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Joint Markov Blankets in Feature Sets Extracted from Wavelet Packet Decompositions
Laboratorium voor Neuro- en Psychofysiologie, Computational Neuroscience Research Group, Katholieke Universiteit Leuven, O&N II Herestraat 49 - bus 1021, B-3000 Leuven, Belgium
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Received: 1 June 2011; in revised form: 12 July 2011 / Accepted: 18 July 2011 / Published: 22 July 2011
Abstract: Since two decades, wavelet packet decompositions have been shown effective as a generic approach to feature extraction from time series and images for the prediction of a target variable. Redundancies exist between the wavelet coefficients and between the energy features that are derived from the wavelet coefficients. We assess these redundancies in wavelet packet decompositions by means of the Markov blanket filtering theory. We introduce the concept of joint Markov blankets. It is shown that joint Markov blankets are a natural extension of Markov blankets, which are defined for single features, to a set of features. We show that these joint Markov blankets exist in feature sets consisting of the wavelet coefficients. Furthermore, we prove that wavelet energy features from the highest frequency resolution level form a joint Markov blanket for all other wavelet energy features. The joint Markov blanket theory indicates that one can expect an increase of classification accuracy with the increase of the frequency resolution level of the energy features.
Keywords: feature subset selection; joint Markov blanket; Markov blanket; mutual information; wavelet packet decomposition
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Van Dijck, G.; Van Hulle, M.M. Joint Markov Blankets in Feature Sets Extracted from Wavelet Packet Decompositions. Entropy 2011, 13, 1403-1424.
Van Dijck G, Van Hulle MM. Joint Markov Blankets in Feature Sets Extracted from Wavelet Packet Decompositions. Entropy. 2011; 13(7):1403-1424.
Van Dijck, Gert; Van Hulle, Marc M. 2011. "Joint Markov Blankets in Feature Sets Extracted from Wavelet Packet Decompositions." Entropy 13, no. 7: 1403-1424.