1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of ne...

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...

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 to determine the class of the query. This approach to classification is of particular importance today because issues of poor run-time performance is not such...

Multimedia databases usually deal with huge amounts of data and it is necessary to have an indexing structure such that eecient retrieval of data can be provided. R-Tree with its variations, is a commonly cited indexing method. In this paper we propose an improved nearest neighbor search algorithm on the R-tree and its variants. The improvement lies in the removal of two hueristics that have be...

Perhaps the most straightforward classifier in arsenal or Machine Learning techniques is Nearest Neighbour Classifier—classification achieved by identifying nearest neighbours to a query example and using those determine class of query. This approach classification particular importance, because issues poor runtime performance not such problem these days with computational power that available....

Periodic patterns of synchrony are lattice networks whose cells are coloured according to a local rule, or balanced colouring, and such that the overall system has spatial periodicity. These patterns depict the finite-dimensional flow-invariant subspaces for all the lattice dynamical systems, in the given lattice network, that exhibit those periods. Previous results relate the existence of peri...