Discussiones Mathematicae Probability and Statistics 25(2) (2005) 217-239


Tomasz Górecki

Faculty of Mathematics and Computer Science,
Adam Mickiewicz University,
Umultowska 87, 61-614 Poznań



In this paper we will precisely analyze the nearest neighbor method for different dissimilarity measures, classical and weighed, for which methods of distinguishing were worked out. We will propose looking for weights in the space of discriminant coordinates. Experimental results based on a number of real data sets are presented and analyzed to illustrate the benefits of the proposed methods. As classical dissimilarity measures we will use the Euclidean metric, Manhattan and post office metric. We gave the first two metrics weights and now these measures are not metrics because the triangle inequality does not hold. Howeover, it does not make them useless for the nearest neighbor classification method. Additionally, we will analyze different methods of tie-breaking.

Keywords and Phrases: nearest neighbor method, discriminant coordinates, dissimilarity measures, estimators of classification error.

2000 Mathematics Subject Classification: 62H30, 62J05.


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Received 18 June 2004
Revised 4 August 2005