Related papers: Kinetic Reverse $k$-Nearest Neighbor Problem
Let $P$ be a set of $n$ colored points. We develop efficient data structures that store $P$ and can answer chromatic $k$-nearest neighbor ($k$-NN) queries. Such a query consists of a query point $q$ and a number $k$, and asks for the color…
k Nearest Neighbor (kNN) method is a simple and popular statistical method for classification and regression. For both classification and regression problems, existing works have shown that, if the distribution of the feature vector has…
Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours…
Nearest neighbor search is known as a challenging issue that has been studied for several decades. Recently, this issue becomes more and more imminent in viewing that the big data problem arises from various fields. In this paper, a…
Given a set $P$ of $n$ points in $\mathbf{R}^d$, and a positive integer $k \leq n$, the $k$-dispersion problem is that of selecting $k$ of the given points so that the minimum inter-point distance among them is maximized (under Euclidean…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
The problem of identifying the k-Nearest Neighbors (kNNS) of a point has proven to be very useful both as a standalone application and as a subroutine in larger applications. Given its far-reaching applicability in areas such as machine…
The k-Nearest Neighbors (kNN) classifier is a fundamental non-parametric machine learning algorithm. However, it is well known that it suffers from the curse of dimensionality, which is why in practice one often applies a kNN classifier on…
Big data mining is well known to be an important task for data science, because it can provide useful observations and new knowledge hidden in given large datasets. Proximity-based data analysis is particularly utilized in many real-life…
K-nearest neighbor classification algorithm is one of the most basic algorithms in machine learning, which determines the sample's category by the similarity between samples. In this paper, we propose a quantum K-nearest neighbor…
The k-nearest neighbors (k-NN) is a basic machine learning (ML) algorithm, and several quantum versions of it, employing different distance metrics, have been presented in the last few years. Although the Euclidean distance is one of the…
Top-k Nearest Neighbors (kNN) problem on road network has numerous applications on location-based services. As direct search using the Dijkstra's algorithm results in a large search space, a plethora of complex-index-based approaches have…
Most natural language processing tasks can be formulated as the approximated nearest neighbor search problem, such as word analogy, document similarity, machine translation. Take the question-answering task as an example, given a question…
The k-means problem consists of finding k centers in the d-dimensional Euclidean space that minimize the sum of the squared distances of all points in an input set P to their closest respective center. Awasthi et. al. recently showed that…
We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may…
We revisit the moving k nearest neighbor (MkNN) query, which computes one's k nearest neighbor set and maintains it while at move. Existing MkNN algorithms are mostly safe region based, which lack efficiency due to either computing small…
We consider the following problem about dispersing points. Given a set of points in the plane, the task is to identify whether by moving a small number of points by small distance, we can obtain an arrangement of points such that no pair of…
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…
k-nearest neighbor graph is a fundamental data structure in many disciplines such as information retrieval, data-mining, pattern recognition, and machine learning, etc. In the literature, considerable research has been focusing on how to…
It is a common problem in robotics to specify the position of each joint of the robot so that the endpoint reaches a certain target in space. This can be solved in two ways, forward kinematics method and inverse kinematics method. However,…