no code implementations • 30 Aug 2022 • 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 setting.
no code implementations • 14 Jul 2022 • Ery Arias-Castro, Phong Alain Chau
While classical scaling, just like principal component analysis, is parameter-free, other methods for embedding multivariate data require the selection of one or several tuning parameters.
no code implementations • 18 Feb 2022 • Ery Arias-Castro, Wanli Qiao
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's.
no code implementations • 19 Nov 2021 • 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 gradient flow as proposed by Fukunaga and Hosteler.
no code implementations • 17 Sep 2021 • 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 Hartigan and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hostetler.
no code implementations • 25 Nov 2020 • Ery Arias-Castro, Phong Alain Chau
We start by considering the problem of estimating intrinsic distances on a smooth submanifold.
no code implementations • 22 Oct 2018 • Ery Arias-Castro, Adel Javanmard, Bruno Pelletier
One of the common tasks in unsupervised learning is dimensionality reduction, where the goal is to find meaningful low-dimensional structures hidden in high-dimensional data.
1 code implementation • 23 Feb 2016 • Ery Arias-Castro, Xiao Pu
Consider the problem of sparse clustering, where it is assumed that only a subset of the features are useful for clustering purposes.
no code implementations • 18 Feb 2016 • Ojash Neopane, Srinjoy Das, Ery Arias-Castro, Kenneth Kreutz-Delgado
Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in probabilistic generative model applications such as image occlusion removal, pattern completion and motion synthesis.
no code implementations • 13 Aug 2013 • Ery Arias-Castro, Nicolas Verzelen
This is formalized as testing for the existence of a dense random subgraph in a random graph.
1 code implementation • 14 Dec 2006 • Ery Arias-Castro, David L. Donoho
We show that median filtering and linear filtering have similar asymptotic worst-case mean-squared error (MSE) when the signal-to-noise ratio (SNR) is of order 1, which corresponds to the case of constant per-pixel noise level in a digital signal.
Statistics Theory Statistics Theory 62G08, 62G20 (Primary) 60G35 (Secondary)