A K th Nearest Neighbour Clustering Procedure

Nc I^^'' Dewey May £6 1981 Working Paper Alfred P. Sloan School of Management a Kth Nearest Neighbour Clustering Procedure a Kth Nearest Neighbour Clustering Procedure a Kth Nearest Neighbour Clustering Procedure

SUMMARY Due to the lack of development in the probabilistic and statistical aspects of clustering research, clustering procedures are often regarded as heuristics generating artificial clusters from a given set of sample data. In this paper, a clustering procedure that is useful for drawing statistical inference about the underlying population from a random sample is developed. It is based on t...

On the Connectivity of Random k-th Nearest Neighbour Graphs

k-Nearest Neighbour Classifiers

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...

Small components in k-nearest neighbour graphs

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,...

Convergence of random k-nearest-neighbour imputation

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...