Despite its short history, the use of Riemannian geometry in brain-computer interface (BCI) decoding is currently attracting increasing attention, due to accumulating documentation of its simplicity, accuracy, robustness and transfer learning capabilities, including the winning score obtained in five recent international predictive modeling BCI data competitions. The Riemannian framework is sharp from a mathematical perspective, yet in practice it is simple, both algorithmically and computationally. This allows the conception of online decoding machines suiting real-world operation in adverse conditions. We provide here a review on the use of Riemannian geometry for BCI and a primer on the classification frameworks based on it. While the theoretical research on Riemannian geometry is technical, our aim here is to show the appeal of the framework on an intuitive geometrical ground. In particular, we provide a rationale for its robustness and transfer learning capabilities and we elucidate the link between a simple Riemannian classifier and a state-of-the-art spatial filtering approach. We conclude by reporting details on the construction of data points to be manipulated in the Riemannian framework in the context of BCI and by providing links to available open-source Matlab and Python code libraries for designing BCI decoders.

This paper presents a Transfer Learning approach for dealing with the statistical variability of electroencephalographic (EEG) signals recorded on different sessions and/or from different subjects. This is a common problem faced by brain-computer interfaces (BCI) and poses a challenge for systems that try to reuse data from previous recordings to avoid a calibration phase for new users or new sessions for the same user. We propose a method based on Procrustes analysis for matching the statistical distributions of two datasets using simple geometrical transformations (translation, scaling, and rotation) over the data points. We use symmetric positive definite matrices (SPD) as statistical features for describing the EEG signals, so the geometrical operations on the data points respect the intrinsic geometry of the SPD manifold. Because of its geometry-aware nature, we call our method the Riemannian Procrustes analysis (RPA). We assess the improvement in transfer learning via RPA by performing classification tasks on simulated data and on eight publicly available BCI datasets covering three experimental paradigms (243 subjects in total). Our results show that the classification accuracy with RPA is superior in comparison to other geometry-aware methods proposed in the literature. We also observe improvements in ensemble classification strategies when the statistics of the datasets are matched via RPA. We present a simple yet powerful method for matching the statistical distributions of two datasets, thus paving the way to BCI systems capable of reusing data from previous sessions and avoid the need of a calibration procedure.

Interpersonal touch is of paramount importance in human social bonding and close relationships, allowing a unique channel for affect communication. So far the effect of touch on human physiology has been studied at an individual level. The present study aims at extending the study of affective touch from isolated individuals to truly interacting dyads. We have designed an ecological paradigm where romantic partners interact only via touch and we manipulate their empathic states. Simultaneously, we collected their autonomic activity (skin conductance, pulse, respiration). 14 couples participated to the experiment. We found that interpersonal touch increased coupling of electrodermal activity between the interacting partners, regardless the intensity and valence of the emotion felt. In addition, physical touch induced strong and reliable changes in physiological states within individuals. These results support an instrumental role of interpersonal touch for affective support in close relationships. Furthermore, they suggest that touch alone allows the emergence of a somatovisceral resonance between interacting individuals, which in turn is likely to form the prerequisites for emotional contagion and empathy.

We couple standardized low-resolution electromagnetic tomography, an inverse solution for electroencephalography (EEG) and the common spatial pattern, which is here conceived as a data-driven beamformer, to classify the benchmark BCI (brain-computer interface) competition 2003, data set IV. The data set is from an experiment where a subject performed a self-paced left and right finger tapping task. Available for analysis are 314 training trials whereas 100 unlabelled test trials have to be classified. The EEG data from 28 electrodes comprise the recording of the 500 ms before the actual finger movements, hence represent uniquely the left and right finger movement intention. Despite our use of an untrained classifier, and our extraction of only one attribute per class, our method yields accuracy similar to the winners of the competition for this data set. The distinct advantages of the approach presented here are the use of an untrained classifier and the processing speed, which make the method suitable for actual BCI applications. The proposed method is favourable over existing classification methods based on an EEG inverse solution, which rely either on iterative algorithms for single-trial independent component analysis or on trained classifiers.

We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate joint diagonalization (AJD). Today there is a considerable interest in estimating the geometric mean of a SPD matrix set in the manifold of SPD matrices endowed with the Fisher information metric. The resulting mean has several important invariance properties and has proven very useful in diverse engineering applications such as biomedical and image data processing. While for two SPD matrices the mean has an algebraic closed form solution, for a set of more than two SPD matrices it can only be estimated by iterative algorithms. However, none of the existing iterative algorithms feature at the same time fast convergence, low computational complexity per iteration and guarantee of convergence. For this reason, recently other definitions of geometric mean based on symmetric divergence measures, such as the Bhattacharyya divergence, have been considered. The resulting means, although possibly useful in practice, do not satisfy all desirable invariance properties. In this paper we consider geometric means of covariance matrices estimated on high-dimensional time-series, assuming that the data is generated according to an instantaneous mixing model, which is very common in signal processing. We show that in these circumstances we can approximate the Fisher information geometric mean by employing an efficient AJD algorithm. Our approximation is in general much closer to the Fisher information geometric mean as compared to its competitors and verifies many invariance properties. Furthermore, convergence is guaranteed, the computational complexity is low and the convergence rate is quadratic. The accuracy of this new geometric mean approximation is demonstrated by means of simulations.