Given a query point q and a set D of data points, a nearest neighbor (NN) query returns the data point p in D that minimizes the distance DIST(q,p), where the distance function DIST(,) is the L2 norm. One important variant of this query type is kNN query, which returns k data points with the minimum distances. When taking the temporal dimension into account, the kNN query result may change over...

A novel approach for k-nearest neighbor (k-NN) searching with Euclidean metric is described. It is well known that many sophisticated algorithms cannot beat the brute-force algorithm when the dimensionality is high. In this study, a probably correct approach, in which the correct set of k-nearest neighbors is obtained in high probability, is proposed for greatly reducing the searching time. We ...

Approximate kNN (k-nearest neighbor) techniques using binary hash functions are among the most commonly used approaches for overcoming the prohibitive cost of performing exact kNN queries. However, the success of these techniques largely depends on their hash functions’ ability to distinguish kNN items; that is, the kNN items retrieved based on data items’ hashcodes, should include as many true...

A Reverse k -Nearest-Neighbor (RkNN) query finds the objects that take the query object as one of their k nearest neighbors. In this paper we propose new solutions for evaluating RkNN queries and its variant bichromatic RkNN queries on 2-dimensional location data. We present an algorithm named INCH that can compute a RkNN query’s search region (from which the query result candidates are drawn)....

Several methods (independent subsamples, leave-one-out, cross-validation, and bootstrapping) have been proposed for estimating the error rates of classiers. The rationale behind the various estimators and the causes of the sometimes con BLOCKINicting claims regarding their bias and precision are explored in this paper. The biases and variances of each of the estimators are examined empirically....

Many natural language processing problems involve constructing large nearest-neighbor graphs. We propose a system called FLAG to construct such graphs approximately from large data sets. To handle the large amount of data, our algorithm maintains approximate counts based on sketching algorithms. To find the approximate nearest neighbors, our algorithm pairs a new distributed online-PMI algorith...

We examine the Bayes-consistency of a recently proposed 1-nearest-neighbor-based multiclass learning algorithm. This algorithm is derived from sample compression bounds and enjoys the statistical advantages of tight, fully empirical generalization bounds, as well as the algorithmic advantages of a faster runtime and memory savings. We prove that this algorithm is strongly Bayes-consistent in me...

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...

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...

Photon mapping is one of the most important algorithms for computing global illumination. Especially for efficiently producing convincing caustics, there are no real alternatives to photon mapping. On the other hand, photon mapping is also quite costly: Each radiance lookup requires to find the k nearest neighbors in a kd-tree, which can be more costly than shooting several rays. Therefore, the...