## 1 Introduction  
Obstructive sleep apnea (OSA) is a respiratory disorder of repetitive episodes of breathing arrests during sleep [1]. It has also been associated with increased morbidity and decreased quality of life [1]. OSA sufferers often report daytime somnolence, which can lead to diminished work performance, psychological disturbances, and road accidents in the most severe cases [2]. Moreover, OSA prevalence is estimated to be notably high, affecting between 9% and 38% of general population [3]. However, recent studies highlight a brightening underdiagnosis of this disorder, particularly in individuals with cardiovascular diseases (CVDs), with reported rates exceeding 90% of the surveyed population [4]. Hence, given the substantial comorbidity between OSA and CVDs [5], the early detection of OSA has become a major concern in recent years [6]. Polysomnography (PSG) remains the gold standard for OSA detection but is time consuming and resource-intensive, limiting its availability and delaying diagnosis [7]. It requires placing multiple sensors on the patient, often disrupting sleep quality, and demandsovernight monitoring by clinical experts [8; 9]. To address these issues, portable technologies for home-based OSA detection, without expert supervision, have been explored by analyzing a limited set of physiological signals from PSG [6]. Among these, heart rate variability (HRV) analysis has shown particular promise [6]. Accordingly, the significance of HRV-based techniques in OSA detection and cardiovascular risk assessment has been underscored by previous research [10]. HRV analysis has gained considerable acclian for its ability to reflect the autonomic nervous system activity, which is strongly correlated with respiratory control [11]. In this context, the HRV extracted from ECG rather than from other physiological signals (e.g., the photoplethysmogram) has provided more accurate results in identifying arrhythmias [12], sleep apnea [13], and other cardiovascular diseases [14]. So far, most of the proposed HRV-based OSA detectors were based on the combination of hand-crafted features through common machine learning (ML) classifiers, such as support vector machine (SVM), k-nearest neighbors (KNN), decision tree (DT), and so forth [7]. For this purpose, common time and frequency HRV features described by the Electrophysiology Task Force of the European Society of Cardiology and the North American Society of Pacing [15] have been widely used [16]. In recent years, other features computed by transforming the HRV signal using wavelet transforms [17; 18], Lomb-Scargle periodgrams [19], and complexity planes [20; 21] have also been broadly analyzed. In a complementary way and with the aim of improving characterization of the intricate dynamics of OSA episodes, the structural changes and transitions occurring along time in the HRV signal have also been recently considered. Thus, a few works have combined nonlinear features obtained by quantifying recurrence behavior of the HRV signal [22; 23; 24]. Such analysis primarily relies on the recurrence plot (RP), a graphical tool widely employed in nonlinear dynamics and statistical physics with various applications in pattern analysis and meteorology [25]. This graph results from transforming a time series into a 2D image which represents the times at which a trajectory approximately revisits the same area in the phase space [26]. This plot therefore shows hidden information about the nonlinear dynamics in the time series as well as global information about its recurrence behavior [27]. However, to objectively characterize and compare different types of RP, it is common to quantify the number and duration of recurrences using specific parameters. This process begins by setting a distance threshold to determine if two neighboring data points in the phase space should be considered as recurrence, bringing a binazired image of black and white dots.