz:
http://arxiv.org/abs/2104.12314
Autor:
Qiao, Wanli, Shehu, Amarda
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 gradient ascent. In this paper we develop a mean-shift-inspired algorithm to
Externí odkaz:
http://arxiv.org/abs/2104.10103
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 bandwidth, achieves the minimax rate that we establish for the setting t
Externí odkaz:
http://arxiv.org/abs/2104.07870
Autor:
Qiao, Wanli
Depending on a parameter $h\in (0,1]$, let $\{X_h(\mathbf{t})$, $\mathbf{t}\in\mathcal{M}_h\}$ be a class of centered Gaussian fields indexed by compact manifolds $\mathcal{M}_h$. For locally stationary Gaussian fields $X_h$, we study the asymptotic
Externí odkaz:
http://arxiv.org/abs/2005.07185