Wedding the Wavelet Transform and Multivariate Data Analysis |
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Authors: | Fionn Murtagh |
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Institution: | (1) University of Ulster, UK |
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Abstract: | We discuss the use of orthogonal wavelet transforms in preprocessing multivariate data for subsequent analysis, e.g., by
clustering the dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale
nonparametric regression or smoothing, in a natural and integrated way into the data analysis. As will be explained in the
first part of the paper, this approach is of greatest interest for multivariate data analysis when we use (i) datasets with
ordered variables, e.g., time series, and (ii) object dimensionalities which are not too small, e.g., 16 and upwards. In
the second part of the paper, a different type of wavelet decomposition is used. Applications illustrate the powerfulness
of this new perspective on data analysis. |
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Keywords: | |
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