RenyiBS: Renyi entropy basis selection from wavelet packet decomposition tree for phonocardiogram classification
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RenyiBS: Renyi entropy basis selection from wavelet packet decomposition tree for phonocardiogram classification Fatemeh Safara1 · Asri Ranga Abdullah Ramaiah2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Wavelet packet transform (WPT) is a powerful mathematical tool for analyzing nonlinear biomedical signals, such as phonocardiogram (PCG). WPT decomposes a PCG signal into a full binary tree of details and approximation coefficients. Appropriate nodes of the tree could be selected as a basis for generating features. Motivated by this, we propose the Renyi entropy basis selection (RenyiBS) method. In RenyiBS method, we use the Renyi entropy as an information measure to choose the best basis of the wavelet packet tree of PCG signals for feature selection and classification. The Renyi entropy estimates the spectral complexity of a signal, which is vital for characterizing nonlinear signals such as PCGs. After selecting the best basis, we define features on the coefficients of the selected nodes. Then, we classify PCGs using the support vector machine (SVM) classifier. In the simulation, we examine a set of 820 heart sound cycles, including normal heart sounds and three types of heart murmurs. The three murmurs examined include aortic regurgitation, mitral regurgitation, and aortic stenosis. We achieved the promising result of 99.74% accuracy, confirming the ability of Renyi entropy to select an appropriate basis of the wavelet packet tree and extracting the nonlinear behavior of particular heart sounds. Besides, the superiority of our proposed information measure in comparison with other information measures reported before is shown. Keywords Wavelet packet transforms · Renyi entropy · Information measure · Phonocardiogram · Heart murmur · Support vector machine (SVM)
* Fatemeh Safara [email protected] 1
Department of Computer Engineering, Islamic Azad University, Islamshahr Branch, Tehran, Iran
2
Cardiology Department, Serdang Hospital, Serdang, Jalan Puchong, 43000 Kajang, Selangor Darul Ehsan, Malaysia
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F. Safara, A. R. A. Ramaiah
1 Introduction Wavelet packet transform (WPT) is one of the best signal analysis transform which extracts the nonlinear characteristic of a signal [1]. However, generating features from all nodes of a wavelet packet tree is not cost-effective. Therefore, an information measure is required to determine the informative nodes of all nodes in a wavelet packet tree. This determination of informative nodes with the capability of characterizing the signal behavior is called the best basis selection. Best basis selection examines a full wavelet packet tree for suitable bases. Best basis selection was first introduced by Coifman et al. [2]. In that paper, a basis selection method using Shannon entropy is proposed to choose the informative bases from a WPT tree with the aim to analyze nonlinear signals. Several recent studies also examined the power of different entropies for capturing characteristics of nonlinear signals. Sam
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