## 1 Introduction
Later, different indices are computed from that binarized image, such as the percentage of recurrence points (recurrence rate), percentage of points that form vertical lines (laminarity), average length of diagonal lines, and length of the longest diagonal line [27]. This quantitative study of the recurrences in the RP is known as recurrence quantification analysis (RQA) and has provided promising results in a variety of disciplines [28; 29]. Previous works have explored RQA and other recurrence-based methods combined with ML for OSA classification, but few have investigated the use of recurrence images from HRV in deep learning (DL) models. Early studies, like those by [PERSON] et al. [30] and [PERSON] et al. [22] used traditional ML techniques such as artificial neural network (ANN) and SVM with RQA features derived from ECG or HRV. More recent works, such as [PERSON] et al. [18], employed CNNs with RPs from multiple signals including ECG and respiration, showing improved performance. Moreover, [PERSON] et al. [31] are the only researchers to use CNNs with distance matrices derived from ECG signals. However, while they applied CNNs and RPs to ECGs, this approach may depend on the morphology of the signal, which varies based on the recording system (e.g., conventional, Holter, wearable, etc.). In contrast, HRV signals do not exhibit morphological changes regardless of the recording system, even though this aspect is yet underexplored. However, RQA strongly depends on the selected threshold for recurrence quantification. Choosing an incorrect threshold can result in recurrence plots dominated by ones or zeros, making it difficult to identify discriminative patterns [32]. Furthermore, recent studies have shown that RQA features provide only a limited representation of the phase space's characteristics, potentially underestimating important temporal trends and dynamic changes in the original time series [33]. While other nonlinear measures, such as entropy-based indicators, have been explored, they primarily focus on the randomness or complexity of signals and often fail to capture spatial recurrence patterns comprehensively. In contrast, recurrence plots provide unique insights into the spatial organization of recurring states within a signal, offering a richer perspective on the dynamics of physiological processes. This spatial recurrence information has not yet been analyzed in sufficient depth within the context of OSA. In this context, CNNs present a significant advantage by leveraging recurrence images directly without requiring predefined thresholds or explicit feature engineering. Unlike traditional RQA, CNNs can extract richer spatial and temporal features from recurrence plots, capturing patterns and trends that might otherwise be overlooked. Moreover, CNNs are better suited to generalize across diverse datasets, addressing challenges such as variability in HRV signals or differences in recording conditions. Despite these advantages, none of the previous works explicitly utilized recurrence images derived from HRV signals in combination with CNN architectures. This highlights a clear gap in the literature, where the potential of HRV-based recurrence information combined with deep learning remains largely unexplored. To this respect, assessing the distances within the phase space (unthresholded RP) instead of focusing on quantitative measures derived from the RP could bring further information on the underlying nonlinear dynamics of HRV. One possible approach can be introducing such unthresholded representations into DL algorithms and letting them automatically extract hidden recurrence patterns to make better extrapolations of OSA episodes. In fact, the global assessment of unthresholded RPs when imputed to different DL-based schemes has revealed more information than RQA, which has been evidenced in different areas of health and engineering, including human activities [34] and heart rate measurement [35].