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Feature Relevance in Ward’s Hierarchical Clustering Using the L p Norm

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  • Renato Amorim

Abstract

In this paper we introduce a new hierarchical clustering algorithm called Ward p . Unlike the original Ward, Ward p generates feature weights, which can be seen as feature rescaling factors thanks to the use of the L p norm. The feature weights are cluster dependent, allowing a feature to have different degrees of relevance at different clusters. We validate our method by performing experiments on a total of 75 real-world and synthetic datasets, with and without added features made of uniformly random noise. Our experiments show that: (i) the use of our feature weighting method produces results that are superior to those produced by the original Ward method on datasets containing noise features; (ii) it is indeed possible to estimate a good exponent p under a totally unsupervised framework. The clusterings produced by Ward p are dependent on p. This makes the estimation of a good value for this exponent a requirement for this algorithm, and indeed for any other also based on the L p norm. Copyright Classification Society of North America 2015

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  • Renato Amorim, 2015. "Feature Relevance in Ward’s Hierarchical Clustering Using the L p Norm," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 46-62, April.
    • Handle: RePEc:spr:jclass:v:32:y:2015:i:1:p:46-62
    DOI: 10.1007/s00357-015-9167-1
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