Review of Riemannian Distances and Divergences, Applied to SSVEP-based BCI.

The firstgeneration of brain-computer interfaces (BCI) classifies multi-channel electroencephalographic (EEG) signals, enhanced by optimized spatial filters.The second generation directly classifies covariance matrices estimated on EEG signals, based on straightforward algorithms such as the minimum-distance-to-Riemannian-mean (MDRM). Classification results vary greatly depending on the chosen Riemannian distance or divergence, whose definitions and reference implementations are spread across a wide mathematical literature. This paper reviews all the Riemannian distances and divergences to process covariance matrices, with an implementation compatible with BCI constraints. The impact of using different metrics is assessed on a steady-state visually evoked potentials (SSVEP) dataset, evaluating centers of classes and classification accuracy. Riemannian approaches embed crucial properties to process EEG data. The Riemannian centers of classes outperform Euclidean ones both in offline and online setups. Some Riemannian distances and divergences have better performances in terms of classification accuracy, while others have appealing computational efficiency.

Impact of Modifiable Risk Factors on Bone Loss During Periodontal Maintenance.

OBJECTIVES: The aim of this study was to analyze modifiable patient risk factors from dental chart histories and radiographs for progressive mild-moderate periodontitis during periodontal maintenance (PM). METHODS AND MATERIALS: Bitewing radiographs of 442 elderly periodontal maintenance patients were taken before and after two years of periodontal maintenance. Each progressive periodontitis (PP) patient (with at least one site of posterior interproximal bone loss of ≥2 mm, n=71) was matched to a periodontitis stable (PS) patient (no sites with bone loss, n=71) of the same gender and age (±five years) to control for these variables and was compared for measurements of general patient (medical history, smoking, hygiene and compliance habits) and tooth-related (bone loss, overhangs, interproximal dimensions) factors at baseline. Fisher exact and t-tests were used to compare groups. RESULTS: While the elderly PM patients with mild-moderate periodontitis were generally stable, 71 of 442 were PP patients. No significant differences from PS patients were observed at baseline with regard to the systemic factors measured. However, the PP group had less cementoenamel junction to bone length (bone loss p<0.0001) and more interproximal width (2.3±1.0 mm) than did the PS group (1.7±0.6 mm, p=0.0016). This was reflected in more open sites without adjacent tooth contact in PP (42% vs 15%, p=0.0006). CONCLUSIONS: In the short term, systemic and behavior factors are of limited value in identifying mild-moderate periodontitis patients on PM at increased risk of bone loss. However, interproximal width and lack of adjacent tooth contacts are related to the likelihood of losing interproximal bone during periodontal maintenance, suggesting the need for restorative therapy.