Let G = Gn,k denote the graph formed by placing points in a square of area n according to a Poisson process of density 1 and joining each point to its k nearest neighbours. In [2] Balister, Bollobás, Sarkar and Walters proved that if k < 0.3043 logn then the probability that G is connected tends to 0, whereas if k > 0.5139 logn then the probability that G is connected tends to 1. We prove that,...

Random k-nearest-neighbour (RKNN) imputation is an established algorithm for filling in missing values in data sets. Assume that data are missing in a random way, so that missingness is independent of unobserved values (MAR), and assume there is a minimum positive probability of a response vector being complete. Then RKNN, with k equal to the square root of the sample size, asymptotically produ...

The nearest neighbor (NN) approach is a powerfd nonparametric technique for pattern classification tasks. In this paper, algorithms for prototype reduction, hierarchical prototype organization and fast NN search are described. To remove redundant category prototypes and to avoid redundant comparisons, the algorithms exploit geometrical information of a given prototype set which is represented a...

The nearest neighbor classifier is a powerful, straightforward, and very popular approach to solving many classification problems. It also enables users to easily incorporate weights of training instances into its model, allowing users to highlight more promising examples. Instance weighting schemes proposed to date were based either on attribute values or external knowledge. In this paper, we ...

LetP be a Poisson process of intensity one in a squareSn of arean. We construct a random geometric graph Gn,k by joining each point of P to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that Gn,k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that Gn,k is connected tends to 1 as n → ∞. They conject...

A fast nearest neighbor algorithm for pattern classiication is proposed and tested on real data. The patterns (points in d-dimensional Euclidean space) are sorted along a space-lling curve. This way the multidi-mensional problem is compressed to the simplest case of the nearest neighbor search in one dimension.

Building an index tree is a common approach to speed up the k nearest neighbour search in large databases of many-dimensional records. Many applications require varying distance metrics by putting a weight on diierent dimensions. The main problem with k nearest neighbour searches using weighted euclidean metrics in a high dimensional space is whether the searches can be done eeciently We presen...

The nearest neighbour (NN) and k-nearest neighbour (kNN) classi cation rules have been widely used in pattern recognition due to its simplicity and good behaviour. Exhaustive nearest neighbour search can become unpractical when facing large training sets, high dimensional data or expensive similarity measures. In the last years a lot of NN search algorithms have been developed to overcome those...

The (k-)nearest neighbour problem is well known in a wide range of areas. Many algorithms to tackle this problem suffer from the “curse of dimensionality” which means that the execution time grows exponentially with increasing dimension. Therefore, it is important to have efficient algorithms for the problem. In this report, some well known tree-based algorithms for the k-nearest neighbour are ...