arXiv research

Characterizes Lebesgue points using nearest neighbor methods.

VNNGP uses nearest neighbors to approximate GPs, improving scalability and performance.

If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to connect every point to $c_{d,1} \log{\log{n}}$ points chosen randomly among its $…

The nearest neighbor problem is defined as follows: Given a set $P$ of $n$ points in some metric space $(X,D)$, build a data structure that, given any point $q$, returns a point in $P$ that is closest to $q$ (its "nearest neighbor" in $P$). The data structure stores additional information about the set $P$, which is th…

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the pr…

Both supervised and unsupervised machine learning algorithms have been used to learn partition-based index structures for approximate nearest neighbor (ANN) search. Existing supervised algorithms formulate the learning task as finding a partition in which the nearest neighbors of a training set point belong to the same…

Study of $f$-neighbors in Riemannian manifolds, proving infinite set of distances.

The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points ac…

The paper analyzes how much data points can be altered to change their rank in nearest neighbor searches.

In our previous works, we proposed a physically-inspired rule to organize the data points into an in-tree (IT) structure, in which some undesired edges are allowed to occur. By removing those undesired or redundant edges, this IT structure is divided into several separate parts, each representing one cluster. In this w…

Ball k-means reduces point-centroid distance computations for faster k-means clustering.

Study on the structure of classifier boundaries in DNA sequencing.

New method speeds up k-means clustering for large k by improving nearest-neighbor search.

This paper introduces PM and PMLP to enhance SSL by considering probability density and cluster assumptions.

Explains SNE, t-SNE, and their variants for manifold learning.

Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings (e.g., vulnerability to adversarial inputs) and general inability to rationalize…

$\newcommand{\ball}{\mathbb{B}}\newcommand{\dsQ}{\mathcal{Q}}\newcommand{\dsS}{\mathcal{S}}$In this work we study a fair variant of the near neighbor problem. Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the points, such that given a query point $q$, any point in the $r$-neighbor…

We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance between two points $i$ and $j$ is smaller than the distance between the points $i$ an…

Improves visualization of high-dimensional data by correcting misleading artifacts in neighbor embedding methods.

Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear, global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring region selection. However, so far for the references we know, few of which propos…

Neighbor embeddings balance attraction and repulsion to visualize data.

We explore and expand the $\textit{Soft Nearest Neighbor Loss}$ to measure the $\textit{entanglement}$ of class manifolds in representation space: i.e., how close pairs of points from the same class are relative to pairs of points from different classes. We demonstrate several use cases of the loss. As an analytical to…

ASK-NN detects distribution drifts in LLM-generated text.

Improves time series classification with forest proximities.

The paper studies empirical processes from nearest neighbors in regression.

The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have r…

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 is based on fitting K-nearest neighbor regression to the unsupervised regressio…

DSNE visualizes data velocity in lower dimensions.

Sparse subspace clustering (SSC) using greedy-based neighbor selection, such as matching pursuit (MP) and orthogonal matching pursuit (OMP), has been known as a popular computationally-efficient alternative to the conventional L1-minimization based methods. Under deterministic bounded noise corruption, in this paper we…

This paper proposes a new hashing-based KNN technique for faster nearest neighbor selection.

A new ensemble method improves kNN performance by extending the neighborhood rule.

New methods explain NE embeddings by identifying key variables.

SPlit optimizes dataset splitting for better model performance.

New method selects recent similar periods for better electricity price forecasting.

Take N sites distributed randomly and uniformly on a smooth closed surface. We express the expected distance <D_k(N)> from an arbitrary point on the surface to its kth-nearest neighboring site, in terms of the function A(l) giving the area of a disc of radius l about that point. We then find two universalities. First, …

Algorithm finds adversarial examples for k-NN classifiers using Voronoi diagrams.

Paper tackles NNS under uncertainty with improved algorithms.

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a …

This paper introduces CloudLSTM, a new branch of recurrent neural models tailored to forecasting over data streams generated by geospatial point-cloud sources. We design a Dynamic Point-cloud Convolution (DConv) operator as the core component of CloudLSTMs, which performs convolution directly over point-clouds and extr…

The recently proposed self-ensembling methods have achieved promising results in deep semi-supervised learning, which penalize inconsistent predictions of unlabeled data under different perturbations. However, they only consider adding perturbations to each single data point, while ignoring the connections between data…

New topological methods for hypergraph data improve community detection and pattern recognition.

A new approach to $L_2$-consistent estimation of a general density functional using $k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function $f$ of the densities at each point. The estimator is designed to be asymptotically unbiased, using t…

The paper extends Hopf's theorem to convex surfaces and discrete triangulations.

The paper investigates learning conditional distributions on multi-dimensional spaces using clustering and neural networks.

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges …

This work is an endeavor to develop a deep learning methodology for automated anatomical labeling of a given region of interest (ROI) in brain computed tomography (CT) scans. We combine both local and global context to obtain a representation of the ROI. We then use Relation Networks (RNs) to predict the corresponding …

The DEBS Grand Challenge 2018 is set in the context of maritime route prediction. Vessel routes are modeled as streams of Automatic Identification System (AIS) data points selected from real-world tracking data. The challenge requires to correctly estimate the destination ports and arrival times of vessel trips, as ear…

We show that a simple modification of the 1-nearest neighbor classifier yields a strongly Bayes consistent learner. Prior to this work, the only strongly Bayes consistent proximity-based method was the k-nearest neighbor classifier, for k growing appropriately with sample size. We will argue that a margin-regularized 1…