Location-adaptive density estimation and nearest-neighbor distance

Uniform-in-Bandwidth Nearest-Neighbor Density Estimation

We are concerned with the nonparametric estimation of the density f(·) of a random variable [rv] X ∈ R by the nearest-neighbor [NN] method. The NN estimators are motivated as follows (see, e.g., Fix and Hodges [17]). Let X1,X2, . . . be independent and identically distributed [iid] random copies of X, with distribution function [df] F(x) := P(X ≤ x), for x ∈ R. Denote the empirical df based upo...

Location-Adaptive Density Estimation

Improving Nearest Neighbor Rule with a Simple Adaptive Distance Measure

The k-nearest neighbor rule is one of the simplest and most attractive pattern classification algorithms. However, it faces serious challenges when patterns of different classes overlap in some regions in the feature space. In the past, many researchers developed various adaptive or discriminant metrics to improve its performance. In this paper, we demonstrate that an extremely simple adaptive ...

Bayesian adaptive nearest neighbor

The k nearest neighbor classification (k-NN) is a very simple and popular method for classification. However, it suffers from a major drawback, it assumes constant local class posterior probability. It is also highly dependent on and sensitive to the choice of the number of neighbors k. In addition, it severely lacks the desired probabilistic formulation. In this article, we propose a Bayesian ...

Density estimation from unweighted k-nearest neighbor graphs: a roadmap

Consider an unweighted k-nearest neighbor graph on n points that have been sampled i.i.d. from some unknown density p on R. We prove how one can estimate the density p just from the unweighted adjacency matrix of the graph, without knowing the points themselves or any distance or similarity scores. The key insights are that local differences in link numbers can be used to estimate a local funct...