Related papers: Kneser's method of neighbors

kNN is a very effective Instance based learning method, and it is easy to implement. Due to heterogeneous nature of data, noises from different possible sources are also widespread in nature especially in case of large-scale databases. For…

We construct some families of quadratic fields whose class numbers are divisible by $3.$ The main tools used are a trinomial introduced by Kishi and a parametrization of Kishi and Miyake of a family of quadratic fields whose class numbers…

An exciting new algorithmic breakthrough has been advanced for how to carry out inferences in a Dempster-Shafer (DS) formulation of a categorical data generating model. The developed sampling mechanism, which draws on theory for directed…

The K Nearest Neighbors (KNN) classifier is widely used in many fields such as fingerprint-based localization or medicine. It determines the class membership of unlabelled sample based on the class memberships of the K labelled samples, the…

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…

$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning…

We present an algorithm to enumerate isometry classes of integral quadratic lattices of a given rank and determinant, and analyze its running time by giving bounds on the number of genus symbols for a fixed rank and determinant. We build on…

In this paper, we introduce a type of tensor neural network. For the first time, we propose its numerical integration scheme and prove the computational complexity to be the polynomial scale of the dimension. Based on the tensor product…

Let L and L' be two integral Euclidean lattices in the same genus. We give an asymptotic formula for the number of Kneser p-neighbors of L which are isometric to L', when the prime p goes to infinity. In the case L is unimodular, and if we…

We prove that the ideal used in recent works to categorify the cyclotomic integers is generated by a cyclotomic polynomial. Moreover, we publish a proof by T. Ekedahl that the $q$-binomial relations used in the tensor product of…

In the mid-1960s A. Pfister discovered extraordinary, strongly multiplicative forms which are now called Pfister forms. From that time on, these forms played a dominant role in the theory of quadratic forms. One of the key properties of a…

Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…

Kepler's thinking is highly original and the inspiration for discovering his famous third law is based on his rather curious geometric approach in his Harmonices mundi for explaining consonances. In this article we try to use a modern…

Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, for example, as a fast search procedure with two tower deep learning models. Graph-based methods for AKNNS in particular have received great…

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in…

This paper proposes a spatial k-nearest neighbor method for nonparametric prediction of real-valued spatial data and supervised classification for categorical spatial data. The proposed method is based on a double nearest neighbor rule…

In machine learning, classifiers are used to predict a class of a given query based on an existing (classified) database. Given a database S of n d-dimensional points and a d-dimensional query q, the k-nearest neighbors (kNN) classifier…

Neighbor-scattering number is a useful measure for graph vulnerability. For some special kinds of graphs, explicit formulas are given for this number. However, for general graphs it is shown that to compute this number is NP-complete. In…

Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…