Correntropy Based Robust Decomposition of Neuromodulations

Neuromodulations as observed in the extracellular electrical potential recordings obtained from Electroencephalograms (EEG) manifest as organized, transient patterns that differ statistically from their featureless noisy background. Leveraging on this statistical dissimilarity, we propose a noniterative robust classification algorithm to isolate, in time, these neuromodulations from the temporally disorganized but structured background activity while simultaneously incorporating temporal sparsity of the events. Specifically, we exploit the ability of correntropy to asses higher - order moments as well as imply the degree of similarity between two random variables in the joint space regulated by the kernel bandwidth. We test our algorithm on DREAMS Sleep Spindle Database and further elaborate on the hyperparameters introduced. Finally, we compare the performance of the algorithm with two algorithms designed on similar ideas; one of which is a quick, simple norm based technique while the other parallels the state-of-the-art Robust Principal Component Analysis (RPCA) to achieve classification. The algorithm is able to match the performance of the state-of-the-art techniques while saving tremendously on computation time and complexity.Comment: 4 pages, Engineering in Medicine and Biolog

Local power estimation of neuromodulations using point process modeling

Extracellular electrical potentials (EEP) recorded from the brain are an active manifestation of all cellular processes that propagate within a volume of brain tissue. A standard approach for their quantification are power spectral analyses methods that reflect the global distribution of signal power over frequency. However, these methods incorporate analysis windows to achieve locality and therefore, are limited by the inherent trade - off between time and frequency resolutions. In this paper, we present a novel approach to estimate local power more precisely at a resolution as high as the sampling frequency. Our methods are well grounded on established neurophysiology of the bio-signals where we model EEPs as comprising of two components: neuromodulations and background activity. A local measure of power, we call Marked Point Process (MPP) spectrogram, is then derived as a power - weighted intensity function of the point process for neuromodulations. We demonstrate our results on two datasets: 1) local field potentials recorded from the prefrontal cortex of 3 rats performing a working memory task and 2) EEPs recorded via electroencephalography from the visual cortex of human subjects performing a conditioned stimulus task. A detailed analysis of the power - specific marked features of neuromodulations confirm high correlation between power spectral density and power in neuromodulations establishing the aptness of MPP spectrogram as a finer measure of power where it is able to track local variations in power while preserving the global structure of signal power distribution.Comment: 6 page