Background and objectives: while traditional sleep staging is achieved through the visual - expert-based - annotation of a polysomnography, it has the disadvantages of being unpractical and expensive. Alternatives have been developed over the years to relieve sleep staging from its heavy requirements, through the collection of more easily assessable signals and its automation using machine learning. However, these alternatives have their limitations, some due to variabilities among and between subjects, other inherent to their use of sub-discriminative signals.

Many new solutions rely on the evaluation of the Autonomic Nervous System (ANS) activation through the assessment of the heart-rate (HR); the latter is modulated by the aforementioned variabilities, which may result in data and concept shifts between what was learned and what we want to classify. Such adversary effects are usually tackled by Transfer Learning, dealing with problems where there are differences between what is known (source) and what we want to classify (target). In this paper, we propose two new kernel-based methods of transfer learning and assess their performances in Rapid-Eye-Movement (REM) sleep stage detection, using solely the heart rate.

Methods: our first contribution is the introduction of Kernel-Cross Alignment (KCA), a measure of similarity between a source and a target, which is a direct extension of Kernel-Target Alignment (KTA). To our knowledge, KCA has currently never been studied in the literature.

Our second contribution is two alignment-based methods of transfer learning: Kernel-Target Alignment Transfer Learning (KTATL) and Kernel-Cross Alignment Transfer Learning (KCATL). Both methods differ from KTA, whose traditional use is kernel-tuning: in our methods, the kernel has been fixed beforehand, and our objective is the improvement of the estimation of unknown target labels by taking into account how observations relate to each other, which, as it will be explained, allows to transfer knowledge (transfer learning).

Results: we compare performances with transfer learning (KCATL, KTATL) to performances without transfer using a fixed classifier (a Support Vector Classifier - SVC). In most cases, both transfer learning methods result in an improvement of performances (higher detection rates for a fixed false-alarm rate). Our methods do not require iterative computations.

Conclusion: we observe improved performances using our transfer methods, which are computationally efficient, as they only require the computation of a kernel matrix and are non-iterative. However, some optimisation aspects are still under investigation.

背景和目标：虽然传统的睡眠分期是通过多导睡眠图的视觉-基于专家的-注释来实现的，但它具有不切实际和昂贵的缺点。多年来，通过收集更容易评估的信号及其使用机器学习的自动化，已经开发出替代方案，以减轻睡眠分期的繁重需求。然而，这些替代方案有其局限性，一些是由于受试者之间和之间的可变性，另一些是由于它们使用次判别信号所固有的。

许多新解决方案依赖于通过评估心率 (HR) 来评估自主神经系统 (ANS) 激活；后者受上述变量的影响，这可能导致数据和概念在所学内容和我们想要分类的内容之间发生转变。这种对抗性影响通常通过迁移学习来解决，处理已知（源）和我们想要分类的（目标）之间存在差异的问题。在本文中，我们提出了两种新的基于内核的迁移学习方法，并仅使用心率评估它们在快速眼动 (REM) 睡眠阶段检测中的性能。

方法：我们的第一个贡献是引入了 Kernel-Cross Alignment (KCA)，这是一种衡量源和目标之间相似性的方法，它是 Kernel-Target Alignment (KTA) 的直接扩展。据我们所知，目前文献中从未研究过 KCA。

我们的第二个贡献是两种基于对齐的迁移学习方法：内核-目标对齐迁移学习 (KTATL) 和内核-交叉对齐迁移学习 (KCATL)。这两种方法都不同于 KTA，后者的传统用途是内核调优：在我们的方法中，内核已经预先固定，我们的目标是通过考虑观察之间的相互关系来改进对未知目标标签的估计，即，正如将要解释的，允许转移知识（转移学习）。

结果：我们将使用迁移学习（KCATL、KTATL）的性能与不使用固定分类器（支持向量分类器 - SVC）的性能进行比较。在大多数情况下，两种迁移学习方法都会提高性能（固定误报率的检测率更高）。我们的方法不需要迭代计算。

结论：我们使用我们的传输方法观察到性能的提高，这些方法在计算上是有效的，因为它们只需要计算核矩阵并且是非迭代的。然而，一些优化方面仍在研究中。