Feature selection in wavelet domain

A similar procedure can be performed in the wavelet domain [27]. In this case, there is no need for adding noisy variables, but instead, wavelet coefficients associated with the data noise can be used to calculate the threshold value of the stability of the b-coefficients. 

Let us consider this approach in a more detailed way, assuming that Discrete Wavelet Transform (DWT) is used for data decomposition. 

The information content of both matrices X and W is identical, but in the scale-frequency domain signals have sparse representations, i.e. many wavelet coefficients approach zero. 

To calculate the number of significant coefficients (i.e. the number of the Wsorted columns, describing the majority of the data variance), different criteria can be applied, e.g. only the n largest coefficients that together describe a predefined variance (i.e., 99.9 %) can be retained as the important 

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