A closed-form unsupervised geometry-aware dimensionality reduction method in the Riemannian Manifold of SPD matrices.

Riemannian geometry has been found accurate and robust for classifying multidimensional data, for instance, in brain-computer interfaces based on electroencephalography. Given a number of data points on the manifold of symmetric positive-definite matrices, it is often of interest to embed these points in a manifold of smaller dimension. This is necessary for large dimensions in order to preserve accuracy and useful in general to speed up computations. Geometry-aware methods try to accomplish this task while respecting as much as possible the geometry of the original data points. We provide a closed-form solution for this problem in a fully unsupervised setting. Through the analysis of three brain-computer interface data bases we show that our method allows substantial dimensionality reduction without affecting the classification accuracy.

Single-trial detection of event-related fields in MEG from the presentation of happy faces: Results of the Biomag 2016 data challenge.

The recognition of brain evoked responses at the single-trial level is a challenging task. Typical non-invasive brain-computer interfaces based on event-related brain responses use eletroencephalograhy. In this study, we consider brain signals recorded with magnetoencephalography (MEG), and we expect to take advantage of the high spatial and temporal resolution for the detection of targets in a series of images. This study was used for the data analysis competition held in the 20th International Conference on Biomagnetism (Biomag) 2016, wherein the goal was to provide a method for single-trial detection of even-related fields corresponding to the presentation of happy faces during the rapid presentation of images of faces with six different facial expressions (anger, disgust, fear, neutrality, sadness, and happiness). The datasets correspond to 204 gradiometers signals obtained from four participants. The best method is based on the combination of several approaches, and mainly based on Riemannian geometry, and it provided an area under the ROC curve of 0.956±0.043. The results show that a high recognition rate of facial expressions can be obtained at the signal-trial level using advanced signal processing and machine learning methodologies.