Cross-Gram matrices and their use in transfer learning: Application to automatic REM detection using heart rate

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.

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).

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.

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.