A signal invariant wavelet function selection algorithm

Abstract

This paper addresses the problem of mother wavelet selection for wavelet signal processing in feature extraction and pattern recognition. The problem is formulated as an optimization criterion, where a wavelet library is defined using a set of parameters to find the best mother wavelet function. For estimating the fitness function, adopted to evaluate the performance of the wavelet function, analysis of variance is used. Genetic algorithm is exploited to optimize the determination of the best mother wavelet function. For experimental evaluation, solutions for best mother wavelet selection are evaluated on various biomedical signal classification problems, where the solutions of the proposed algorithm are assessed and compared with manual hit-and-trial methods. The results show that the solutions of automated mother wavelet selection algorithm are consistent with the manual selection of wavelet functions. The algorithm is found to be invariant to the type of signals used for classification.

Appendices

Appendix 1

1.1 Dataset I

Data described in [3], which is publicly available, is used for epilepsy detection. The complete dataset consists of five sets (denoted A–E), each containing 100 single-channel electroencephalogram (EEG) signals of 23.6 s. Sets A and B have been taken from surface EEG recordings of five healthy volunteers with eyes open and closed, respectively. Signals in two sets have been measured in seizure-free intervals from five patients in the epileptogenic zone (D) and from the hippocampal formation of the opposite hemisphere of the brain (C). Set E contains seizure activity, selected from all recording sites exhibiting ictal activity. EEG signals from Set A and Set C representing normal and pre-ictal brain activities, respectively, are used for epilepsy detection. Instead of Set E, Set C is used for the application since in practical situation it is not viable to detect epilepsy at the time of seizure from the ictal activity EEG.

1.2 Dataset II

In this case, the sleep EEG dataset provided by physiobank [17] is used. The recordings were obtained from Caucasian males and females (21–35 years old) without any medication; they contain horizontal EOG, Fpz-Cz and Pz-Oz EEG, each sampled at 100 Hz. Sleep scoring is done using Fpz-Cz EEG signals, and the hypnogram is used as the target output for training and evaluating the performance of the classifier. The scoring is done in three classes, namely waking, REM sleep and NREM sleep.

1.3 Dataset III

Data contributed by Dr. Thomas Penzel of Phillips University, Marburg, Germany, for physionet bank are used for apnea detection using ECG signals [23]. The data consist of 70 records, divided into a learning set of 35 record and a test set of 35 records. The ECG signals are digitized at 100 samples per second, and the gain is 200 A/D units per mV. ECG signals of 10 s duration are used for this study.

1.4 Dataset IV

The ECG data collected from MIT-BIH arrhythmia database [20] are used for multi-class classification of different types of arrhythmia namely, normal sinus rhythm, right bundle branch block (RBBB), left bundle branch block (LBBB) and atrial fibrillation (AF). The recordings were digitized at 360 samples per second per channel with 11-bit resolution over a 10 mV range and gain of 200 A/D per unit mV. The ECG segments from MLII signals of records 101, 109, 212 and 202 are used for NSR, LBBB, RBBB and AF, respectively.

1.5 Dataset V

The electrohysterogram (EHG) records (uterine EMG records) included in the Term–Preterm ElectroHysteroGram Database obtained at the University Medical Centre Ljubljana, Department of Obstetrics and Gynecology, are used for classification of term–preterm deliveries using EHG signals [28]. The records were obtained during regular checkups either around the 22nd week of gestation or around the 32nd week of gestation. Each record is composed of three channels, recorded from four electrodes. The differences in the electrical potentials of the electrodes were recorded, producing three channels:

• S1 = E2–E1 (first channel);

• S2 = E2–E3 (second channel);

• S3 = E4–E3 (third channel).

Each signal has been digitized at 20 samples per second per channel, and the gain is 13107 A/D units per mV. For classification purposes, signal S3 is used as the EHG signal without any filtering.

1.6 Dataset VI

The EMG data provided by Department of Neurology, Beth Israel Deaconess Medical Center, is used to classify between Healthy, Neuropathic and Myopathic EMG signals [16]. The data were recorded at 50 KHz and then down sampled to 4 KHz. During the recording process, two analog filters were used: a 20-Hz high-pass filter and a 5-KHz low-pass filter.

Appendix 2

See Table 4.

Table 4 Wavelet library