Major Depressive Disorder (MDD), often referred to as clinical depression, is a pervasive and debilitating condition that poses a significant threat to global public health. This condition carries the potential for severe morbidity and even mortality, affecting millions of individuals worldwide. While the conventional approach to treating MDD involves a specific class of antidepressants, a sobering reality persists – a substantial proportion of patients, ranging from 50 % to 70 %, exhibit pronounced resistance to medication-based therapies (Ebrahimzadeh et al., 2021; Leichsenring et al., 2022; Turner et al., 2022; Chekroud et al., 2017). This enduring challenge has fueled an ongoing quest for alternative therapeutic avenues to address the needs of individuals grappling with treatment-resistant depression.

In the quest for solutions, repetitive Transcranial Magnetic Stimulation (rTMS) has gained growing recognition as a promising and secure option, either independently or in combination with other methods, for MDD (Čukić, 2020). rTMS involves the precise delivery of a series of short magnetic pulses directed at the brain, with the aim of stimulating nerve cells. These magnetic pulses activate neurons in specific brain areas, instigating changes in the function of the brain circuits involved. This non-invasive treatment method specifically targets the left or right dorsolateral prefrontal cortex (DLPFC) at regular intervals, thereby prompting neuronal activity and the initiation of action potentials. rTMS can be utilized as an adjunctive therapy to enhance or expedite the efficacy of conventional pharmacotherapy by influencing and modulating cortical activity. The overall effectiveness of rTMS combined with its minimal side effects, has been substantiated by numerous studies. However, clinicians often prescribe rTMS after conducting comprehensive assessments and a series of trial-and-error tests, not only to improve diagnostic precision and treatment outcomes but also to forestall potential relapse, which may occur if a patient proves unresponsive to rTMS. This underscores the pressing need to develop reliable indicators capable of predicting an individual's response to rTMS, thus enabling patients to reap the benefits of this treatment while avoiding costly and ineffective procedures.

To address this challenge, a range of neurophysiological modalities have been employed, including functional Magnetic Resonance Imaging (fMRI) and Electroencephalography (EEG). Among these, EEG, noted for its widespread availability and cost-effectiveness, has emerged as a robust biomarker (Patel et al., 2015; Redlich et al., 2016; Wade et al., 2016; Bachmann et al., 2013; Čukić et al., 2020). As a result, a growing body of research has turned to EEG-based machine learning techniques and statistical methods to differentiate between individuals who respond to rTMS treatment and those who do not (O'Reardon et al., 2007; Arns et al., 2012; Kito et al., 2012; Bares et al., 2007; Khodayari-Rostamabad et al., 2011; Arns et al., 2014).

Beyond the use of rTMS, similar efforts have been undertaken to assess the responsiveness of other approaches for treating resistant MDD. For instance, a previous study have explored changes in QEEG prefrontal cordance as a potential predictor of response to antidepressants (Bares et al., 2007). The effectiveness of selective serotonin reuptake inhibitors (SSRIs) as another predictor of treatment response has been scrutinized in (Ebrahimzadeh et al., 2022). In this study, the patient's initial EEG was analyzed to extract features, and a mixture of factor analysis (MFA) model yielded a classification accuracy of 87.9 %. SSRI efficacy was also the subject of investigation in another study, where logistic regression was applied to wavelet features of baseline EEG, resulting in an accuracy of 87.5 % (Mumtaz et al., 2017). Furthermore, transcranial direct current stimulation (tDCS), an alternative treatment aimed at enhancing mood and cognition in MDD patients (Al-Kaysi et al., 2017). In this study Linear Support Vector Machine (LSVM), Linear Discriminant Analysis (LDA), and neural networks were used to classify features extracted from EEG data, achieving accuracy rates of 76 % for mood and 92 % for cognition labeling, respectively.

