## 6 Discussion  
In this study, we assessed the effectiveness of three methods for detecting changes in nonlinear biomedical signals: classical statistical techniques, time-frequency analysis using Continuous Wavelet Transform (CWT), and machine learning with Support Vector Machines (SVMs). Each method showed varying degrees of success based on signal characteristics and the nature of the changes. The comparative analysis of these methods reveals that each has specific strengths and limitations influenced by signal characteristics and the nature of changes. Classical statistical techniques are simple but can fail in the presence of outliers or non-Gaussian distributions. Time-Frequency analysis using CWT offers detailed insights but requires careful selection of wavelets and thresholds. SVMs were used for change detection, showing mixed results. In the first example with synthetic nonlinear signals, using raw signal values as features did not help the SVMs detect changes due to the lack of distinct patterns. The complexity of the signal's dynamics further complicated detection. In contrast, in the second example with synthetic signals exhibiting abrupt changes, SVMs performed better when trained on features indicative of changes, such as shifts in amplitude or frequency. This highlights the importance of feature extraction and specific training data for effective SVM-based change detection. SVMs provide a powerful machine learning approach but depend heavily on feature representation and training data quality. For effective change detection in nonlinear biomedical signals, a hybrid approach that combines these methods, leveraging their complementary strengths, may offer the most robust solution.  
Classical statistical techniques, while straightforward to implement, may struggle with complex biomedical signals that deviate from Gaussian distributions or contain outliers. Time-Frequency analysis, such as the Continuous Wavelet Transform (CWT), offers a more dynamic approach by analyzing signals in both the time and frequency domains. However, CWT performance depends on careful parameter tuning. Support Vector Machines (SVMs) can be effective for change detection, but their performance relies on feature extraction and the availability of informative training data [46; 47; 48; 49].  
By comparing these methods, we can see the trade-offs involved. Classical statistical techniques are simple but often ineffective for complex signals. Time-Frequency analysis offers more detailed insights but requires careful parameter selection. Machine learning approaches like SVMs can be powerful but depend heavily on the quality of feature extraction and training data (see Figures 11 and 12).  
Figure 11: Analysis of synthetic EEG signal and change detection. (**Top**) Mean and standard deviation of EEG signal: This subplot displays the mean (red dashed line) and one standard deviation above and below the mean (black dashed lines) of the generated EEG signal over time. The underlying blue line represents the raw EEG-like time series data, showcasing the variations around the average signal level. (**Middle**) Time–Frequency analysis (Spectrogram): The spectrogram in this subplot illustrates the time–frequency representation of the EEG signal using the short-time Fourier transform (STFT). The x-axis denotes time (in seconds), while the y-axis represents frequency (in Hz). The color intensity indicates the magnitude of the frequency components in decibels (dB), revealing the distribution of power across different frequency bands over time. (**Bottom**) SVM change detection: This subplot depicts the predicted labels for the EEG signal using a Support Vector Machine (SVM) model. The green line indicates detected changes across the time series, with ’1’ representing no spike and ’2’ indicating spike events. The visualization helps demonstrate the effectiveness of the SVM algorithm in identifying significant changes (spikes) in the EEG data.  
Figure 12: _Cont._