Related papers: SVD Provably Denoises Nearest Neighbor Data

We consider the deconvolution problem for densities supported on a $(d-1)$-dimensional sphere with unknown center and unknown radius, in the situation where the distribution of the noise is unknown and without any other observations. We…

Noise manifests ubiquitously in nonlinear spectroscopy, where multiple sources contribute to experimental signals generating interrelated unwanted components, from random point-wise fluctuations to structured baseline signals. Mitigating…

In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It…

Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how…

For a given dataset $\mathcal{D}$ and structured label $f$, the goal of Filtered Approximate Nearest Neighbor Search (FANNS) algorithms is to find top-$k$ points closest to a query that satisfy label constraints, while ensuring both recall…

Geometric data structures have been extensively studied in the regime where the dimension is much smaller than the number of input points. But in many scenarios in Machine Learning, the dimension can be much higher than the number of points…

We initiate the study of approximation algorithms and computational barriers for constructing sparse $\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an…

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…

We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…

Suppose $V$ is an $n$-element set where for each $x \in V$, the elements of $V \setminus \{x\}$ are ranked by their similarity to $x$. The $K$-nearest neighbor graph is a directed graph including an arc from each $x$ to the $K$ points of $V…

The problem of finding K-nearest neighbors in the given dataset for a given query point has been worked upon since several years. In very high dimensional spaces the K-nearest neighbor search (KNNS) suffers in terms of complexity in…

In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points…

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements. The general assumption is that the signal has only a few non-zero entries. The recovery can be performed by multiple different…

We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm. This algorithm is derived from sample compression bounds and enjoys the statistical advantages of tight, fully empirical…

A Shared Nearest Neighbor (SNN) graph is a type of graph construction using shared nearest neighbor information, which is a secondary similarity measure based on the rankings induced by a primary $k$-nearest neighbor ($k$-NN) measure. SNN…

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases,…

During the last decade, hyperspectral images have attracted increasing interest from researchers worldwide. They provide more detailed information about an observed area and allow an accurate target detection and precise discrimination of…

The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same…

The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…

Although the advances of self-supervised blind denoising are significantly superior to conventional approaches without clean supervision in synthetic noise scenarios, it shows poor quality in real-world images due to spatially correlated…