Turning our attention back to rTMS, a meta-analysis reported relatively low response rates of 40.9% and remission rates of 16.4% (Cao et al., 2018). In another study, the EEG recordings were examined during participants' completion of a Working Memory (WM) task and predicted rTMS responses with an accuracy of 91 % (Bailey et al., 2018). The same researchers also collected resting-state EEG data at baseline and one week after treatment initiation, combining mood and EEG features using an LSVM classifier, ultimately achieving a classification accuracy of 86.6 % (Bailey et al., 2019). The extracted EEG features encompassed EEG power and weighted phase lag index (wPLI) in alpha and theta frequency bands (Bailey et al., 2019), gamma frequency band (Bailey et al., 2018), alpha peak frequency (iAPF), and frontal theta cordance (Bailey et al., 2019; Jaworska et al., 2019). The literature also encompasses a wide array of EEG features employed for the same purpose, such as power spectral features (Ebrahimzadeh et al., 2022; Al-Kaysi et al., 2017), coherence (Ebrahimzadeh et al., 2022; Mumtaz et al., 2017), mutual information (MI) (Ebrahimzadeh et al., 2022), nonlinear features (Hasanzadeh et al., 2019), time-frequency processing (Ebrahimzadeh et al., 2021), and wavelet coefficients (Mumtaz et al., 2017). Among these features, EEG power in different frequency bands and their combinations have received substantial attention in predicting MDD treatment (Wade et al., 2016; Arns et al., 2012; Bruder et al., 2008; Cook et al., 2002; Knott et al., 2000; Pellicciari et al., 2013; Spronk et al., 2011; Suffin and Emory, 1995; Tenke et al., 2011; Lebiecka et al., 2018). Notably, treatment response has been linked to cordance measures (Leuchter et al., 1994) and an Antidepressant Treatment Response (ATR) index (Iosifescu et al., 2009). The impact of rTMS on functional connectivity in MDD and bipolar disorder using directed transfer function and graph theory-based indices was assessed in previous study (Olejarczyk et al., 2020).

Numerous investigations have directed their focus towards the non-Gaussian and higher-order characteristics of EEG, aiming to unveil additional insights that remain concealed within the power spectrum. Non-linear and bispectral attributes to discern and classify responses to rTMS were used in previous study (Hasanzadeh et al., 2019).

Moreover, a considerable body of research has tended to concentrate on three prefrontal electrodes, namely FP1, FP2, and FPz. This is due to the belief that the frontal lobe undergoes significant changes in MDD. However, this approach oversimplifies the matter, as there is little guarantee that frontal components do not influence channels in other brain regions, such as the central, parietal, temporal, and occipital areas. It is plausible that components from the frontal lobe play a more pivotal role than those from other regions. Identifying these components and extracting features from their time series may yield more accurate results compared to other EEG channels. In essence, the frontal components form a neural network involved in rTMS treatment, and the EEG channels reflect their activity. Given this perspective, our study seeks to shift the focus to the component domain. To achieve this, we initially decomposed the EEG channels into their components and identified the relevant components based on their spatial locations and their association with the MNI model dipoles. Subsequently, we utilized the time series of these selected components to extract a comprehensive set of time-series features, including spectral, bispectral, and nonlinear features such as bispectrum features, Lempel-Ziv Complexity (LZC), correlation dimension (CD), fractal dimension (FD), component power in all frequency bands (delta, theta, alpha, and beta), and frontal and prefrontal cordance in the theta band. These features were extracted from pretreatment resting EEG data. In addition to the classification task, we conducted a statistical analysis to assess the differences in these features between two groups: responders (R) and non-responders (NR). Finally, we employed Reinforcement Learning (RL) for feature selection. To the best of our knowledge, this is the first study that simultaneously investigates the predictive potential of selected bispectral, nonlinear, and spectral features based on component time-series for predicting treatment response.

Fig. 1 illustrates our research methodology, commencing with participant information and EEG data acquisition. After the extraction of relevant components and features, we proceed to the classification and statistical analysis phases. The Results Section evaluates the predictive power of these feature sets, categorizing subjects into R and NR based on our statistical findings. The Discussion Section will delve into the implications of our results, including limitations and suggestions for future research. Finally, the conclusion for this study is in the Conclusion section.