The k-NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct k-NN graphs remains a challenge, especially for large-scale high-dimensional data. In this paper, we propose a new approach to construct approximate k-NN graphs with emphasis in: efficiency and accuracy. We hierar...

Multivariate Hensel construction with floating-point numbers often cause large cancellation errors which are errors due to a cancellation of almost the same numbers. Sasaki and Yamaguchi [SY98] showed that multivariate Hensel construction causes large cancellation errors if the expansion point is chosen near a singular point, and Sasaki [Sas00] studied four mechanisms of term cancellations near...

Algorithms that use point-cloud models make heavy use of the neighborhoods of the points. These neighborhoods are used to compute the surface normals for each point, mollification, and noise removal. All of these primitive operations require the seemingly repetitive process of finding the k nearest neighbors of each point. These algorithms are primarily designed to run in main memory. However, ...

The Reverse Nearest Neighbor (RNN) problem is to find all points in a given data set whose nearest neighbor is a given query point. Given a set of blue points and a set of red points, the bichromatic version of the RNN problem, for a query blue point, is to find all the red points whose blue nearest neighbour is the given query point. In this paper, we introduce and investigate new optimization...

In this paper, we present algorithms for the top-k nearest neighbor searching where the input points are exact and the query point is uncertain under the L1 metric in the plane. The uncertain query point is represented by a discrete probability distribution function, and the goal is to efficiently return the top-k expected nearest neighbors, which have the smallest expected distances to the que...

The goal of this paper is to quantitatively describe some statistical properties of higher-dimensional determinantal point processes with a primary focus on the nearest-neighbor distribution functions. Toward this end, we express these functions as determinants of NxN matrices and then extrapolate to N-->infinity . This formulation allows for a quick and accurate numerical evaluation of these q...

Nearest neighbour searches in the image plane are among the most frequent problems in a variety of computer vision and image processing tasks. They can be used to replace missing values in image filtering, or to group close objects in image segmentation, or to access neighbouring points of interest in feature extraction. In particular, we address two nearest neighbour problems: The nearest neig...

Given a set S of n data points in some metric space. Given a query point q in this space, a nearest neighbor query asks for the nearest point of S to q. Throughout we will assume that the space is real d-dimensional space <d, and the metric is Euclidean distance. The goal is to preprocess S into a data structure so that such queries can be answered efficiently. Nearest neighbor searching has ap...

1 Singh, S. "Forecasting using a Fuzzy Nearest Neighbour Method", Proc. 6th International Conference on Fuzzy Theory and Technology , Fourth Joint Conference on Information Sciences (JCIS'98), North Carolina, vol. 1, pp.80-83, 1998 (23-28 October ,1998) ABSTRACT This paper explores a nearest neighbour pattern recognition method for time-series forecasting. A nearest neighbour method (FNNM) base...

We propose new summary statistics quantifying several forms of dependence between types in a spatial pattern of points classiied into distinct types. These statistics are the multivariate counterparts of the J-function for point processes of a single type, introduced in 18]. They are based on comparing distances from a type i point to either the nearest type j point or to the nearest point in t...