Subspaces offer convenient means of representing information in many Pattern Recognition, Machine Vision, and Statistical Learning applications. Contrary to the growing popularity of subspace representations, the problem of efficiently searching through large subspace databases has received little attention in the past. In this paper we present a general solution to the Approximate Nearest Subs...

A k-nearest neighbor (kNN) query determines the k nearest points, using distance metrics, from a given location. An all k-nearest neighbor (AkNN) query constitutes a variation of a kNN query and retrieves the k nearest points for each point inside a database. Their main usage resonates in spatial databases and they consist the backbone of many location-based applications and not only. In this w...

We give laws of large numbers (in the Lp sense) for the total length of the k-nearest neighbours (directed) graph and the j-th nearest neighbour (directed) graph in Rd, d ∈ N, with power-weighted edges. We deduce a law of large numbers for the standard nearest neighbour (undirected) graph. We give the limiting constants, in the case of uniform random points in (0, 1)d, explicitly. Also, we give...

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...

Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is to construct a neighborhood graph on the sample points such that clusters are “identified”: that is, the subgraph induced by points from the same cluster is connected, while subgraphs corresponding to different clusters are not connected to each other. We derive bounds ...

We present a new approach for approximate nearest neighbor queries for sets of high dimensional points under any L t-metric, t = 1; : : : ; 1. The proposed algorithm is eecient and simple to implement. The algorithm uses multiple shifted copies of the data points and stores them in up to (d + 1) B-trees where d is the dimensionality of the data, sorted according to their position along a space ...

User preference queries are very important in spatial databases. With the help of these queries, one can found best location among points saved in database. In many situation users evaluate quality of a location with its distance from its nearest neighbor among a special set of points. There has been less attention about evaluating a location with its distance to nearest neighbors in spatial us...

In nearest neighbor searching we are given a set of n data points in real d-dimensional space, <d, and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported efficiently. Because data sets can be quite large, we are interested in data structures that use optimal O(dn) storage. In this paper we consi...

Reverse nearest neighbor queries are defined as follows: Given an input point-set P , and a query point q, find all the points p in P whose nearest point in P ∪ {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).

Reverse nearest neighbor queries are defined as follows: Given an input point-set P , and a query point q, find all the points p in P whose nearest point in P ∪ {q} \ {p} is q. We give a data structure to answer reverse nearest neighbor queries in fixed-dimensional Euclidean space. Our data structure uses O(n) space, its preprocessing time is O(n log n), and its query time is O(log n).