Transactions on Case-Based Reasoning

Volume 2 - Number 1 - October 2009 - Pages 3-14

Distances in Classification

C. Weihs and G. Szepannek

Department of Statistics University of Dortmund


The notion of distance is the most important basis for classification. This is especially true for unsupervised learning, i.e. clustering, since there is no validation mechanism by means of objects with known groups. But also for supervised learning standard distances often do not lead to appropriate results. For every individual problem the adequate distance is to be decided upon. This is demonstrated by means of three practical examples from very different application areas, namely social science, music science, and production economics. In social science, clustering is applied to spatial regions resulting in unconnected clusters. However, connectedness is sometimes important for interpretation, and may have to be taken into account for clustering. In statistical musicology the main problem is often to find an adequate transformation of the input time series as an adequate basis for distance definition. Also, local modelling is proposed in order to account for different subpopulations, e.g. instruments. In production economics often many quality criteria have to be taken into account with very different scaling. In order to find a compromise optimum classification, this leads to a pre-transformation onto the same scale, called desirability.

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