 # Selection of Wavelet Features for Biomedical Signals Using SVM Learning

Girisha Garg (BBDIT, India) and Vijander Singh (NSIT, India)
DOI: 10.4018/978-1-5225-0075-9.ch015

## Abstract

Signal processing problems require feature extraction and selection techniques. A novel Wavelet Feature Selection algorithm is proposed for ranking and selecting the features from the wavelet decompositions. The algorithm makes use of support vector machine to rank the features and backward feature elimination to remove the features. The finally selected features are used as patterns for the classification system. Two EEG datasets are used to test the algorithm. The results confirm that the algorithm is able to improve the efficiency of wavelet features in terms of accuracy and feature space.
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## 2. Methods

Wavelet transforms of a signal can be viewed as a step by step transformation of the signal from the time domain to the frequency domain. Discrete Wavelet Transform (DWT) analyses the signal using multi resolution analysis by decomposing the signal into approximations and detail information by employing two functions: scaling and wavelet function. The approximation coefficient is subsequently divided into new approximation and detailed coefficients. This process is carried out iteratively producing a set of approximation coefficients and detailed coefficients at different levels of decomposition.

If the scaling functions and wavelets form an orthogonal basis, Parseval’s theorem relates the energy of the signal x(t) to the energy in each of the components and their wavelet coefficients. The energy of the detailed signal at each resolution level, j is given by:

(1)(2)

The wavelet energy can be used to extract only the useful information from the signal about the process under study.

For this work the concept of relative energy is used. Relative Wavelet Energy (RWE) gives information about relative energy with associated frequency bands and can detect the degree of similarity between segments of a signal. RWE is defined by the ratio of detail energy at the specific decomposition level to the total energy. Thus the relative energy is given by:

(3)

RWE resolves the wavelet representation of the signal in one wavelet decomposition level corresponding to the representative signal frequency. Thus this method accurately detects and characterizes the specific phenomenon related to the different frequency bands of the EEG signal. RWE gains the advantages over DWT based feature extraction in terms of speed, computation efficiency and classification rate. The RWE features are ranked and selected in order to further improve the computational efficiency. This is done by evaluating how well an individual energy feature contributes to the classification accuracy.

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