Epilepsy is a neurological disorder characterized by the sudden occurrence of unprovoked seizures. There is extensive evidence of significantly altered brain connectivity during seizure periods in the human brain. Research on analyzing human brain functional connectivity during epileptic seizures has been limited predominantly to the use of the correlation method. However, spurious connectivity can be measured between two brain regions without having direct connection or interaction between them. Correlations can be due to the apparent interactions of the two brain regions resulting from common input from a third region, which may or may not be observed. Hence, researchers have recently proposed a sparse-plus-latent-regularized precision matrix (SLRPM) when there are unobserved or latent regions interacting with the observed regions. The SLRPM method yields partial correlations of the conditional statistics of the observed regions given the latent regions, thus identifying observed regions that are conditionally independent of both the observed and latent regions. We evaluate the performance of the methods using a spring-mass artificial network and assuming that some nodes cannot be observed, thus constituting the latent variables in the example. Several cases have been considered, including both sparse and dense connections, short-range and long-range connections, and a varying number of latent variables. The SLRPM method is then applied to estimate brain connectivity during epileptic seizures from human ECoG recordings. Seventy-four clinical seizures from five patients, all having complex partial epilepsy, were analyzed using SLRPM, and brain connectivity was quantified using modularity index, clustering coefficient, and eigenvector centrality. Furthermore, using a measure of latent inputs estimated by the SLRPM method, it was possible to automatically detect 72 of the 74 seizures with four false positives and find six seizures that were not marked manually.

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