Edited by Charlie Karlsson
10 Clustering using wavelet transformation Abdullah Almasri and Ghazi Shukur This chapter introduces and describes an alternative clustering approach based on the Discrete Wavelet Transform (DWT) which satisﬁes requirements that other clustering methods, like discriminative-based clustering and model-based clustering approaches, do not satisfy. The clustering method has been constructed using wavelet analysis that has the ability of decomposing a data set into diﬀerent scales. Wavelet algorithm is then used to specify the number of the clusters and quality of the clustering results at each scale. The same algorithm can be generalized for more than one-dimensional data. Some examples about how to use this approach are presented in this chapter, using diﬀerent sample sizes, and where diﬀerent kinds of noises are imposed on simulated data. These examples show the successfulness and eﬃciency of this kind of methodology in detecting clusters under diﬀerent situations. 1 Introduction Cluster analysis (originally used by Tryon, 1939) combines a number of diﬀerent classiﬁcation algorithms that are usually done to join cases or a set of data objects into groups or clusters when the group membership is not known a priori. Hence, it is a technique for linking individuals or objects into unknown groups or clusters such that those within each group or cluster are more closely related to one another than those assigned to other clusters. An observation or object can be explained by a number of measurements or by its relation to other observations or objects. Clustering,...
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