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Clustering Using Wavelet Transformation

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Abstract

This paper 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 generalised for more than one-dimensional data. Some examples about how to use this approach are presented in the paper 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.

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  • Almasri, Abdullah & Shukur, Ghazi, 2006. "Clustering Using Wavelet Transformation," CAFO Working Papers 2006:3, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.
    • Handle: RePEc:hhs:vxcafo:2006_003
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    1. Ramsey, James B. & Lampart, Camille, 1998. "Decomposition Of Economic Relationships By Timescale Using Wavelets," Macroeconomic Dynamics, Cambridge University Press, vol. 2(1), pages 49-71, March.
    2. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
    3. Abdullah Almasri & Ghazi Shukur, 2003. "An illustration of the causality relation between government spending and revenue using wavelet analysis on Finnish data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(5), pages 571-584.
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    More about this item

    Keywords

    Cluster analysis; discrete wavelet transform; multiresolution;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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