Hausdorr metrics are used in geometric settings for measuring the distance between sets of points. They have been used extensively in areas such as computer vision , pattern recognition and computational chemistry. While computing the distance between a single pair of sets under the Hausdorr metric has been well studied, no results were known for the Nearest Neighbor problem under Hausdorr metr...

This paper points out and analyzes the advantages and drawbacks of the Nearest Feature Line (NFL) classifier. To overcome the shortcomings, a new feature subspace with two simple and effective improvements is built to represent each class. The proposed method, termed Rectified Nearest Feature Line Segment (RNFLS), is shown to possess a novel property of concentration as a result of the added li...

In this paper, we propose a thorough investigation of a nearest neighbor rule which we call the “Symmetric Nearest Neighbor (sNN) rule”. Basically, it symmetrises the classical nearest neighbor relationship from which are computed the points voting for some instances. Experiments on 29 datasets, most of which are readily available, show that the method significantly outperforms the traditional ...

A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., “find all my nearest gas stations during my route from point s to point e”). The result contains a set of tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitiv...

This paper presents an algorithm, called the winnerupdate algorithm, for accelerating the nearest neighbor search. By constructing a hierarchical structure for each feature point in the lp metric space, this algorithm can save a large amount of computation at the expense of moderate preprocessing and twice the memory storage. Given a query point, the cost for computing the distances from this p...

This paper concerns the efficient processing of multiple k nearest neighbor queries in a road-network setting. The assumed setting covers a range of scenarios such as the one where a large population of mobile service users that are constrained to a road network issue nearest-neighbor queries for points of interest that are accessible via the road network. Given multiple k nearest neighbor quer...

We investigate uniqueness issues that arise in l∞-optimization to linear spaces and Bergman fans of matroids. For linear spaces, we give a polyhedral decomposition of R based on the dimension of the set of l∞-nearest neighbors. This implies that the l∞-nearest neighbor in a linear space is unique if and only if the underlying matroid is uniform. For Bergman fans of matroids, we show that the se...

Methods of nearest neighbors are essential in wide range of applications where it is necessary to estimate probability density (e.g. Bayes’s classifier, problems of searching in large databases). This paper contemplates on features of distribution of nearest neighbors’ distances in high-dimensional spaces. It shows that for uniform distribution of points in n-dimensional Euclidean space the dis...

This paper presents the development of fuzzy‐ appearance manifold and fuzzy‐nearest distance calculation in the eigenspace domain for pose estimation of degraded face images. In order to obtain a robust pose estimation system which can deal with the fuzziness of face data caused by statistical errors, we proposed the fuzzy‐vector representation in eigenspace domain of the...

This article describes the results of applying four unsupervised anomaly detection algorithms to data from two rocket propulsion testbeds. The first testbed uses historical data from the Space Shuttle Main Engine. The second testbed uses data from an experimental rocket engine test stand located at NASA Stennis Space Center. The article describes nine anomalies detected by the four algorithms. ...