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Found 11 papers, 2 papers with code
Embedding Functional Data: Multidimensional Scaling and Manifold Learning
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting.
On the Selection of Tuning Parameters for Patch-Stitching Embedding Methods
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.
Clustering by Hill-Climbing: Consistency Results
We consider several hill-climbing approaches to clustering as formulated by Fukunaga and Hostetler in the 1970's.
An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree
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.
Moving Up the Cluster Tree with the Gradient Flow
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.
Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting
We start by considering the problem of estimating intrinsic distances on a smooth submanifold.
Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning
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.
A Simple Approach to Sparse Clustering
Consider the problem of sparse clustering, where it is assumed that only a subset of the features are useful for clustering purposes.
A Nonparametric Framework for Quantifying Generative Inference on Neuromorphic Systems
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.
Community Detection in Sparse Random Networks
This is formalized as testing for the existence of a dense random subgraph in a random graph.
Does median filtering truly preserve edges better than linear filtering?
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)
