Quantitative EEG Analysis based on Riemannian metric
Presenting author:
Abstract
Quantitative EEG based on spectrum analysis has been a mature and reliable method in neuropathology research and medical diagnosis. The diagnosis model - ‘Development surfaces’ (Ahn et al., 1980) was build based on the log-spectrum to characterize the age-frequency distribution for mean and standard deviation (Valdés et al., 1992) regression. However, the spectrum (diagnose part of cross-spectrum) is not live on the Euclidean space but the Riemannian manifold that the symmetric positive-defined (SPD) matrix is a differential manifold under the metric of Riemannian (Deza and Deza, 2013). This means that the tactics only took logarithm of spectrum is not enough, the more reasonable way is to migrate the whole work on Riemannian geometry. Here we collected normal multinational dataset from seven countries (Barbados, Cuba, China, Colombia, Germany, American and Switzerland) which including 1341 subjects in total (Table1). The whole dataset expands the whole lifespan (age range: 5yers-97yers) and have balanced gender distribution (Fig1: A - C). Based on Riemannian metric, we took spectrum to their tangent space by geometric mean (Bhatia and Holbrook, 2006) and instead of using spline, we got the development surface by more robust method – Nadaraya-Watson regression(Nadaraya, 1964). First, we reproduced the results (Szava et al., 1994) (Fig2: a)used the same dataset from Cuba 1990 (age spans the whole lifespan Fig1:D ) by using log-spectrum(Bosch-Bayard et al., 2020) and log mapping-spectrum (Fig2: A - C). The results show that the alpha peak go forward form around 9Hz at younger, plateau at 25-30 and then go back at elder people which not only for dataset of Cuba 1990 but for also for the whole dataset, the theta wave fade away with age. Second, the results form log mapping algorithm maintain the phenomenon and it took off the background noise (1/f) and make the phenomenon of theta wave and alpha peak more obvious (Fig2: D - E).
Reference:
Ahn, H., Prichep, L., John, E., Baird, H., Trepetin, M., and Kaye, H. (1980). Developmental equations reflect brain dysfunctions. Science 210, 1259–1262.
Bhatia, R., and Holbrook, J. (2006). Riemannian geometry and matrix geometric means. Linear Algebra Its Appl. 413, 594–618.
Bosch-Bayard, J., Galan, L., Aubert Vazquez, E., Virues Alba, T., and Valdes-Sosa, P.A. (2020). Resting State Healthy EEG: The First Wave of the Cuban Normative Database. Front. Neurosci. 14.
Deza, M.M., and Deza, E. (2013). Riemannian and Hermitian Metrics. In Encyclopedia of Distances, (Berlin, Heidelberg: Springer Berlin Heidelberg), pp. 125–155.
Nadaraya, E.A. (1964). On Estimating Regression. Theory Probab. Its Appl. 9, 141–142.
Szava, S., Valdes, P., Biscay, R., Galan, L., Bosch, J., Clark, I., and Jimenez, J.C. (1994). High resolution quantitative EEG analysis. Brain Topogr. 6, 211–219.
Valdés, P., Bosch, J., Grave, R., Hernandez, J., Riera, J., Pascual, R., and Biscay, R. (1992). Frequency domain models of the EEG. Brain Topogr. 4, 309–319.
Quantitative EEG based on spectrum analysis has been a mature and reliable method in neuropathology research and medical diagnosis. The diagnosis model - ‘Development surfaces’ (Ahn et al., 1980) was build based on the log-spectrum to characterize the age-frequency distribution for mean and standard deviation (Valdés et al., 1992) regression. However, the spectrum (diagnose part of cross-spectrum) is not live on the Euclidean space but the Riemannian manifold that the symmetric positive-defined (SPD) matrix is a differential manifold under the metric of Riemannian (Deza and Deza, 2013). This means that the tactics only took logarithm of spectrum is not enough, the more reasonable way is to migrate the whole work on Riemannian geometry. Here we collected normal multinational dataset from seven countries (Barbados, Cuba, China, Colombia, Germany, American and Switzerland) which including 1341 subjects in total (Table1). The whole dataset expands the whole lifespan (age range: 5yers-97yers) and have balanced gender distribution (Fig1: A - C). Based on Riemannian metric, we took spectrum to their tangent space by geometric mean (Bhatia and Holbrook, 2006) and instead of using spline, we got the development surface by more robust method – Nadaraya-Watson regression(Nadaraya, 1964). First, we reproduced the results (Szava et al., 1994) (Fig2: a)used the same dataset from Cuba 1990 (age spans the whole lifespan Fig1:D ) by using log-spectrum(Bosch-Bayard et al., 2020) and log mapping-spectrum (Fig2: A - C). The results show that the alpha peak go forward form around 9Hz at younger, plateau at 25-30 and then go back at elder people which not only for dataset of Cuba 1990 but for also for the whole dataset, the theta wave fade away with age. Second, the results form log mapping algorithm maintain the phenomenon and it took off the background noise (1/f) and make the phenomenon of theta wave and alpha peak more obvious (Fig2: D - E).
Reference:
Ahn, H., Prichep, L., John, E., Baird, H., Trepetin, M., and Kaye, H. (1980). Developmental equations reflect brain dysfunctions. Science 210, 1259–1262.
Bhatia, R., and Holbrook, J. (2006). Riemannian geometry and matrix geometric means. Linear Algebra Its Appl. 413, 594–618.
Bosch-Bayard, J., Galan, L., Aubert Vazquez, E., Virues Alba, T., and Valdes-Sosa, P.A. (2020). Resting State Healthy EEG: The First Wave of the Cuban Normative Database. Front. Neurosci. 14.
Deza, M.M., and Deza, E. (2013). Riemannian and Hermitian Metrics. In Encyclopedia of Distances, (Berlin, Heidelberg: Springer Berlin Heidelberg), pp. 125–155.
Nadaraya, E.A. (1964). On Estimating Regression. Theory Probab. Its Appl. 9, 141–142.
Szava, S., Valdes, P., Biscay, R., Galan, L., Bosch, J., Clark, I., and Jimenez, J.C. (1994). High resolution quantitative EEG analysis. Brain Topogr. 6, 211–219.
Valdés, P., Bosch, J., Grave, R., Hernandez, J., Riera, J., Pascual, R., and Biscay, R. (1992). Frequency domain models of the EEG. Brain Topogr. 4, 309–319.