Hilbert-Huang transformation, wavelet transformation, and Fourier transformation are the principal time-frequency analysis methods. These transformations can be used to discuss the frequency characteristics of linear and stationary signals, the time-frequency features of linear and non-stationary signals, the time-frequency features of non-linear and non-stationary signals, respectively. The Hilbert-Huang transformation is a combination of empirical mode decomposition and Hilbert spectral analysis. The empirical mode decomposition uses the characteristics of signals to adaptively decompose them to several intrinsic mode functions. Hilbert transforms are then used to transform the intrinsic mode functions into instantaneous frequencies, to obtain the signal's time-frequency-energy distributions and features. Hilbert-Huang transformation-based time-frequency analysis can be applied to natural physical signals such as earthquake waves, winds, ocean acoustic signals, mechanical diagnosis signals, and biomedical signals. In previous studies, we examined Hilbert-Huang transformation-based time-frequency analysis of the electroencephalogram FPI signals of clinical alcoholics, and 'sharp I' wave-based Hilbert-Huang transformation time-frequency features. In this paper, we discuss the application of Hilbert-Huang transformation-based time-frequency analysis to biomedical signals, such as electroencephalogram, electrocardiogram signals, electrogastrogram recordings, and speech signals.

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

In this paper, we used the Hilbert-Huang transform (HHT) analysis method to examine the time-frequency characteristics of spike waves for detecting epilepsy symptoms. We obtained a sample of spike waves and nonspike waves for HHT decomposition by using numerous intrinsic mode functions (IMFs) of the Hilbert transform (HT) to determine the instantaneous, marginal, and Hilbert energy spectra. The Pearson correlation coefficients of the IMFs, and energy-IMF distributions for the electroencephalogram (EEG) signal without spike waves, Spike I, Spike II and Spike III sample waves were determined. The analysis results showed that the ratios of the referred wave and Spike III wave to the referred total energy for IMF1, IMF2, and the residual function exceeded 10%. Furthermore, the energy ratios for IMF1, IMF2, IMF3 and the residual function of Spike I, Spike II to their total energy exceeded 10%. The Pearson correlation coefficients of the IMF3 of the EEG signal without spike waves and Spike I wave, EEG signal without spike waves and Spike II wave, EEG signal without spike waves and Spike III wave, Spike I and II waves, Spike I and III waves, and Spike II and III waves were 0.002, 0.06, 0.01, 0.17, 0.03, and 0.3, respectively. The energy ratios of IMF3 in the δ band to its referred total energy for the EEG signal without spike waves, and of the Spike I, II, and III waves were 4.72, 6.75, 5.41, and 5.55%, respectively. The weighted average frequency of the IMF1, IMF2, and IMF3 of the EEG signal without spike waves was lower than that of the IMF1, IMF2, and IMF3 of the spike waves, respectively. The weighted average magnitude of the IMF3, IMF4, and IMF5 of the EEG signal without spike waves was lower than that of the IMF1, IMF2, and IMF3 of spike waves, respectively.

In this paper, a unique analysis method for sperm whale clicks based on Hilbert-Huang transform (HHT) is proposed. Four sperm whale click samples with durations of 10 ms (defined as click I), and four sperm whale click samples with durations of 5 ms (defined as click II) were illustrated. These click samples were recorded in the Mediterranean Sea by Centro Interdisciplinare di Bioacusticae Ricerche Ambientali, Università degli Studi di Pavia. The empirical mode decomposition method was used to decompose click I samples into seven intrinsic mode functions (IMFs) and one residue function (RF), and click II samples were decomposed into six IMFs and one RF. The average energy distributions of multiple IMFs and the single RF domain for click I and click II samples were explored using the HHT analysis method. The average energy-frequency representations were also investigated for the same click I and click II samples. The analysis results show that the energy-frequency characteristics of sperm whale clicks can be extracted and understood by applying several IMFs and one RF signal with a high-resolution analysis.

The problem of learning the kernel function with linear combinations of multiple kernels has attracted considerable attention recently in machine learning. Specially, by imposing anlp-norm penalty on the kernel combination coefficient, multiple kernel learning (MKL) was proved useful and effective for theoretical analysis and practical applications (Kloft et al., 2009, 2011). In this paper, we present a theoretical analysis on the approximation error and learning ability of thelp-norm MKL. Our analysis shows explicit learning rates forlp-norm MKL and demonstrates some notable advantages compared with traditional kernel-based learning algorithms where the kernel is fixed.